diff --git a/sign/dilithium/example_test.go b/sign/dilithium/example_test.go
index 4f4de0d99..bf687b202 100644
--- a/sign/dilithium/example_test.go
+++ b/sign/dilithium/example_test.go
@@ -51,6 +51,6 @@ func Example() {
 	fmt.Printf("O.K.")
 
 	// Output:
-	// Supported modes: [Dilithium2 Dilithium2-AES Dilithium3 Dilithium3-AES Dilithium5 Dilithium5-AES]
+	// Supported modes: [Dilithium2 Dilithium2-AES Dilithium3 Dilithium3-AES Dilithium5 Dilithium5-AES ML-DSA-44 ML-DSA-65 ML-DSA-87]
 	// O.K.
 }
diff --git a/sign/dilithium/gen.go b/sign/dilithium/gen.go
index c0d0df378..64d134714 100644
--- a/sign/dilithium/gen.go
+++ b/sign/dilithium/gen.go
@@ -14,12 +14,11 @@ import (
 	"strings"
 	"text/template"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common/params"
+	"github.com/cloudflare/circl/sign/internal/dilithium/params"
 )
 
 type Mode struct {
 	Name          string
-	UseAES        bool
 	K             int
 	L             int
 	Eta           int
@@ -28,26 +27,47 @@ type Mode struct {
 	Tau           int
 	Gamma1Bits    int
 	Gamma2        int
+	TRSize        int
+	CTildeSize    int
 }
 
 func (m Mode) Pkg() string {
 	return strings.ToLower(m.Mode())
 }
 
+func (m Mode) PkgPath() string {
+	if m.NIST() {
+		return path.Join("..", "mldsa", m.Pkg())
+	}
+
+	return m.Pkg()
+}
+
 func (m Mode) Impl() string {
 	return "impl" + m.Mode()
 }
 
 func (m Mode) Mode() string {
+	if m.NIST() {
+		return strings.ReplaceAll(m.Name, "-", "")
+	}
+
 	return strings.ReplaceAll(strings.ReplaceAll(m.Name,
 		"Dilithium", "Mode"), "-AES", "AES")
 }
 
+func (m Mode) UseAES() bool {
+	return strings.HasSuffix(m.Name, "-AES")
+}
+
+func (m Mode) NIST() bool {
+	return strings.HasPrefix(m.Name, "ML-DSA-")
+}
+
 var (
 	Modes = []Mode{
 		{
 			Name:          "Dilithium2",
-			UseAES:        false,
 			K:             4,
 			L:             4,
 			Eta:           2,
@@ -56,10 +76,11 @@ var (
 			Tau:           39,
 			Gamma1Bits:    17,
 			Gamma2:        (params.Q - 1) / 88,
+			TRSize:        32,
+			CTildeSize:    32,
 		},
 		{
 			Name:          "Dilithium2-AES",
-			UseAES:        true,
 			K:             4,
 			L:             4,
 			Eta:           2,
@@ -68,10 +89,11 @@ var (
 			Tau:           39,
 			Gamma1Bits:    17,
 			Gamma2:        (params.Q - 1) / 88,
+			TRSize:        32,
+			CTildeSize:    32,
 		},
 		{
 			Name:          "Dilithium3",
-			UseAES:        false,
 			K:             6,
 			L:             5,
 			Eta:           4,
@@ -80,10 +102,11 @@ var (
 			Tau:           49,
 			Gamma1Bits:    19,
 			Gamma2:        (params.Q - 1) / 32,
+			TRSize:        32,
+			CTildeSize:    32,
 		},
 		{
 			Name:          "Dilithium3-AES",
-			UseAES:        true,
 			K:             6,
 			L:             5,
 			Eta:           4,
@@ -92,10 +115,11 @@ var (
 			Tau:           49,
 			Gamma1Bits:    19,
 			Gamma2:        (params.Q - 1) / 32,
+			TRSize:        32,
+			CTildeSize:    32,
 		},
 		{
 			Name:          "Dilithium5",
-			UseAES:        false,
 			K:             8,
 			L:             7,
 			Eta:           2,
@@ -104,10 +128,11 @@ var (
 			Tau:           60,
 			Gamma1Bits:    19,
 			Gamma2:        (params.Q - 1) / 32,
+			TRSize:        32,
+			CTildeSize:    32,
 		},
 		{
 			Name:          "Dilithium5-AES",
-			UseAES:        true,
 			K:             8,
 			L:             7,
 			Eta:           2,
@@ -116,6 +141,47 @@ var (
 			Tau:           60,
 			Gamma1Bits:    19,
 			Gamma2:        (params.Q - 1) / 32,
+			TRSize:        32,
+			CTildeSize:    32,
+		},
+		{
+			Name:          "ML-DSA-44",
+			K:             4,
+			L:             4,
+			Eta:           2,
+			DoubleEtaBits: 3,
+			Omega:         80,
+			Tau:           39,
+			Gamma1Bits:    17,
+			Gamma2:        (params.Q - 1) / 88,
+			TRSize:        64,
+			CTildeSize:    32,
+		},
+		{
+			Name:          "ML-DSA-65",
+			K:             6,
+			L:             5,
+			Eta:           4,
+			DoubleEtaBits: 4,
+			Omega:         55,
+			Tau:           49,
+			Gamma1Bits:    19,
+			Gamma2:        (params.Q - 1) / 32,
+			TRSize:        64,
+			CTildeSize:    48,
+		},
+		{
+			Name:          "ML-DSA-87",
+			K:             8,
+			L:             7,
+			Eta:           2,
+			DoubleEtaBits: 3,
+			Omega:         75,
+			Tau:           60,
+			Gamma1Bits:    19,
+			Gamma2:        (params.Q - 1) / 32,
+			TRSize:        64,
+			CTildeSize:    64,
 		},
 	}
 	TemplateWarning = "// Code generated from"
@@ -153,7 +219,7 @@ func generateParamsFiles() {
 		if offset == -1 {
 			panic("Missing template warning in params.templ.go")
 		}
-		err = os.WriteFile(mode.Pkg()+"/internal/params.go",
+		err = os.WriteFile(mode.PkgPath()+"/internal/params.go",
 			[]byte(res[offset:]), 0o644)
 		if err != nil {
 			panic(err)
@@ -206,7 +272,7 @@ func generateModePackageFiles() {
 		if offset == -1 {
 			panic("Missing template warning in modePkg.templ.go")
 		}
-		err = os.WriteFile(mode.Pkg()+"/dilithium.go", []byte(res[offset:]), 0o644)
+		err = os.WriteFile(mode.PkgPath()+"/dilithium.go", []byte(res[offset:]), 0o644)
 		if err != nil {
 			panic(err)
 		}
@@ -246,10 +312,10 @@ func generateSourceFiles() {
 			continue
 		}
 
-		fs, err = os.ReadDir(path.Join(mode.Pkg(), "internal"))
+		fs, err = os.ReadDir(path.Join(mode.PkgPath(), "internal"))
 		for _, f := range fs {
 			name := f.Name()
-			fn := path.Join(mode.Pkg(), "internal", name)
+			fn := path.Join(mode.PkgPath(), "internal", name)
 			if ignored(name) {
 				continue
 			}
@@ -273,7 +339,7 @@ func generateSourceFiles() {
 			}
 		}
 		for name, expected := range files {
-			fn := path.Join(mode.Pkg(), "internal", name)
+			fn := path.Join(mode.PkgPath(), "internal", name)
 			expected = []byte(fmt.Sprintf(
 				"%s mode3/internal/%s by gen.go\n\n%s",
 				TemplateWarning,
diff --git a/sign/dilithium/kat_test.go b/sign/dilithium/kat_test.go
index 2280e988d..dae3690ac 100644
--- a/sign/dilithium/kat_test.go
+++ b/sign/dilithium/kat_test.go
@@ -6,24 +6,32 @@ package dilithium
 import (
 	"crypto/sha256"
 	"fmt"
+	"strings"
 	"testing"
 
 	"github.com/cloudflare/circl/internal/nist"
 )
 
 func TestPQCgenKATSign(t *testing.T) {
-	// Generated from reference implementation commit 61b51a71701b8ae9f546a1e5,
-	// which can be found at https://github.com/pq-crystals/dilithium
 	for _, tc := range []struct {
 		name string
 		want string
 	}{
+		// Generated from reference implementation commit 61b51a71701b8ae9f546a1e5,
+		// which can be found at https://github.com/pq-crystals/dilithium
 		{"Dilithium2", "38ed991c5ca11e39ab23945ca37af89e059d16c5474bf8ba96b15cb4e948af2a"},
 		{"Dilithium3", "8196b32212753f525346201ffec1c7a0a852596fa0b57bd4e2746231dab44d55"},
 		{"Dilithium5", "7ded97a6e6c809b43b54c248171d7504fa6a0cab651bf288bb00034782667481"},
 		{"Dilithium2-AES", "b6673f8da5bba7dfae63adbbdf559f4fcfb715d1f91da98d4b52e26203d69196"},
 		{"Dilithium3-AES", "482f4d672a9f1dc38cc8bcf8b1731b03fe99fcb6f2b73aa4a376b99faf89ccbe"},
 		{"Dilithium5-AES", "54dfa85013d1b3da4f1d7c6dd270bc91a083cfece3d320c97906da125fd2a48f"},
+
+		// Generated from reference implementation commit e7bed6258b9a3703ce78d4ec3,
+		// which can be found on the standard branch
+		// of https://github.com/pq-crystals/dilithium
+		{"ML-DSA-44", "4657f244d1204e5847b3cacea4fc6116579571bee8ac89b8cba6771f303ee260"},
+		{"ML-DSA-65", "99a95d7ef804020a666f455c5003232d0c0200dfc4f5df85dceb8f56256dcba8"},
+		{"ML-DSA-87", "3377835fffb7cf9aac52947225c8974335bc05532ddf672a8b706ab8991435a2"},
 	} {
 		t.Run(tc.name, func(t *testing.T) {
 			mode := ModeByName(tc.name)
@@ -38,7 +46,18 @@ func TestPQCgenKATSign(t *testing.T) {
 			}
 			f := sha256.New()
 			g := nist.NewDRBG(&seed)
-			fmt.Fprintf(f, "# %s\n\n", tc.name)
+			nameInKat := tc.name
+			if !strings.HasPrefix(tc.name, "Dilithium") {
+				switch tc.name {
+				case "ML-DSA-44":
+					nameInKat = "Dilithium2"
+				case "ML-DSA-65":
+					nameInKat = "Dilithium3"
+				case "ML-DSA-87":
+					nameInKat = "Dilithium5"
+				}
+			}
+			fmt.Fprintf(f, "# %s\n\n", nameInKat)
 			for i := 0; i < 100; i++ {
 				mlen := 33 * (i + 1)
 				g.Fill(seed[:])
diff --git a/sign/dilithium/mldsa44.go b/sign/dilithium/mldsa44.go
new file mode 100644
index 000000000..1cbaf0174
--- /dev/null
+++ b/sign/dilithium/mldsa44.go
@@ -0,0 +1,91 @@
+// Code generated from mode.templ.go. DO NOT EDIT.
+
+package dilithium
+
+import (
+	"fmt"
+	"io"
+
+	"github.com/cloudflare/circl/sign/mldsa/mldsa44"
+
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+)
+
+// implMLDSA44 implements the mode.Mode interface for ML-DSA-44.
+type implMLDSA44 struct{}
+
+// MLDSA44 is ML-DSA-44.
+var MLDSA44 Mode = &implMLDSA44{}
+
+func (m *implMLDSA44) GenerateKey(rand io.Reader) (
+	PublicKey, PrivateKey, error) {
+	return mldsa44.GenerateKey(rand)
+}
+
+func (m *implMLDSA44) NewKeyFromSeed(seed []byte) (PublicKey,
+	PrivateKey) {
+	if len(seed) != common.SeedSize {
+		panic(fmt.Sprintf("seed must be of length %d", common.SeedSize))
+	}
+	seedBuf := [common.SeedSize]byte{}
+	copy(seedBuf[:], seed)
+	return mldsa44.NewKeyFromSeed(&seedBuf)
+}
+
+func (m *implMLDSA44) Sign(sk PrivateKey, msg []byte) []byte {
+	isk := sk.(*mldsa44.PrivateKey)
+	ret := [mldsa44.SignatureSize]byte{}
+	mldsa44.SignTo(isk, msg, ret[:])
+	return ret[:]
+}
+
+func (m *implMLDSA44) Verify(pk PublicKey, msg []byte, signature []byte) bool {
+	ipk := pk.(*mldsa44.PublicKey)
+	return mldsa44.Verify(ipk, msg, signature)
+}
+
+func (m *implMLDSA44) PublicKeyFromBytes(data []byte) PublicKey {
+	var ret mldsa44.PublicKey
+	if len(data) != mldsa44.PublicKeySize {
+		panic("packed public key must be of mldsa44.PublicKeySize bytes")
+	}
+	var buf [mldsa44.PublicKeySize]byte
+	copy(buf[:], data)
+	ret.Unpack(&buf)
+	return &ret
+}
+
+func (m *implMLDSA44) PrivateKeyFromBytes(data []byte) PrivateKey {
+	var ret mldsa44.PrivateKey
+	if len(data) != mldsa44.PrivateKeySize {
+		panic("packed public key must be of mldsa44.PrivateKeySize bytes")
+	}
+	var buf [mldsa44.PrivateKeySize]byte
+	copy(buf[:], data)
+	ret.Unpack(&buf)
+	return &ret
+}
+
+func (m *implMLDSA44) SeedSize() int {
+	return common.SeedSize
+}
+
+func (m *implMLDSA44) PublicKeySize() int {
+	return mldsa44.PublicKeySize
+}
+
+func (m *implMLDSA44) PrivateKeySize() int {
+	return mldsa44.PrivateKeySize
+}
+
+func (m *implMLDSA44) SignatureSize() int {
+	return mldsa44.SignatureSize
+}
+
+func (m *implMLDSA44) Name() string {
+	return "ML-DSA-44"
+}
+
+func init() {
+	modes["ML-DSA-44"] = MLDSA44
+}
diff --git a/sign/dilithium/mldsa65.go b/sign/dilithium/mldsa65.go
new file mode 100644
index 000000000..8c39363e8
--- /dev/null
+++ b/sign/dilithium/mldsa65.go
@@ -0,0 +1,91 @@
+// Code generated from mode.templ.go. DO NOT EDIT.
+
+package dilithium
+
+import (
+	"fmt"
+	"io"
+
+	"github.com/cloudflare/circl/sign/mldsa/mldsa65"
+
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+)
+
+// implMLDSA65 implements the mode.Mode interface for ML-DSA-65.
+type implMLDSA65 struct{}
+
+// MLDSA65 is ML-DSA-65.
+var MLDSA65 Mode = &implMLDSA65{}
+
+func (m *implMLDSA65) GenerateKey(rand io.Reader) (
+	PublicKey, PrivateKey, error) {
+	return mldsa65.GenerateKey(rand)
+}
+
+func (m *implMLDSA65) NewKeyFromSeed(seed []byte) (PublicKey,
+	PrivateKey) {
+	if len(seed) != common.SeedSize {
+		panic(fmt.Sprintf("seed must be of length %d", common.SeedSize))
+	}
+	seedBuf := [common.SeedSize]byte{}
+	copy(seedBuf[:], seed)
+	return mldsa65.NewKeyFromSeed(&seedBuf)
+}
+
+func (m *implMLDSA65) Sign(sk PrivateKey, msg []byte) []byte {
+	isk := sk.(*mldsa65.PrivateKey)
+	ret := [mldsa65.SignatureSize]byte{}
+	mldsa65.SignTo(isk, msg, ret[:])
+	return ret[:]
+}
+
+func (m *implMLDSA65) Verify(pk PublicKey, msg []byte, signature []byte) bool {
+	ipk := pk.(*mldsa65.PublicKey)
+	return mldsa65.Verify(ipk, msg, signature)
+}
+
+func (m *implMLDSA65) PublicKeyFromBytes(data []byte) PublicKey {
+	var ret mldsa65.PublicKey
+	if len(data) != mldsa65.PublicKeySize {
+		panic("packed public key must be of mldsa65.PublicKeySize bytes")
+	}
+	var buf [mldsa65.PublicKeySize]byte
+	copy(buf[:], data)
+	ret.Unpack(&buf)
+	return &ret
+}
+
+func (m *implMLDSA65) PrivateKeyFromBytes(data []byte) PrivateKey {
+	var ret mldsa65.PrivateKey
+	if len(data) != mldsa65.PrivateKeySize {
+		panic("packed public key must be of mldsa65.PrivateKeySize bytes")
+	}
+	var buf [mldsa65.PrivateKeySize]byte
+	copy(buf[:], data)
+	ret.Unpack(&buf)
+	return &ret
+}
+
+func (m *implMLDSA65) SeedSize() int {
+	return common.SeedSize
+}
+
+func (m *implMLDSA65) PublicKeySize() int {
+	return mldsa65.PublicKeySize
+}
+
+func (m *implMLDSA65) PrivateKeySize() int {
+	return mldsa65.PrivateKeySize
+}
+
+func (m *implMLDSA65) SignatureSize() int {
+	return mldsa65.SignatureSize
+}
+
+func (m *implMLDSA65) Name() string {
+	return "ML-DSA-65"
+}
+
+func init() {
+	modes["ML-DSA-65"] = MLDSA65
+}
diff --git a/sign/dilithium/mldsa87.go b/sign/dilithium/mldsa87.go
new file mode 100644
index 000000000..bc125430b
--- /dev/null
+++ b/sign/dilithium/mldsa87.go
@@ -0,0 +1,91 @@
+// Code generated from mode.templ.go. DO NOT EDIT.
+
+package dilithium
+
+import (
+	"fmt"
+	"io"
+
+	"github.com/cloudflare/circl/sign/mldsa/mldsa87"
+
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+)
+
+// implMLDSA87 implements the mode.Mode interface for ML-DSA-87.
+type implMLDSA87 struct{}
+
+// MLDSA87 is ML-DSA-87.
+var MLDSA87 Mode = &implMLDSA87{}
+
+func (m *implMLDSA87) GenerateKey(rand io.Reader) (
+	PublicKey, PrivateKey, error) {
+	return mldsa87.GenerateKey(rand)
+}
+
+func (m *implMLDSA87) NewKeyFromSeed(seed []byte) (PublicKey,
+	PrivateKey) {
+	if len(seed) != common.SeedSize {
+		panic(fmt.Sprintf("seed must be of length %d", common.SeedSize))
+	}
+	seedBuf := [common.SeedSize]byte{}
+	copy(seedBuf[:], seed)
+	return mldsa87.NewKeyFromSeed(&seedBuf)
+}
+
+func (m *implMLDSA87) Sign(sk PrivateKey, msg []byte) []byte {
+	isk := sk.(*mldsa87.PrivateKey)
+	ret := [mldsa87.SignatureSize]byte{}
+	mldsa87.SignTo(isk, msg, ret[:])
+	return ret[:]
+}
+
+func (m *implMLDSA87) Verify(pk PublicKey, msg []byte, signature []byte) bool {
+	ipk := pk.(*mldsa87.PublicKey)
+	return mldsa87.Verify(ipk, msg, signature)
+}
+
+func (m *implMLDSA87) PublicKeyFromBytes(data []byte) PublicKey {
+	var ret mldsa87.PublicKey
+	if len(data) != mldsa87.PublicKeySize {
+		panic("packed public key must be of mldsa87.PublicKeySize bytes")
+	}
+	var buf [mldsa87.PublicKeySize]byte
+	copy(buf[:], data)
+	ret.Unpack(&buf)
+	return &ret
+}
+
+func (m *implMLDSA87) PrivateKeyFromBytes(data []byte) PrivateKey {
+	var ret mldsa87.PrivateKey
+	if len(data) != mldsa87.PrivateKeySize {
+		panic("packed public key must be of mldsa87.PrivateKeySize bytes")
+	}
+	var buf [mldsa87.PrivateKeySize]byte
+	copy(buf[:], data)
+	ret.Unpack(&buf)
+	return &ret
+}
+
+func (m *implMLDSA87) SeedSize() int {
+	return common.SeedSize
+}
+
+func (m *implMLDSA87) PublicKeySize() int {
+	return mldsa87.PublicKeySize
+}
+
+func (m *implMLDSA87) PrivateKeySize() int {
+	return mldsa87.PrivateKeySize
+}
+
+func (m *implMLDSA87) SignatureSize() int {
+	return mldsa87.SignatureSize
+}
+
+func (m *implMLDSA87) Name() string {
+	return "ML-DSA-87"
+}
+
+func init() {
+	modes["ML-DSA-87"] = MLDSA87
+}
diff --git a/sign/dilithium/mode2.go b/sign/dilithium/mode2.go
index e88d090b0..7e27eff2c 100644
--- a/sign/dilithium/mode2.go
+++ b/sign/dilithium/mode2.go
@@ -6,8 +6,8 @@ import (
 	"fmt"
 	"io"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
 	"github.com/cloudflare/circl/sign/dilithium/mode2"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // implMode2 implements the mode.Mode interface for Dilithium2.
diff --git a/sign/dilithium/mode2/dilithium.go b/sign/dilithium/mode2/dilithium.go
index 13ac869a5..16ce78351 100644
--- a/sign/dilithium/mode2/dilithium.go
+++ b/sign/dilithium/mode2/dilithium.go
@@ -1,9 +1,11 @@
 // Code generated from modePkg.templ.go. DO NOT EDIT.
 
+
 // mode2 implements the CRYSTALS-Dilithium signature scheme Dilithium2
 // as submitted to round3 of the NIST PQC competition and described in
 //
 // https://pq-crystals.org/dilithium/data/dilithium-specification-round3-20210208.pdf
+
 package mode2
 
 import (
@@ -11,8 +13,10 @@ import (
 	"errors"
 	"io"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+
 	"github.com/cloudflare/circl/sign/dilithium/mode2/internal"
+
 )
 
 const (
diff --git a/sign/dilithium/mode2/internal/dilithium.go b/sign/dilithium/mode2/internal/dilithium.go
index 79a17d504..7869d0475 100644
--- a/sign/dilithium/mode2/internal/dilithium.go
+++ b/sign/dilithium/mode2/internal/dilithium.go
@@ -8,7 +8,7 @@ import (
 	"io"
 
 	"github.com/cloudflare/circl/internal/sha3"
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 const (
@@ -29,13 +29,13 @@ const (
 	Alpha = 2 * Gamma2
 
 	// Size of a packed private key
-	PrivateKeySize = 32 + 32 + 32 + PolyLeqEtaSize*(L+K) + common.PolyT0Size*K
+	PrivateKeySize = 32 + 32 + TRSize + PolyLeqEtaSize*(L+K) + common.PolyT0Size*K
 
 	// Size of a packed public key
 	PublicKeySize = 32 + common.PolyT1Size*K
 
 	// Size of a packed signature
-	SignatureSize = L*PolyLeGamma1Size + Omega + K + 32
+	SignatureSize = L*PolyLeGamma1Size + Omega + K + CTildeSize
 
 	// Size of packed w₁
 	PolyW1Size = (common.N * (common.QBits - Gamma1Bits)) / 8
@@ -49,7 +49,7 @@ type PublicKey struct {
 	// Cached values
 	t1p [common.PolyT1Size * K]byte
 	A   *Mat
-	tr  *[32]byte
+	tr  *[TRSize]byte
 }
 
 // PrivateKey is the type of Dilithium private keys.
@@ -59,7 +59,7 @@ type PrivateKey struct {
 	s1  VecL
 	s2  VecK
 	t0  VecK
-	tr  [32]byte
+	tr  [TRSize]byte
 
 	// Cached values
 	A   Mat  // ExpandA(ρ)
@@ -71,14 +71,14 @@ type PrivateKey struct {
 type unpackedSignature struct {
 	z    VecL
 	hint VecK
-	c    [32]byte
+	c    [CTildeSize]byte
 }
 
 // Packs the signature into buf.
 func (sig *unpackedSignature) Pack(buf []byte) {
 	copy(buf[:], sig.c[:])
-	sig.z.PackLeGamma1(buf[32:])
-	sig.hint.PackHint(buf[32+L*PolyLeGamma1Size:])
+	sig.z.PackLeGamma1(buf[CTildeSize:])
+	sig.hint.PackHint(buf[CTildeSize+L*PolyLeGamma1Size:])
 }
 
 // Sets sig to the signature encoded in the buffer.
@@ -89,11 +89,11 @@ func (sig *unpackedSignature) Unpack(buf []byte) bool {
 		return false
 	}
 	copy(sig.c[:], buf[:])
-	sig.z.UnpackLeGamma1(buf[32:])
+	sig.z.UnpackLeGamma1(buf[CTildeSize:])
 	if sig.z.Exceeds(Gamma1 - Beta) {
 		return false
 	}
-	if !sig.hint.UnpackHint(buf[32+L*PolyLeGamma1Size:]) {
+	if !sig.hint.UnpackHint(buf[CTildeSize+L*PolyLeGamma1Size:]) {
 		return false
 	}
 	return true
@@ -115,7 +115,7 @@ func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) {
 	pk.A.Derive(&pk.rho)
 
 	// tr = CRH(ρ ‖ t1) = CRH(pk)
-	pk.tr = new([32]byte)
+	pk.tr = new([TRSize]byte)
 	h := sha3.NewShake256()
 	_, _ = h.Write(buf[:])
 	_, _ = h.Read(pk.tr[:])
@@ -125,8 +125,8 @@ func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) {
 func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) {
 	copy(buf[:32], sk.rho[:])
 	copy(buf[32:64], sk.key[:])
-	copy(buf[64:96], sk.tr[:])
-	offset := 96
+	copy(buf[64:64+TRSize], sk.tr[:])
+	offset := 64 + TRSize
 	sk.s1.PackLeqEta(buf[offset:])
 	offset += PolyLeqEtaSize * L
 	sk.s2.PackLeqEta(buf[offset:])
@@ -138,8 +138,8 @@ func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) {
 func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) {
 	copy(sk.rho[:], buf[:32])
 	copy(sk.key[:], buf[32:64])
-	copy(sk.tr[:], buf[64:96])
-	offset := 96
+	copy(sk.tr[:], buf[64:64+TRSize])
+	offset := 64 + TRSize
 	sk.s1.UnpackLeqEta(buf[offset:])
 	offset += PolyLeqEtaSize * L
 	sk.s2.UnpackLeqEta(buf[offset:])
@@ -250,7 +250,7 @@ func Verify(pk *PublicKey, msg []byte, signature []byte) bool {
 	var zh VecL
 	var Az, Az2dct1, w1 VecK
 	var ch common.Poly
-	var cp [32]byte
+	var cp [CTildeSize]byte
 	var w1Packed [PolyW1Size * K]byte
 
 	// Note that Unpack() checked whether ‖z‖_∞ < γ₁ - β
@@ -279,7 +279,7 @@ func Verify(pk *PublicKey, msg []byte, signature []byte) bool {
 	// which is small enough for NTT().
 	Az2dct1.MulBy2toD(&pk.t1)
 	Az2dct1.NTT()
-	PolyDeriveUniformBall(&ch, &sig.c)
+	PolyDeriveUniformBall(&ch, sig.c[:32])
 	ch.NTT()
 	for i := 0; i < K; i++ {
 		Az2dct1[i].MulHat(&Az2dct1[i], &ch)
@@ -330,6 +330,11 @@ func SignTo(sk *PrivateKey, msg []byte, signature []byte) {
 	// ρ' = CRH(key ‖ μ)
 	h.Reset()
 	_, _ = h.Write(sk.key[:])
+	if NIST {
+		// We implement the deterministic variant  where rnd is all zeroes.
+		// TODO expose randomized variant?
+		_, _ = h.Write(make([]byte, 32))
+	}
 	_, _ = h.Write(mu[:])
 	_, _ = h.Read(rhop[:])
 
@@ -368,7 +373,7 @@ func SignTo(sk *PrivateKey, msg []byte, signature []byte) {
 		_, _ = h.Write(w1Packed[:])
 		_, _ = h.Read(sig.c[:])
 
-		PolyDeriveUniformBall(&ch, &sig.c)
+		PolyDeriveUniformBall(&ch, sig.c[:32])
 		ch.NTT()
 
 		// Ensure ‖ w₀ - c·s2 ‖_∞ < γ₂ - β.
diff --git a/sign/dilithium/mode2/internal/dilithium_test.go b/sign/dilithium/mode2/internal/dilithium_test.go
index ca347a831..825e7da08 100644
--- a/sign/dilithium/mode2/internal/dilithium_test.go
+++ b/sign/dilithium/mode2/internal/dilithium_test.go
@@ -6,7 +6,7 @@ import (
 	"encoding/binary"
 	"testing"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // Checks whether p is normalized.  Only used in tests.
diff --git a/sign/dilithium/mode2/internal/mat.go b/sign/dilithium/mode2/internal/mat.go
index cb473c149..ceaf634fa 100644
--- a/sign/dilithium/mode2/internal/mat.go
+++ b/sign/dilithium/mode2/internal/mat.go
@@ -3,7 +3,7 @@
 package internal
 
 import (
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // A k by l matrix of polynomials.
diff --git a/sign/dilithium/mode2/internal/pack.go b/sign/dilithium/mode2/internal/pack.go
index 0285dfd8e..1854b4197 100644
--- a/sign/dilithium/mode2/internal/pack.go
+++ b/sign/dilithium/mode2/internal/pack.go
@@ -3,7 +3,7 @@
 package internal
 
 import (
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // Writes p with norm less than or equal η into buf, which must be of
diff --git a/sign/dilithium/mode2/internal/pack_test.go b/sign/dilithium/mode2/internal/pack_test.go
index 24f568e4d..f952c6a09 100644
--- a/sign/dilithium/mode2/internal/pack_test.go
+++ b/sign/dilithium/mode2/internal/pack_test.go
@@ -5,7 +5,7 @@ package internal
 import (
 	"testing"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 func TestPolyPackLeqEta(t *testing.T) {
diff --git a/sign/dilithium/mode2/internal/params.go b/sign/dilithium/mode2/internal/params.go
index b49db55b3..74810fbad 100644
--- a/sign/dilithium/mode2/internal/params.go
+++ b/sign/dilithium/mode2/internal/params.go
@@ -13,4 +13,7 @@ const (
 	Tau           = 39
 	Gamma1Bits    = 17
 	Gamma2        = 95232
+	NIST          = false
+	TRSize        = 32
+	CTildeSize    = 32
 )
diff --git a/sign/dilithium/mode2/internal/params_test.go b/sign/dilithium/mode2/internal/params_test.go
index 6dbc04cb8..f1f1715b7 100644
--- a/sign/dilithium/mode2/internal/params_test.go
+++ b/sign/dilithium/mode2/internal/params_test.go
@@ -3,7 +3,7 @@ package internal
 import (
 	"testing"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // Tests specific to the current mode
diff --git a/sign/dilithium/mode2/internal/rounding.go b/sign/dilithium/mode2/internal/rounding.go
index 71360cb29..58123c090 100644
--- a/sign/dilithium/mode2/internal/rounding.go
+++ b/sign/dilithium/mode2/internal/rounding.go
@@ -3,7 +3,7 @@
 package internal
 
 import (
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // Splits 0 ≤ a < q into a₀ and a₁ with a = a₁*α + a₀ with -α/2 < a₀ ≤ α/2,
diff --git a/sign/dilithium/mode2/internal/rounding_test.go b/sign/dilithium/mode2/internal/rounding_test.go
index 5824f2656..ad653ca3f 100644
--- a/sign/dilithium/mode2/internal/rounding_test.go
+++ b/sign/dilithium/mode2/internal/rounding_test.go
@@ -6,7 +6,7 @@ import (
 	"flag"
 	"testing"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 var runVeryLongTest = flag.Bool("very-long", false, "runs very long tests")
diff --git a/sign/dilithium/mode2/internal/sample.go b/sign/dilithium/mode2/internal/sample.go
index c47185ada..62c261332 100644
--- a/sign/dilithium/mode2/internal/sample.go
+++ b/sign/dilithium/mode2/internal/sample.go
@@ -6,7 +6,7 @@ import (
 	"encoding/binary"
 
 	"github.com/cloudflare/circl/internal/sha3"
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 	"github.com/cloudflare/circl/simd/keccakf1600"
 )
 
@@ -246,12 +246,12 @@ func PolyDeriveUniformLeGamma1(p *common.Poly, seed *[64]byte, nonce uint16) {
 // Can only be called when DeriveX4Available is true.
 //
 // This function is currently not used (yet).
-func PolyDeriveUniformBallX4(ps [4]*common.Poly, seed *[32]byte) {
+func PolyDeriveUniformBallX4(ps [4]*common.Poly, seed []byte) {
 	var perm keccakf1600.StateX4
 	state := perm.Initialize(false)
 
 	// Absorb the seed in the four states
-	for i := 0; i < 4; i++ {
+	for i := 0; i < 32/8; i++ {
 		v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)])
 		for j := 0; j < 4; j++ {
 			state[i*4+j] = v
@@ -260,7 +260,7 @@ func PolyDeriveUniformBallX4(ps [4]*common.Poly, seed *[32]byte) {
 
 	// SHAKE256 domain separator and padding
 	for j := 0; j < 4; j++ {
-		state[4*4+j] ^= 0x1f
+		state[(32/8)*4+j] ^= 0x1f
 		state[16*4+j] ^= 0x80 << 56
 	}
 	perm.Permute()
@@ -327,7 +327,7 @@ func PolyDeriveUniformBallX4(ps [4]*common.Poly, seed *[32]byte) {
 // Samples p uniformly with τ non-zero coefficients in {q-1,1}.
 //
 // The polynomial p will be normalized.
-func PolyDeriveUniformBall(p *common.Poly, seed *[32]byte) {
+func PolyDeriveUniformBall(p *common.Poly, seed []byte) {
 	var buf [136]byte // SHAKE-256 rate is 136
 
 	h := sha3.NewShake256()
diff --git a/sign/dilithium/mode2/internal/sample_test.go b/sign/dilithium/mode2/internal/sample_test.go
index 1a0a4f72c..2059599eb 100644
--- a/sign/dilithium/mode2/internal/sample_test.go
+++ b/sign/dilithium/mode2/internal/sample_test.go
@@ -6,7 +6,7 @@ import (
 	"encoding/binary"
 	"testing"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 func TestVectorDeriveUniform(t *testing.T) {
@@ -155,7 +155,7 @@ func TestDeriveUniformBall(t *testing.T) {
 	var seed [32]byte
 	for i := 0; i < 100; i++ {
 		binary.LittleEndian.PutUint64(seed[:], uint64(i))
-		PolyDeriveUniformBall(&p, &seed)
+		PolyDeriveUniformBall(&p, seed[:])
 		nonzero := 0
 		for j := 0; j < common.N; j++ {
 			if p[j] != 0 {
@@ -203,10 +203,10 @@ func TestDeriveUniformBallX4(t *testing.T) {
 	var seed [32]byte
 	PolyDeriveUniformBallX4(
 		[4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]},
-		&seed,
+		seed[:],
 	)
 	for j := 0; j < 4; j++ {
-		PolyDeriveUniformBall(&p, &seed)
+		PolyDeriveUniformBall(&p, seed[:])
 		if ps[j] != p {
 			t.Fatalf("%d\n%v\n%v", j, ps[j], p)
 		}
@@ -219,7 +219,7 @@ func BenchmarkPolyDeriveUniformBall(b *testing.B) {
 	var w1 VecK
 	for i := 0; i < b.N; i++ {
 		w1[0][0] = uint32(i)
-		PolyDeriveUniformBall(&p, &seed)
+		PolyDeriveUniformBall(&p, seed[:])
 	}
 }
 
@@ -231,7 +231,7 @@ func BenchmarkPolyDeriveUniformBallX4(b *testing.B) {
 		w1[0][0] = uint32(i)
 		PolyDeriveUniformBallX4(
 			[4]*common.Poly{&p, &p, &p, &p},
-			&seed,
+			seed[:],
 		)
 	}
 }
diff --git a/sign/dilithium/mode2/internal/vec.go b/sign/dilithium/mode2/internal/vec.go
index f52973e45..d07d3b245 100644
--- a/sign/dilithium/mode2/internal/vec.go
+++ b/sign/dilithium/mode2/internal/vec.go
@@ -3,7 +3,7 @@
 package internal
 
 import (
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // A vector of L polynomials.
diff --git a/sign/dilithium/mode2aes.go b/sign/dilithium/mode2aes.go
index e3c996d92..e973a70f6 100644
--- a/sign/dilithium/mode2aes.go
+++ b/sign/dilithium/mode2aes.go
@@ -6,8 +6,8 @@ import (
 	"fmt"
 	"io"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
 	"github.com/cloudflare/circl/sign/dilithium/mode2aes"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // implMode2AES implements the mode.Mode interface for Dilithium2-AES.
diff --git a/sign/dilithium/mode2aes/dilithium.go b/sign/dilithium/mode2aes/dilithium.go
index 0b44077bb..93e5058d5 100644
--- a/sign/dilithium/mode2aes/dilithium.go
+++ b/sign/dilithium/mode2aes/dilithium.go
@@ -1,9 +1,11 @@
 // Code generated from modePkg.templ.go. DO NOT EDIT.
 
+
 // mode2aes implements the CRYSTALS-Dilithium signature scheme Dilithium2-AES
 // as submitted to round3 of the NIST PQC competition and described in
 //
 // https://pq-crystals.org/dilithium/data/dilithium-specification-round3-20210208.pdf
+
 package mode2aes
 
 import (
@@ -11,8 +13,10 @@ import (
 	"errors"
 	"io"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+
 	"github.com/cloudflare/circl/sign/dilithium/mode2aes/internal"
+
 )
 
 const (
diff --git a/sign/dilithium/mode2aes/internal/dilithium.go b/sign/dilithium/mode2aes/internal/dilithium.go
index 79a17d504..7869d0475 100644
--- a/sign/dilithium/mode2aes/internal/dilithium.go
+++ b/sign/dilithium/mode2aes/internal/dilithium.go
@@ -8,7 +8,7 @@ import (
 	"io"
 
 	"github.com/cloudflare/circl/internal/sha3"
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 const (
@@ -29,13 +29,13 @@ const (
 	Alpha = 2 * Gamma2
 
 	// Size of a packed private key
-	PrivateKeySize = 32 + 32 + 32 + PolyLeqEtaSize*(L+K) + common.PolyT0Size*K
+	PrivateKeySize = 32 + 32 + TRSize + PolyLeqEtaSize*(L+K) + common.PolyT0Size*K
 
 	// Size of a packed public key
 	PublicKeySize = 32 + common.PolyT1Size*K
 
 	// Size of a packed signature
-	SignatureSize = L*PolyLeGamma1Size + Omega + K + 32
+	SignatureSize = L*PolyLeGamma1Size + Omega + K + CTildeSize
 
 	// Size of packed w₁
 	PolyW1Size = (common.N * (common.QBits - Gamma1Bits)) / 8
@@ -49,7 +49,7 @@ type PublicKey struct {
 	// Cached values
 	t1p [common.PolyT1Size * K]byte
 	A   *Mat
-	tr  *[32]byte
+	tr  *[TRSize]byte
 }
 
 // PrivateKey is the type of Dilithium private keys.
@@ -59,7 +59,7 @@ type PrivateKey struct {
 	s1  VecL
 	s2  VecK
 	t0  VecK
-	tr  [32]byte
+	tr  [TRSize]byte
 
 	// Cached values
 	A   Mat  // ExpandA(ρ)
@@ -71,14 +71,14 @@ type PrivateKey struct {
 type unpackedSignature struct {
 	z    VecL
 	hint VecK
-	c    [32]byte
+	c    [CTildeSize]byte
 }
 
 // Packs the signature into buf.
 func (sig *unpackedSignature) Pack(buf []byte) {
 	copy(buf[:], sig.c[:])
-	sig.z.PackLeGamma1(buf[32:])
-	sig.hint.PackHint(buf[32+L*PolyLeGamma1Size:])
+	sig.z.PackLeGamma1(buf[CTildeSize:])
+	sig.hint.PackHint(buf[CTildeSize+L*PolyLeGamma1Size:])
 }
 
 // Sets sig to the signature encoded in the buffer.
@@ -89,11 +89,11 @@ func (sig *unpackedSignature) Unpack(buf []byte) bool {
 		return false
 	}
 	copy(sig.c[:], buf[:])
-	sig.z.UnpackLeGamma1(buf[32:])
+	sig.z.UnpackLeGamma1(buf[CTildeSize:])
 	if sig.z.Exceeds(Gamma1 - Beta) {
 		return false
 	}
-	if !sig.hint.UnpackHint(buf[32+L*PolyLeGamma1Size:]) {
+	if !sig.hint.UnpackHint(buf[CTildeSize+L*PolyLeGamma1Size:]) {
 		return false
 	}
 	return true
@@ -115,7 +115,7 @@ func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) {
 	pk.A.Derive(&pk.rho)
 
 	// tr = CRH(ρ ‖ t1) = CRH(pk)
-	pk.tr = new([32]byte)
+	pk.tr = new([TRSize]byte)
 	h := sha3.NewShake256()
 	_, _ = h.Write(buf[:])
 	_, _ = h.Read(pk.tr[:])
@@ -125,8 +125,8 @@ func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) {
 func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) {
 	copy(buf[:32], sk.rho[:])
 	copy(buf[32:64], sk.key[:])
-	copy(buf[64:96], sk.tr[:])
-	offset := 96
+	copy(buf[64:64+TRSize], sk.tr[:])
+	offset := 64 + TRSize
 	sk.s1.PackLeqEta(buf[offset:])
 	offset += PolyLeqEtaSize * L
 	sk.s2.PackLeqEta(buf[offset:])
@@ -138,8 +138,8 @@ func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) {
 func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) {
 	copy(sk.rho[:], buf[:32])
 	copy(sk.key[:], buf[32:64])
-	copy(sk.tr[:], buf[64:96])
-	offset := 96
+	copy(sk.tr[:], buf[64:64+TRSize])
+	offset := 64 + TRSize
 	sk.s1.UnpackLeqEta(buf[offset:])
 	offset += PolyLeqEtaSize * L
 	sk.s2.UnpackLeqEta(buf[offset:])
@@ -250,7 +250,7 @@ func Verify(pk *PublicKey, msg []byte, signature []byte) bool {
 	var zh VecL
 	var Az, Az2dct1, w1 VecK
 	var ch common.Poly
-	var cp [32]byte
+	var cp [CTildeSize]byte
 	var w1Packed [PolyW1Size * K]byte
 
 	// Note that Unpack() checked whether ‖z‖_∞ < γ₁ - β
@@ -279,7 +279,7 @@ func Verify(pk *PublicKey, msg []byte, signature []byte) bool {
 	// which is small enough for NTT().
 	Az2dct1.MulBy2toD(&pk.t1)
 	Az2dct1.NTT()
-	PolyDeriveUniformBall(&ch, &sig.c)
+	PolyDeriveUniformBall(&ch, sig.c[:32])
 	ch.NTT()
 	for i := 0; i < K; i++ {
 		Az2dct1[i].MulHat(&Az2dct1[i], &ch)
@@ -330,6 +330,11 @@ func SignTo(sk *PrivateKey, msg []byte, signature []byte) {
 	// ρ' = CRH(key ‖ μ)
 	h.Reset()
 	_, _ = h.Write(sk.key[:])
+	if NIST {
+		// We implement the deterministic variant  where rnd is all zeroes.
+		// TODO expose randomized variant?
+		_, _ = h.Write(make([]byte, 32))
+	}
 	_, _ = h.Write(mu[:])
 	_, _ = h.Read(rhop[:])
 
@@ -368,7 +373,7 @@ func SignTo(sk *PrivateKey, msg []byte, signature []byte) {
 		_, _ = h.Write(w1Packed[:])
 		_, _ = h.Read(sig.c[:])
 
-		PolyDeriveUniformBall(&ch, &sig.c)
+		PolyDeriveUniformBall(&ch, sig.c[:32])
 		ch.NTT()
 
 		// Ensure ‖ w₀ - c·s2 ‖_∞ < γ₂ - β.
diff --git a/sign/dilithium/mode2aes/internal/dilithium_test.go b/sign/dilithium/mode2aes/internal/dilithium_test.go
index ca347a831..825e7da08 100644
--- a/sign/dilithium/mode2aes/internal/dilithium_test.go
+++ b/sign/dilithium/mode2aes/internal/dilithium_test.go
@@ -6,7 +6,7 @@ import (
 	"encoding/binary"
 	"testing"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // Checks whether p is normalized.  Only used in tests.
diff --git a/sign/dilithium/mode2aes/internal/mat.go b/sign/dilithium/mode2aes/internal/mat.go
index cb473c149..ceaf634fa 100644
--- a/sign/dilithium/mode2aes/internal/mat.go
+++ b/sign/dilithium/mode2aes/internal/mat.go
@@ -3,7 +3,7 @@
 package internal
 
 import (
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // A k by l matrix of polynomials.
diff --git a/sign/dilithium/mode2aes/internal/pack.go b/sign/dilithium/mode2aes/internal/pack.go
index 0285dfd8e..1854b4197 100644
--- a/sign/dilithium/mode2aes/internal/pack.go
+++ b/sign/dilithium/mode2aes/internal/pack.go
@@ -3,7 +3,7 @@
 package internal
 
 import (
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // Writes p with norm less than or equal η into buf, which must be of
diff --git a/sign/dilithium/mode2aes/internal/pack_test.go b/sign/dilithium/mode2aes/internal/pack_test.go
index 24f568e4d..f952c6a09 100644
--- a/sign/dilithium/mode2aes/internal/pack_test.go
+++ b/sign/dilithium/mode2aes/internal/pack_test.go
@@ -5,7 +5,7 @@ package internal
 import (
 	"testing"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 func TestPolyPackLeqEta(t *testing.T) {
diff --git a/sign/dilithium/mode2aes/internal/params.go b/sign/dilithium/mode2aes/internal/params.go
index 751ad149b..77305b51b 100644
--- a/sign/dilithium/mode2aes/internal/params.go
+++ b/sign/dilithium/mode2aes/internal/params.go
@@ -13,4 +13,7 @@ const (
 	Tau           = 39
 	Gamma1Bits    = 17
 	Gamma2        = 95232
+	NIST          = false
+	TRSize        = 32
+	CTildeSize    = 32
 )
diff --git a/sign/dilithium/mode2aes/internal/params_test.go b/sign/dilithium/mode2aes/internal/params_test.go
index 50665d6a9..14d70d1a7 100644
--- a/sign/dilithium/mode2aes/internal/params_test.go
+++ b/sign/dilithium/mode2aes/internal/params_test.go
@@ -3,7 +3,7 @@ package internal
 import (
 	"testing"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // Tests specific to the current mode
diff --git a/sign/dilithium/mode2aes/internal/rounding.go b/sign/dilithium/mode2aes/internal/rounding.go
index 71360cb29..58123c090 100644
--- a/sign/dilithium/mode2aes/internal/rounding.go
+++ b/sign/dilithium/mode2aes/internal/rounding.go
@@ -3,7 +3,7 @@
 package internal
 
 import (
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // Splits 0 ≤ a < q into a₀ and a₁ with a = a₁*α + a₀ with -α/2 < a₀ ≤ α/2,
diff --git a/sign/dilithium/mode2aes/internal/rounding_test.go b/sign/dilithium/mode2aes/internal/rounding_test.go
index 5824f2656..ad653ca3f 100644
--- a/sign/dilithium/mode2aes/internal/rounding_test.go
+++ b/sign/dilithium/mode2aes/internal/rounding_test.go
@@ -6,7 +6,7 @@ import (
 	"flag"
 	"testing"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 var runVeryLongTest = flag.Bool("very-long", false, "runs very long tests")
diff --git a/sign/dilithium/mode2aes/internal/sample.go b/sign/dilithium/mode2aes/internal/sample.go
index c47185ada..62c261332 100644
--- a/sign/dilithium/mode2aes/internal/sample.go
+++ b/sign/dilithium/mode2aes/internal/sample.go
@@ -6,7 +6,7 @@ import (
 	"encoding/binary"
 
 	"github.com/cloudflare/circl/internal/sha3"
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 	"github.com/cloudflare/circl/simd/keccakf1600"
 )
 
@@ -246,12 +246,12 @@ func PolyDeriveUniformLeGamma1(p *common.Poly, seed *[64]byte, nonce uint16) {
 // Can only be called when DeriveX4Available is true.
 //
 // This function is currently not used (yet).
-func PolyDeriveUniformBallX4(ps [4]*common.Poly, seed *[32]byte) {
+func PolyDeriveUniformBallX4(ps [4]*common.Poly, seed []byte) {
 	var perm keccakf1600.StateX4
 	state := perm.Initialize(false)
 
 	// Absorb the seed in the four states
-	for i := 0; i < 4; i++ {
+	for i := 0; i < 32/8; i++ {
 		v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)])
 		for j := 0; j < 4; j++ {
 			state[i*4+j] = v
@@ -260,7 +260,7 @@ func PolyDeriveUniformBallX4(ps [4]*common.Poly, seed *[32]byte) {
 
 	// SHAKE256 domain separator and padding
 	for j := 0; j < 4; j++ {
-		state[4*4+j] ^= 0x1f
+		state[(32/8)*4+j] ^= 0x1f
 		state[16*4+j] ^= 0x80 << 56
 	}
 	perm.Permute()
@@ -327,7 +327,7 @@ func PolyDeriveUniformBallX4(ps [4]*common.Poly, seed *[32]byte) {
 // Samples p uniformly with τ non-zero coefficients in {q-1,1}.
 //
 // The polynomial p will be normalized.
-func PolyDeriveUniformBall(p *common.Poly, seed *[32]byte) {
+func PolyDeriveUniformBall(p *common.Poly, seed []byte) {
 	var buf [136]byte // SHAKE-256 rate is 136
 
 	h := sha3.NewShake256()
diff --git a/sign/dilithium/mode2aes/internal/sample_test.go b/sign/dilithium/mode2aes/internal/sample_test.go
index 1a0a4f72c..2059599eb 100644
--- a/sign/dilithium/mode2aes/internal/sample_test.go
+++ b/sign/dilithium/mode2aes/internal/sample_test.go
@@ -6,7 +6,7 @@ import (
 	"encoding/binary"
 	"testing"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 func TestVectorDeriveUniform(t *testing.T) {
@@ -155,7 +155,7 @@ func TestDeriveUniformBall(t *testing.T) {
 	var seed [32]byte
 	for i := 0; i < 100; i++ {
 		binary.LittleEndian.PutUint64(seed[:], uint64(i))
-		PolyDeriveUniformBall(&p, &seed)
+		PolyDeriveUniformBall(&p, seed[:])
 		nonzero := 0
 		for j := 0; j < common.N; j++ {
 			if p[j] != 0 {
@@ -203,10 +203,10 @@ func TestDeriveUniformBallX4(t *testing.T) {
 	var seed [32]byte
 	PolyDeriveUniformBallX4(
 		[4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]},
-		&seed,
+		seed[:],
 	)
 	for j := 0; j < 4; j++ {
-		PolyDeriveUniformBall(&p, &seed)
+		PolyDeriveUniformBall(&p, seed[:])
 		if ps[j] != p {
 			t.Fatalf("%d\n%v\n%v", j, ps[j], p)
 		}
@@ -219,7 +219,7 @@ func BenchmarkPolyDeriveUniformBall(b *testing.B) {
 	var w1 VecK
 	for i := 0; i < b.N; i++ {
 		w1[0][0] = uint32(i)
-		PolyDeriveUniformBall(&p, &seed)
+		PolyDeriveUniformBall(&p, seed[:])
 	}
 }
 
@@ -231,7 +231,7 @@ func BenchmarkPolyDeriveUniformBallX4(b *testing.B) {
 		w1[0][0] = uint32(i)
 		PolyDeriveUniformBallX4(
 			[4]*common.Poly{&p, &p, &p, &p},
-			&seed,
+			seed[:],
 		)
 	}
 }
diff --git a/sign/dilithium/mode2aes/internal/vec.go b/sign/dilithium/mode2aes/internal/vec.go
index f52973e45..d07d3b245 100644
--- a/sign/dilithium/mode2aes/internal/vec.go
+++ b/sign/dilithium/mode2aes/internal/vec.go
@@ -3,7 +3,7 @@
 package internal
 
 import (
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // A vector of L polynomials.
diff --git a/sign/dilithium/mode3.go b/sign/dilithium/mode3.go
index fb45a29c2..147678612 100644
--- a/sign/dilithium/mode3.go
+++ b/sign/dilithium/mode3.go
@@ -6,8 +6,8 @@ import (
 	"fmt"
 	"io"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
 	"github.com/cloudflare/circl/sign/dilithium/mode3"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // implMode3 implements the mode.Mode interface for Dilithium3.
diff --git a/sign/dilithium/mode3/dilithium.go b/sign/dilithium/mode3/dilithium.go
index 3ab9d6b53..de98b5dd2 100644
--- a/sign/dilithium/mode3/dilithium.go
+++ b/sign/dilithium/mode3/dilithium.go
@@ -1,9 +1,11 @@
 // Code generated from modePkg.templ.go. DO NOT EDIT.
 
+
 // mode3 implements the CRYSTALS-Dilithium signature scheme Dilithium3
 // as submitted to round3 of the NIST PQC competition and described in
 //
 // https://pq-crystals.org/dilithium/data/dilithium-specification-round3-20210208.pdf
+
 package mode3
 
 import (
@@ -11,8 +13,10 @@ import (
 	"errors"
 	"io"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+
 	"github.com/cloudflare/circl/sign/dilithium/mode3/internal"
+
 )
 
 const (
diff --git a/sign/dilithium/mode3/internal/dilithium.go b/sign/dilithium/mode3/internal/dilithium.go
index 59e43cc13..da4ec6262 100644
--- a/sign/dilithium/mode3/internal/dilithium.go
+++ b/sign/dilithium/mode3/internal/dilithium.go
@@ -6,7 +6,7 @@ import (
 	"io"
 
 	"github.com/cloudflare/circl/internal/sha3"
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 const (
@@ -27,13 +27,13 @@ const (
 	Alpha = 2 * Gamma2
 
 	// Size of a packed private key
-	PrivateKeySize = 32 + 32 + 32 + PolyLeqEtaSize*(L+K) + common.PolyT0Size*K
+	PrivateKeySize = 32 + 32 + TRSize + PolyLeqEtaSize*(L+K) + common.PolyT0Size*K
 
 	// Size of a packed public key
 	PublicKeySize = 32 + common.PolyT1Size*K
 
 	// Size of a packed signature
-	SignatureSize = L*PolyLeGamma1Size + Omega + K + 32
+	SignatureSize = L*PolyLeGamma1Size + Omega + K + CTildeSize
 
 	// Size of packed w₁
 	PolyW1Size = (common.N * (common.QBits - Gamma1Bits)) / 8
@@ -47,7 +47,7 @@ type PublicKey struct {
 	// Cached values
 	t1p [common.PolyT1Size * K]byte
 	A   *Mat
-	tr  *[32]byte
+	tr  *[TRSize]byte
 }
 
 // PrivateKey is the type of Dilithium private keys.
@@ -57,7 +57,7 @@ type PrivateKey struct {
 	s1  VecL
 	s2  VecK
 	t0  VecK
-	tr  [32]byte
+	tr  [TRSize]byte
 
 	// Cached values
 	A   Mat  // ExpandA(ρ)
@@ -69,14 +69,14 @@ type PrivateKey struct {
 type unpackedSignature struct {
 	z    VecL
 	hint VecK
-	c    [32]byte
+	c    [CTildeSize]byte
 }
 
 // Packs the signature into buf.
 func (sig *unpackedSignature) Pack(buf []byte) {
 	copy(buf[:], sig.c[:])
-	sig.z.PackLeGamma1(buf[32:])
-	sig.hint.PackHint(buf[32+L*PolyLeGamma1Size:])
+	sig.z.PackLeGamma1(buf[CTildeSize:])
+	sig.hint.PackHint(buf[CTildeSize+L*PolyLeGamma1Size:])
 }
 
 // Sets sig to the signature encoded in the buffer.
@@ -87,11 +87,11 @@ func (sig *unpackedSignature) Unpack(buf []byte) bool {
 		return false
 	}
 	copy(sig.c[:], buf[:])
-	sig.z.UnpackLeGamma1(buf[32:])
+	sig.z.UnpackLeGamma1(buf[CTildeSize:])
 	if sig.z.Exceeds(Gamma1 - Beta) {
 		return false
 	}
-	if !sig.hint.UnpackHint(buf[32+L*PolyLeGamma1Size:]) {
+	if !sig.hint.UnpackHint(buf[CTildeSize+L*PolyLeGamma1Size:]) {
 		return false
 	}
 	return true
@@ -113,7 +113,7 @@ func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) {
 	pk.A.Derive(&pk.rho)
 
 	// tr = CRH(ρ ‖ t1) = CRH(pk)
-	pk.tr = new([32]byte)
+	pk.tr = new([TRSize]byte)
 	h := sha3.NewShake256()
 	_, _ = h.Write(buf[:])
 	_, _ = h.Read(pk.tr[:])
@@ -123,8 +123,8 @@ func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) {
 func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) {
 	copy(buf[:32], sk.rho[:])
 	copy(buf[32:64], sk.key[:])
-	copy(buf[64:96], sk.tr[:])
-	offset := 96
+	copy(buf[64:64+TRSize], sk.tr[:])
+	offset := 64 + TRSize
 	sk.s1.PackLeqEta(buf[offset:])
 	offset += PolyLeqEtaSize * L
 	sk.s2.PackLeqEta(buf[offset:])
@@ -136,8 +136,8 @@ func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) {
 func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) {
 	copy(sk.rho[:], buf[:32])
 	copy(sk.key[:], buf[32:64])
-	copy(sk.tr[:], buf[64:96])
-	offset := 96
+	copy(sk.tr[:], buf[64:64+TRSize])
+	offset := 64 + TRSize
 	sk.s1.UnpackLeqEta(buf[offset:])
 	offset += PolyLeqEtaSize * L
 	sk.s2.UnpackLeqEta(buf[offset:])
@@ -248,7 +248,7 @@ func Verify(pk *PublicKey, msg []byte, signature []byte) bool {
 	var zh VecL
 	var Az, Az2dct1, w1 VecK
 	var ch common.Poly
-	var cp [32]byte
+	var cp [CTildeSize]byte
 	var w1Packed [PolyW1Size * K]byte
 
 	// Note that Unpack() checked whether ‖z‖_∞ < γ₁ - β
@@ -277,7 +277,7 @@ func Verify(pk *PublicKey, msg []byte, signature []byte) bool {
 	// which is small enough for NTT().
 	Az2dct1.MulBy2toD(&pk.t1)
 	Az2dct1.NTT()
-	PolyDeriveUniformBall(&ch, &sig.c)
+	PolyDeriveUniformBall(&ch, sig.c[:32])
 	ch.NTT()
 	for i := 0; i < K; i++ {
 		Az2dct1[i].MulHat(&Az2dct1[i], &ch)
@@ -328,6 +328,11 @@ func SignTo(sk *PrivateKey, msg []byte, signature []byte) {
 	// ρ' = CRH(key ‖ μ)
 	h.Reset()
 	_, _ = h.Write(sk.key[:])
+	if NIST {
+		// We implement the deterministic variant  where rnd is all zeroes.
+		// TODO expose randomized variant?
+		_, _ = h.Write(make([]byte, 32))
+	}
 	_, _ = h.Write(mu[:])
 	_, _ = h.Read(rhop[:])
 
@@ -366,7 +371,7 @@ func SignTo(sk *PrivateKey, msg []byte, signature []byte) {
 		_, _ = h.Write(w1Packed[:])
 		_, _ = h.Read(sig.c[:])
 
-		PolyDeriveUniformBall(&ch, &sig.c)
+		PolyDeriveUniformBall(&ch, sig.c[:32])
 		ch.NTT()
 
 		// Ensure ‖ w₀ - c·s2 ‖_∞ < γ₂ - β.
diff --git a/sign/dilithium/mode3/internal/dilithium_test.go b/sign/dilithium/mode3/internal/dilithium_test.go
index 05320495d..9707772be 100644
--- a/sign/dilithium/mode3/internal/dilithium_test.go
+++ b/sign/dilithium/mode3/internal/dilithium_test.go
@@ -4,7 +4,7 @@ import (
 	"encoding/binary"
 	"testing"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // Checks whether p is normalized.  Only used in tests.
diff --git a/sign/dilithium/mode3/internal/mat.go b/sign/dilithium/mode3/internal/mat.go
index ce39b7f9a..3d6cc47b2 100644
--- a/sign/dilithium/mode3/internal/mat.go
+++ b/sign/dilithium/mode3/internal/mat.go
@@ -1,7 +1,7 @@
 package internal
 
 import (
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // A k by l matrix of polynomials.
diff --git a/sign/dilithium/mode3/internal/pack.go b/sign/dilithium/mode3/internal/pack.go
index 6a152d73e..d9c80d0e1 100644
--- a/sign/dilithium/mode3/internal/pack.go
+++ b/sign/dilithium/mode3/internal/pack.go
@@ -1,7 +1,7 @@
 package internal
 
 import (
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // Writes p with norm less than or equal η into buf, which must be of
diff --git a/sign/dilithium/mode3/internal/pack_test.go b/sign/dilithium/mode3/internal/pack_test.go
index 1b6b2a613..d8143c810 100644
--- a/sign/dilithium/mode3/internal/pack_test.go
+++ b/sign/dilithium/mode3/internal/pack_test.go
@@ -3,7 +3,7 @@ package internal
 import (
 	"testing"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 func TestPolyPackLeqEta(t *testing.T) {
diff --git a/sign/dilithium/mode3/internal/params.go b/sign/dilithium/mode3/internal/params.go
index c22925234..77452958f 100644
--- a/sign/dilithium/mode3/internal/params.go
+++ b/sign/dilithium/mode3/internal/params.go
@@ -13,4 +13,7 @@ const (
 	Tau           = 49
 	Gamma1Bits    = 19
 	Gamma2        = 261888
+	NIST          = false
+	TRSize        = 32
+	CTildeSize    = 32
 )
diff --git a/sign/dilithium/mode3/internal/params_test.go b/sign/dilithium/mode3/internal/params_test.go
index 43d91c3f4..f1c93e297 100644
--- a/sign/dilithium/mode3/internal/params_test.go
+++ b/sign/dilithium/mode3/internal/params_test.go
@@ -3,7 +3,7 @@ package internal
 import (
 	"testing"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // Tests specific to the current mode
diff --git a/sign/dilithium/mode3/internal/rounding.go b/sign/dilithium/mode3/internal/rounding.go
index f44c951d2..4005e569c 100644
--- a/sign/dilithium/mode3/internal/rounding.go
+++ b/sign/dilithium/mode3/internal/rounding.go
@@ -1,7 +1,7 @@
 package internal
 
 import (
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // Splits 0 ≤ a < q into a₀ and a₁ with a = a₁*α + a₀ with -α/2 < a₀ ≤ α/2,
diff --git a/sign/dilithium/mode3/internal/rounding_test.go b/sign/dilithium/mode3/internal/rounding_test.go
index 387815592..8d2310cb2 100644
--- a/sign/dilithium/mode3/internal/rounding_test.go
+++ b/sign/dilithium/mode3/internal/rounding_test.go
@@ -4,7 +4,7 @@ import (
 	"flag"
 	"testing"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 var runVeryLongTest = flag.Bool("very-long", false, "runs very long tests")
diff --git a/sign/dilithium/mode3/internal/sample.go b/sign/dilithium/mode3/internal/sample.go
index 256ec731f..b2b0bbe13 100644
--- a/sign/dilithium/mode3/internal/sample.go
+++ b/sign/dilithium/mode3/internal/sample.go
@@ -4,7 +4,7 @@ import (
 	"encoding/binary"
 
 	"github.com/cloudflare/circl/internal/sha3"
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 	"github.com/cloudflare/circl/simd/keccakf1600"
 )
 
@@ -244,12 +244,12 @@ func PolyDeriveUniformLeGamma1(p *common.Poly, seed *[64]byte, nonce uint16) {
 // Can only be called when DeriveX4Available is true.
 //
 // This function is currently not used (yet).
-func PolyDeriveUniformBallX4(ps [4]*common.Poly, seed *[32]byte) {
+func PolyDeriveUniformBallX4(ps [4]*common.Poly, seed []byte) {
 	var perm keccakf1600.StateX4
 	state := perm.Initialize(false)
 
 	// Absorb the seed in the four states
-	for i := 0; i < 4; i++ {
+	for i := 0; i < 32/8; i++ {
 		v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)])
 		for j := 0; j < 4; j++ {
 			state[i*4+j] = v
@@ -258,7 +258,7 @@ func PolyDeriveUniformBallX4(ps [4]*common.Poly, seed *[32]byte) {
 
 	// SHAKE256 domain separator and padding
 	for j := 0; j < 4; j++ {
-		state[4*4+j] ^= 0x1f
+		state[(32/8)*4+j] ^= 0x1f
 		state[16*4+j] ^= 0x80 << 56
 	}
 	perm.Permute()
@@ -325,7 +325,7 @@ func PolyDeriveUniformBallX4(ps [4]*common.Poly, seed *[32]byte) {
 // Samples p uniformly with τ non-zero coefficients in {q-1,1}.
 //
 // The polynomial p will be normalized.
-func PolyDeriveUniformBall(p *common.Poly, seed *[32]byte) {
+func PolyDeriveUniformBall(p *common.Poly, seed []byte) {
 	var buf [136]byte // SHAKE-256 rate is 136
 
 	h := sha3.NewShake256()
diff --git a/sign/dilithium/mode3/internal/sample_test.go b/sign/dilithium/mode3/internal/sample_test.go
index bae9d4055..1adfaf535 100644
--- a/sign/dilithium/mode3/internal/sample_test.go
+++ b/sign/dilithium/mode3/internal/sample_test.go
@@ -4,7 +4,7 @@ import (
 	"encoding/binary"
 	"testing"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 func TestVectorDeriveUniform(t *testing.T) {
@@ -153,7 +153,7 @@ func TestDeriveUniformBall(t *testing.T) {
 	var seed [32]byte
 	for i := 0; i < 100; i++ {
 		binary.LittleEndian.PutUint64(seed[:], uint64(i))
-		PolyDeriveUniformBall(&p, &seed)
+		PolyDeriveUniformBall(&p, seed[:])
 		nonzero := 0
 		for j := 0; j < common.N; j++ {
 			if p[j] != 0 {
@@ -201,10 +201,10 @@ func TestDeriveUniformBallX4(t *testing.T) {
 	var seed [32]byte
 	PolyDeriveUniformBallX4(
 		[4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]},
-		&seed,
+		seed[:],
 	)
 	for j := 0; j < 4; j++ {
-		PolyDeriveUniformBall(&p, &seed)
+		PolyDeriveUniformBall(&p, seed[:])
 		if ps[j] != p {
 			t.Fatalf("%d\n%v\n%v", j, ps[j], p)
 		}
@@ -217,7 +217,7 @@ func BenchmarkPolyDeriveUniformBall(b *testing.B) {
 	var w1 VecK
 	for i := 0; i < b.N; i++ {
 		w1[0][0] = uint32(i)
-		PolyDeriveUniformBall(&p, &seed)
+		PolyDeriveUniformBall(&p, seed[:])
 	}
 }
 
@@ -229,7 +229,7 @@ func BenchmarkPolyDeriveUniformBallX4(b *testing.B) {
 		w1[0][0] = uint32(i)
 		PolyDeriveUniformBallX4(
 			[4]*common.Poly{&p, &p, &p, &p},
-			&seed,
+			seed[:],
 		)
 	}
 }
diff --git a/sign/dilithium/mode3/internal/vec.go b/sign/dilithium/mode3/internal/vec.go
index 1a5fe4ca5..5817acb7f 100644
--- a/sign/dilithium/mode3/internal/vec.go
+++ b/sign/dilithium/mode3/internal/vec.go
@@ -1,7 +1,7 @@
 package internal
 
 import (
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // A vector of L polynomials.
diff --git a/sign/dilithium/mode3aes.go b/sign/dilithium/mode3aes.go
index c4cca1863..bdbe19020 100644
--- a/sign/dilithium/mode3aes.go
+++ b/sign/dilithium/mode3aes.go
@@ -6,8 +6,8 @@ import (
 	"fmt"
 	"io"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
 	"github.com/cloudflare/circl/sign/dilithium/mode3aes"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // implMode3AES implements the mode.Mode interface for Dilithium3-AES.
diff --git a/sign/dilithium/mode3aes/dilithium.go b/sign/dilithium/mode3aes/dilithium.go
index afc5e3e92..0503f7673 100644
--- a/sign/dilithium/mode3aes/dilithium.go
+++ b/sign/dilithium/mode3aes/dilithium.go
@@ -1,9 +1,11 @@
 // Code generated from modePkg.templ.go. DO NOT EDIT.
 
+
 // mode3aes implements the CRYSTALS-Dilithium signature scheme Dilithium3-AES
 // as submitted to round3 of the NIST PQC competition and described in
 //
 // https://pq-crystals.org/dilithium/data/dilithium-specification-round3-20210208.pdf
+
 package mode3aes
 
 import (
@@ -11,8 +13,10 @@ import (
 	"errors"
 	"io"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+
 	"github.com/cloudflare/circl/sign/dilithium/mode3aes/internal"
+
 )
 
 const (
diff --git a/sign/dilithium/mode3aes/internal/dilithium.go b/sign/dilithium/mode3aes/internal/dilithium.go
index 79a17d504..7869d0475 100644
--- a/sign/dilithium/mode3aes/internal/dilithium.go
+++ b/sign/dilithium/mode3aes/internal/dilithium.go
@@ -8,7 +8,7 @@ import (
 	"io"
 
 	"github.com/cloudflare/circl/internal/sha3"
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 const (
@@ -29,13 +29,13 @@ const (
 	Alpha = 2 * Gamma2
 
 	// Size of a packed private key
-	PrivateKeySize = 32 + 32 + 32 + PolyLeqEtaSize*(L+K) + common.PolyT0Size*K
+	PrivateKeySize = 32 + 32 + TRSize + PolyLeqEtaSize*(L+K) + common.PolyT0Size*K
 
 	// Size of a packed public key
 	PublicKeySize = 32 + common.PolyT1Size*K
 
 	// Size of a packed signature
-	SignatureSize = L*PolyLeGamma1Size + Omega + K + 32
+	SignatureSize = L*PolyLeGamma1Size + Omega + K + CTildeSize
 
 	// Size of packed w₁
 	PolyW1Size = (common.N * (common.QBits - Gamma1Bits)) / 8
@@ -49,7 +49,7 @@ type PublicKey struct {
 	// Cached values
 	t1p [common.PolyT1Size * K]byte
 	A   *Mat
-	tr  *[32]byte
+	tr  *[TRSize]byte
 }
 
 // PrivateKey is the type of Dilithium private keys.
@@ -59,7 +59,7 @@ type PrivateKey struct {
 	s1  VecL
 	s2  VecK
 	t0  VecK
-	tr  [32]byte
+	tr  [TRSize]byte
 
 	// Cached values
 	A   Mat  // ExpandA(ρ)
@@ -71,14 +71,14 @@ type PrivateKey struct {
 type unpackedSignature struct {
 	z    VecL
 	hint VecK
-	c    [32]byte
+	c    [CTildeSize]byte
 }
 
 // Packs the signature into buf.
 func (sig *unpackedSignature) Pack(buf []byte) {
 	copy(buf[:], sig.c[:])
-	sig.z.PackLeGamma1(buf[32:])
-	sig.hint.PackHint(buf[32+L*PolyLeGamma1Size:])
+	sig.z.PackLeGamma1(buf[CTildeSize:])
+	sig.hint.PackHint(buf[CTildeSize+L*PolyLeGamma1Size:])
 }
 
 // Sets sig to the signature encoded in the buffer.
@@ -89,11 +89,11 @@ func (sig *unpackedSignature) Unpack(buf []byte) bool {
 		return false
 	}
 	copy(sig.c[:], buf[:])
-	sig.z.UnpackLeGamma1(buf[32:])
+	sig.z.UnpackLeGamma1(buf[CTildeSize:])
 	if sig.z.Exceeds(Gamma1 - Beta) {
 		return false
 	}
-	if !sig.hint.UnpackHint(buf[32+L*PolyLeGamma1Size:]) {
+	if !sig.hint.UnpackHint(buf[CTildeSize+L*PolyLeGamma1Size:]) {
 		return false
 	}
 	return true
@@ -115,7 +115,7 @@ func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) {
 	pk.A.Derive(&pk.rho)
 
 	// tr = CRH(ρ ‖ t1) = CRH(pk)
-	pk.tr = new([32]byte)
+	pk.tr = new([TRSize]byte)
 	h := sha3.NewShake256()
 	_, _ = h.Write(buf[:])
 	_, _ = h.Read(pk.tr[:])
@@ -125,8 +125,8 @@ func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) {
 func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) {
 	copy(buf[:32], sk.rho[:])
 	copy(buf[32:64], sk.key[:])
-	copy(buf[64:96], sk.tr[:])
-	offset := 96
+	copy(buf[64:64+TRSize], sk.tr[:])
+	offset := 64 + TRSize
 	sk.s1.PackLeqEta(buf[offset:])
 	offset += PolyLeqEtaSize * L
 	sk.s2.PackLeqEta(buf[offset:])
@@ -138,8 +138,8 @@ func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) {
 func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) {
 	copy(sk.rho[:], buf[:32])
 	copy(sk.key[:], buf[32:64])
-	copy(sk.tr[:], buf[64:96])
-	offset := 96
+	copy(sk.tr[:], buf[64:64+TRSize])
+	offset := 64 + TRSize
 	sk.s1.UnpackLeqEta(buf[offset:])
 	offset += PolyLeqEtaSize * L
 	sk.s2.UnpackLeqEta(buf[offset:])
@@ -250,7 +250,7 @@ func Verify(pk *PublicKey, msg []byte, signature []byte) bool {
 	var zh VecL
 	var Az, Az2dct1, w1 VecK
 	var ch common.Poly
-	var cp [32]byte
+	var cp [CTildeSize]byte
 	var w1Packed [PolyW1Size * K]byte
 
 	// Note that Unpack() checked whether ‖z‖_∞ < γ₁ - β
@@ -279,7 +279,7 @@ func Verify(pk *PublicKey, msg []byte, signature []byte) bool {
 	// which is small enough for NTT().
 	Az2dct1.MulBy2toD(&pk.t1)
 	Az2dct1.NTT()
-	PolyDeriveUniformBall(&ch, &sig.c)
+	PolyDeriveUniformBall(&ch, sig.c[:32])
 	ch.NTT()
 	for i := 0; i < K; i++ {
 		Az2dct1[i].MulHat(&Az2dct1[i], &ch)
@@ -330,6 +330,11 @@ func SignTo(sk *PrivateKey, msg []byte, signature []byte) {
 	// ρ' = CRH(key ‖ μ)
 	h.Reset()
 	_, _ = h.Write(sk.key[:])
+	if NIST {
+		// We implement the deterministic variant  where rnd is all zeroes.
+		// TODO expose randomized variant?
+		_, _ = h.Write(make([]byte, 32))
+	}
 	_, _ = h.Write(mu[:])
 	_, _ = h.Read(rhop[:])
 
@@ -368,7 +373,7 @@ func SignTo(sk *PrivateKey, msg []byte, signature []byte) {
 		_, _ = h.Write(w1Packed[:])
 		_, _ = h.Read(sig.c[:])
 
-		PolyDeriveUniformBall(&ch, &sig.c)
+		PolyDeriveUniformBall(&ch, sig.c[:32])
 		ch.NTT()
 
 		// Ensure ‖ w₀ - c·s2 ‖_∞ < γ₂ - β.
diff --git a/sign/dilithium/mode3aes/internal/dilithium_test.go b/sign/dilithium/mode3aes/internal/dilithium_test.go
index ca347a831..825e7da08 100644
--- a/sign/dilithium/mode3aes/internal/dilithium_test.go
+++ b/sign/dilithium/mode3aes/internal/dilithium_test.go
@@ -6,7 +6,7 @@ import (
 	"encoding/binary"
 	"testing"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // Checks whether p is normalized.  Only used in tests.
diff --git a/sign/dilithium/mode3aes/internal/mat.go b/sign/dilithium/mode3aes/internal/mat.go
index cb473c149..ceaf634fa 100644
--- a/sign/dilithium/mode3aes/internal/mat.go
+++ b/sign/dilithium/mode3aes/internal/mat.go
@@ -3,7 +3,7 @@
 package internal
 
 import (
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // A k by l matrix of polynomials.
diff --git a/sign/dilithium/mode3aes/internal/pack.go b/sign/dilithium/mode3aes/internal/pack.go
index 0285dfd8e..1854b4197 100644
--- a/sign/dilithium/mode3aes/internal/pack.go
+++ b/sign/dilithium/mode3aes/internal/pack.go
@@ -3,7 +3,7 @@
 package internal
 
 import (
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // Writes p with norm less than or equal η into buf, which must be of
diff --git a/sign/dilithium/mode3aes/internal/pack_test.go b/sign/dilithium/mode3aes/internal/pack_test.go
index 24f568e4d..f952c6a09 100644
--- a/sign/dilithium/mode3aes/internal/pack_test.go
+++ b/sign/dilithium/mode3aes/internal/pack_test.go
@@ -5,7 +5,7 @@ package internal
 import (
 	"testing"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 func TestPolyPackLeqEta(t *testing.T) {
diff --git a/sign/dilithium/mode3aes/internal/params.go b/sign/dilithium/mode3aes/internal/params.go
index 7523dc09e..425cea3b3 100644
--- a/sign/dilithium/mode3aes/internal/params.go
+++ b/sign/dilithium/mode3aes/internal/params.go
@@ -13,4 +13,7 @@ const (
 	Tau           = 49
 	Gamma1Bits    = 19
 	Gamma2        = 261888
+	NIST          = false
+	TRSize        = 32
+	CTildeSize    = 32
 )
diff --git a/sign/dilithium/mode3aes/internal/params_test.go b/sign/dilithium/mode3aes/internal/params_test.go
index fc246ce73..8e71ef60d 100644
--- a/sign/dilithium/mode3aes/internal/params_test.go
+++ b/sign/dilithium/mode3aes/internal/params_test.go
@@ -3,7 +3,7 @@ package internal
 import (
 	"testing"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // Tests specific to the current mode
diff --git a/sign/dilithium/mode3aes/internal/rounding.go b/sign/dilithium/mode3aes/internal/rounding.go
index 71360cb29..58123c090 100644
--- a/sign/dilithium/mode3aes/internal/rounding.go
+++ b/sign/dilithium/mode3aes/internal/rounding.go
@@ -3,7 +3,7 @@
 package internal
 
 import (
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // Splits 0 ≤ a < q into a₀ and a₁ with a = a₁*α + a₀ with -α/2 < a₀ ≤ α/2,
diff --git a/sign/dilithium/mode3aes/internal/rounding_test.go b/sign/dilithium/mode3aes/internal/rounding_test.go
index 5824f2656..ad653ca3f 100644
--- a/sign/dilithium/mode3aes/internal/rounding_test.go
+++ b/sign/dilithium/mode3aes/internal/rounding_test.go
@@ -6,7 +6,7 @@ import (
 	"flag"
 	"testing"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 var runVeryLongTest = flag.Bool("very-long", false, "runs very long tests")
diff --git a/sign/dilithium/mode3aes/internal/sample.go b/sign/dilithium/mode3aes/internal/sample.go
index c47185ada..62c261332 100644
--- a/sign/dilithium/mode3aes/internal/sample.go
+++ b/sign/dilithium/mode3aes/internal/sample.go
@@ -6,7 +6,7 @@ import (
 	"encoding/binary"
 
 	"github.com/cloudflare/circl/internal/sha3"
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 	"github.com/cloudflare/circl/simd/keccakf1600"
 )
 
@@ -246,12 +246,12 @@ func PolyDeriveUniformLeGamma1(p *common.Poly, seed *[64]byte, nonce uint16) {
 // Can only be called when DeriveX4Available is true.
 //
 // This function is currently not used (yet).
-func PolyDeriveUniformBallX4(ps [4]*common.Poly, seed *[32]byte) {
+func PolyDeriveUniformBallX4(ps [4]*common.Poly, seed []byte) {
 	var perm keccakf1600.StateX4
 	state := perm.Initialize(false)
 
 	// Absorb the seed in the four states
-	for i := 0; i < 4; i++ {
+	for i := 0; i < 32/8; i++ {
 		v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)])
 		for j := 0; j < 4; j++ {
 			state[i*4+j] = v
@@ -260,7 +260,7 @@ func PolyDeriveUniformBallX4(ps [4]*common.Poly, seed *[32]byte) {
 
 	// SHAKE256 domain separator and padding
 	for j := 0; j < 4; j++ {
-		state[4*4+j] ^= 0x1f
+		state[(32/8)*4+j] ^= 0x1f
 		state[16*4+j] ^= 0x80 << 56
 	}
 	perm.Permute()
@@ -327,7 +327,7 @@ func PolyDeriveUniformBallX4(ps [4]*common.Poly, seed *[32]byte) {
 // Samples p uniformly with τ non-zero coefficients in {q-1,1}.
 //
 // The polynomial p will be normalized.
-func PolyDeriveUniformBall(p *common.Poly, seed *[32]byte) {
+func PolyDeriveUniformBall(p *common.Poly, seed []byte) {
 	var buf [136]byte // SHAKE-256 rate is 136
 
 	h := sha3.NewShake256()
diff --git a/sign/dilithium/mode3aes/internal/sample_test.go b/sign/dilithium/mode3aes/internal/sample_test.go
index 1a0a4f72c..2059599eb 100644
--- a/sign/dilithium/mode3aes/internal/sample_test.go
+++ b/sign/dilithium/mode3aes/internal/sample_test.go
@@ -6,7 +6,7 @@ import (
 	"encoding/binary"
 	"testing"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 func TestVectorDeriveUniform(t *testing.T) {
@@ -155,7 +155,7 @@ func TestDeriveUniformBall(t *testing.T) {
 	var seed [32]byte
 	for i := 0; i < 100; i++ {
 		binary.LittleEndian.PutUint64(seed[:], uint64(i))
-		PolyDeriveUniformBall(&p, &seed)
+		PolyDeriveUniformBall(&p, seed[:])
 		nonzero := 0
 		for j := 0; j < common.N; j++ {
 			if p[j] != 0 {
@@ -203,10 +203,10 @@ func TestDeriveUniformBallX4(t *testing.T) {
 	var seed [32]byte
 	PolyDeriveUniformBallX4(
 		[4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]},
-		&seed,
+		seed[:],
 	)
 	for j := 0; j < 4; j++ {
-		PolyDeriveUniformBall(&p, &seed)
+		PolyDeriveUniformBall(&p, seed[:])
 		if ps[j] != p {
 			t.Fatalf("%d\n%v\n%v", j, ps[j], p)
 		}
@@ -219,7 +219,7 @@ func BenchmarkPolyDeriveUniformBall(b *testing.B) {
 	var w1 VecK
 	for i := 0; i < b.N; i++ {
 		w1[0][0] = uint32(i)
-		PolyDeriveUniformBall(&p, &seed)
+		PolyDeriveUniformBall(&p, seed[:])
 	}
 }
 
@@ -231,7 +231,7 @@ func BenchmarkPolyDeriveUniformBallX4(b *testing.B) {
 		w1[0][0] = uint32(i)
 		PolyDeriveUniformBallX4(
 			[4]*common.Poly{&p, &p, &p, &p},
-			&seed,
+			seed[:],
 		)
 	}
 }
diff --git a/sign/dilithium/mode3aes/internal/vec.go b/sign/dilithium/mode3aes/internal/vec.go
index f52973e45..d07d3b245 100644
--- a/sign/dilithium/mode3aes/internal/vec.go
+++ b/sign/dilithium/mode3aes/internal/vec.go
@@ -3,7 +3,7 @@
 package internal
 
 import (
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // A vector of L polynomials.
diff --git a/sign/dilithium/mode5.go b/sign/dilithium/mode5.go
index d6b7a9c73..c9b55dd30 100644
--- a/sign/dilithium/mode5.go
+++ b/sign/dilithium/mode5.go
@@ -6,8 +6,8 @@ import (
 	"fmt"
 	"io"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
 	"github.com/cloudflare/circl/sign/dilithium/mode5"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // implMode5 implements the mode.Mode interface for Dilithium5.
diff --git a/sign/dilithium/mode5/dilithium.go b/sign/dilithium/mode5/dilithium.go
index 3a6a0cb93..7271ad17d 100644
--- a/sign/dilithium/mode5/dilithium.go
+++ b/sign/dilithium/mode5/dilithium.go
@@ -1,9 +1,11 @@
 // Code generated from modePkg.templ.go. DO NOT EDIT.
 
+
 // mode5 implements the CRYSTALS-Dilithium signature scheme Dilithium5
 // as submitted to round3 of the NIST PQC competition and described in
 //
 // https://pq-crystals.org/dilithium/data/dilithium-specification-round3-20210208.pdf
+
 package mode5
 
 import (
@@ -11,8 +13,10 @@ import (
 	"errors"
 	"io"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+
 	"github.com/cloudflare/circl/sign/dilithium/mode5/internal"
+
 )
 
 const (
diff --git a/sign/dilithium/mode5/internal/dilithium.go b/sign/dilithium/mode5/internal/dilithium.go
index 79a17d504..7869d0475 100644
--- a/sign/dilithium/mode5/internal/dilithium.go
+++ b/sign/dilithium/mode5/internal/dilithium.go
@@ -8,7 +8,7 @@ import (
 	"io"
 
 	"github.com/cloudflare/circl/internal/sha3"
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 const (
@@ -29,13 +29,13 @@ const (
 	Alpha = 2 * Gamma2
 
 	// Size of a packed private key
-	PrivateKeySize = 32 + 32 + 32 + PolyLeqEtaSize*(L+K) + common.PolyT0Size*K
+	PrivateKeySize = 32 + 32 + TRSize + PolyLeqEtaSize*(L+K) + common.PolyT0Size*K
 
 	// Size of a packed public key
 	PublicKeySize = 32 + common.PolyT1Size*K
 
 	// Size of a packed signature
-	SignatureSize = L*PolyLeGamma1Size + Omega + K + 32
+	SignatureSize = L*PolyLeGamma1Size + Omega + K + CTildeSize
 
 	// Size of packed w₁
 	PolyW1Size = (common.N * (common.QBits - Gamma1Bits)) / 8
@@ -49,7 +49,7 @@ type PublicKey struct {
 	// Cached values
 	t1p [common.PolyT1Size * K]byte
 	A   *Mat
-	tr  *[32]byte
+	tr  *[TRSize]byte
 }
 
 // PrivateKey is the type of Dilithium private keys.
@@ -59,7 +59,7 @@ type PrivateKey struct {
 	s1  VecL
 	s2  VecK
 	t0  VecK
-	tr  [32]byte
+	tr  [TRSize]byte
 
 	// Cached values
 	A   Mat  // ExpandA(ρ)
@@ -71,14 +71,14 @@ type PrivateKey struct {
 type unpackedSignature struct {
 	z    VecL
 	hint VecK
-	c    [32]byte
+	c    [CTildeSize]byte
 }
 
 // Packs the signature into buf.
 func (sig *unpackedSignature) Pack(buf []byte) {
 	copy(buf[:], sig.c[:])
-	sig.z.PackLeGamma1(buf[32:])
-	sig.hint.PackHint(buf[32+L*PolyLeGamma1Size:])
+	sig.z.PackLeGamma1(buf[CTildeSize:])
+	sig.hint.PackHint(buf[CTildeSize+L*PolyLeGamma1Size:])
 }
 
 // Sets sig to the signature encoded in the buffer.
@@ -89,11 +89,11 @@ func (sig *unpackedSignature) Unpack(buf []byte) bool {
 		return false
 	}
 	copy(sig.c[:], buf[:])
-	sig.z.UnpackLeGamma1(buf[32:])
+	sig.z.UnpackLeGamma1(buf[CTildeSize:])
 	if sig.z.Exceeds(Gamma1 - Beta) {
 		return false
 	}
-	if !sig.hint.UnpackHint(buf[32+L*PolyLeGamma1Size:]) {
+	if !sig.hint.UnpackHint(buf[CTildeSize+L*PolyLeGamma1Size:]) {
 		return false
 	}
 	return true
@@ -115,7 +115,7 @@ func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) {
 	pk.A.Derive(&pk.rho)
 
 	// tr = CRH(ρ ‖ t1) = CRH(pk)
-	pk.tr = new([32]byte)
+	pk.tr = new([TRSize]byte)
 	h := sha3.NewShake256()
 	_, _ = h.Write(buf[:])
 	_, _ = h.Read(pk.tr[:])
@@ -125,8 +125,8 @@ func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) {
 func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) {
 	copy(buf[:32], sk.rho[:])
 	copy(buf[32:64], sk.key[:])
-	copy(buf[64:96], sk.tr[:])
-	offset := 96
+	copy(buf[64:64+TRSize], sk.tr[:])
+	offset := 64 + TRSize
 	sk.s1.PackLeqEta(buf[offset:])
 	offset += PolyLeqEtaSize * L
 	sk.s2.PackLeqEta(buf[offset:])
@@ -138,8 +138,8 @@ func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) {
 func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) {
 	copy(sk.rho[:], buf[:32])
 	copy(sk.key[:], buf[32:64])
-	copy(sk.tr[:], buf[64:96])
-	offset := 96
+	copy(sk.tr[:], buf[64:64+TRSize])
+	offset := 64 + TRSize
 	sk.s1.UnpackLeqEta(buf[offset:])
 	offset += PolyLeqEtaSize * L
 	sk.s2.UnpackLeqEta(buf[offset:])
@@ -250,7 +250,7 @@ func Verify(pk *PublicKey, msg []byte, signature []byte) bool {
 	var zh VecL
 	var Az, Az2dct1, w1 VecK
 	var ch common.Poly
-	var cp [32]byte
+	var cp [CTildeSize]byte
 	var w1Packed [PolyW1Size * K]byte
 
 	// Note that Unpack() checked whether ‖z‖_∞ < γ₁ - β
@@ -279,7 +279,7 @@ func Verify(pk *PublicKey, msg []byte, signature []byte) bool {
 	// which is small enough for NTT().
 	Az2dct1.MulBy2toD(&pk.t1)
 	Az2dct1.NTT()
-	PolyDeriveUniformBall(&ch, &sig.c)
+	PolyDeriveUniformBall(&ch, sig.c[:32])
 	ch.NTT()
 	for i := 0; i < K; i++ {
 		Az2dct1[i].MulHat(&Az2dct1[i], &ch)
@@ -330,6 +330,11 @@ func SignTo(sk *PrivateKey, msg []byte, signature []byte) {
 	// ρ' = CRH(key ‖ μ)
 	h.Reset()
 	_, _ = h.Write(sk.key[:])
+	if NIST {
+		// We implement the deterministic variant  where rnd is all zeroes.
+		// TODO expose randomized variant?
+		_, _ = h.Write(make([]byte, 32))
+	}
 	_, _ = h.Write(mu[:])
 	_, _ = h.Read(rhop[:])
 
@@ -368,7 +373,7 @@ func SignTo(sk *PrivateKey, msg []byte, signature []byte) {
 		_, _ = h.Write(w1Packed[:])
 		_, _ = h.Read(sig.c[:])
 
-		PolyDeriveUniformBall(&ch, &sig.c)
+		PolyDeriveUniformBall(&ch, sig.c[:32])
 		ch.NTT()
 
 		// Ensure ‖ w₀ - c·s2 ‖_∞ < γ₂ - β.
diff --git a/sign/dilithium/mode5/internal/dilithium_test.go b/sign/dilithium/mode5/internal/dilithium_test.go
index ca347a831..825e7da08 100644
--- a/sign/dilithium/mode5/internal/dilithium_test.go
+++ b/sign/dilithium/mode5/internal/dilithium_test.go
@@ -6,7 +6,7 @@ import (
 	"encoding/binary"
 	"testing"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // Checks whether p is normalized.  Only used in tests.
diff --git a/sign/dilithium/mode5/internal/mat.go b/sign/dilithium/mode5/internal/mat.go
index cb473c149..ceaf634fa 100644
--- a/sign/dilithium/mode5/internal/mat.go
+++ b/sign/dilithium/mode5/internal/mat.go
@@ -3,7 +3,7 @@
 package internal
 
 import (
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // A k by l matrix of polynomials.
diff --git a/sign/dilithium/mode5/internal/pack.go b/sign/dilithium/mode5/internal/pack.go
index 0285dfd8e..1854b4197 100644
--- a/sign/dilithium/mode5/internal/pack.go
+++ b/sign/dilithium/mode5/internal/pack.go
@@ -3,7 +3,7 @@
 package internal
 
 import (
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // Writes p with norm less than or equal η into buf, which must be of
diff --git a/sign/dilithium/mode5/internal/pack_test.go b/sign/dilithium/mode5/internal/pack_test.go
index 24f568e4d..f952c6a09 100644
--- a/sign/dilithium/mode5/internal/pack_test.go
+++ b/sign/dilithium/mode5/internal/pack_test.go
@@ -5,7 +5,7 @@ package internal
 import (
 	"testing"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 func TestPolyPackLeqEta(t *testing.T) {
diff --git a/sign/dilithium/mode5/internal/params.go b/sign/dilithium/mode5/internal/params.go
index bad43e320..e8a2b143e 100644
--- a/sign/dilithium/mode5/internal/params.go
+++ b/sign/dilithium/mode5/internal/params.go
@@ -13,4 +13,7 @@ const (
 	Tau           = 60
 	Gamma1Bits    = 19
 	Gamma2        = 261888
+	NIST          = false
+	TRSize        = 32
+	CTildeSize    = 32
 )
diff --git a/sign/dilithium/mode5/internal/params_test.go b/sign/dilithium/mode5/internal/params_test.go
index daabe6969..ac891117e 100644
--- a/sign/dilithium/mode5/internal/params_test.go
+++ b/sign/dilithium/mode5/internal/params_test.go
@@ -3,7 +3,7 @@ package internal
 import (
 	"testing"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // Tests specific to the current mode
diff --git a/sign/dilithium/mode5/internal/rounding.go b/sign/dilithium/mode5/internal/rounding.go
index 71360cb29..58123c090 100644
--- a/sign/dilithium/mode5/internal/rounding.go
+++ b/sign/dilithium/mode5/internal/rounding.go
@@ -3,7 +3,7 @@
 package internal
 
 import (
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // Splits 0 ≤ a < q into a₀ and a₁ with a = a₁*α + a₀ with -α/2 < a₀ ≤ α/2,
diff --git a/sign/dilithium/mode5/internal/rounding_test.go b/sign/dilithium/mode5/internal/rounding_test.go
index 5824f2656..ad653ca3f 100644
--- a/sign/dilithium/mode5/internal/rounding_test.go
+++ b/sign/dilithium/mode5/internal/rounding_test.go
@@ -6,7 +6,7 @@ import (
 	"flag"
 	"testing"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 var runVeryLongTest = flag.Bool("very-long", false, "runs very long tests")
diff --git a/sign/dilithium/mode5/internal/sample.go b/sign/dilithium/mode5/internal/sample.go
index c47185ada..62c261332 100644
--- a/sign/dilithium/mode5/internal/sample.go
+++ b/sign/dilithium/mode5/internal/sample.go
@@ -6,7 +6,7 @@ import (
 	"encoding/binary"
 
 	"github.com/cloudflare/circl/internal/sha3"
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 	"github.com/cloudflare/circl/simd/keccakf1600"
 )
 
@@ -246,12 +246,12 @@ func PolyDeriveUniformLeGamma1(p *common.Poly, seed *[64]byte, nonce uint16) {
 // Can only be called when DeriveX4Available is true.
 //
 // This function is currently not used (yet).
-func PolyDeriveUniformBallX4(ps [4]*common.Poly, seed *[32]byte) {
+func PolyDeriveUniformBallX4(ps [4]*common.Poly, seed []byte) {
 	var perm keccakf1600.StateX4
 	state := perm.Initialize(false)
 
 	// Absorb the seed in the four states
-	for i := 0; i < 4; i++ {
+	for i := 0; i < 32/8; i++ {
 		v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)])
 		for j := 0; j < 4; j++ {
 			state[i*4+j] = v
@@ -260,7 +260,7 @@ func PolyDeriveUniformBallX4(ps [4]*common.Poly, seed *[32]byte) {
 
 	// SHAKE256 domain separator and padding
 	for j := 0; j < 4; j++ {
-		state[4*4+j] ^= 0x1f
+		state[(32/8)*4+j] ^= 0x1f
 		state[16*4+j] ^= 0x80 << 56
 	}
 	perm.Permute()
@@ -327,7 +327,7 @@ func PolyDeriveUniformBallX4(ps [4]*common.Poly, seed *[32]byte) {
 // Samples p uniformly with τ non-zero coefficients in {q-1,1}.
 //
 // The polynomial p will be normalized.
-func PolyDeriveUniformBall(p *common.Poly, seed *[32]byte) {
+func PolyDeriveUniformBall(p *common.Poly, seed []byte) {
 	var buf [136]byte // SHAKE-256 rate is 136
 
 	h := sha3.NewShake256()
diff --git a/sign/dilithium/mode5/internal/sample_test.go b/sign/dilithium/mode5/internal/sample_test.go
index 1a0a4f72c..2059599eb 100644
--- a/sign/dilithium/mode5/internal/sample_test.go
+++ b/sign/dilithium/mode5/internal/sample_test.go
@@ -6,7 +6,7 @@ import (
 	"encoding/binary"
 	"testing"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 func TestVectorDeriveUniform(t *testing.T) {
@@ -155,7 +155,7 @@ func TestDeriveUniformBall(t *testing.T) {
 	var seed [32]byte
 	for i := 0; i < 100; i++ {
 		binary.LittleEndian.PutUint64(seed[:], uint64(i))
-		PolyDeriveUniformBall(&p, &seed)
+		PolyDeriveUniformBall(&p, seed[:])
 		nonzero := 0
 		for j := 0; j < common.N; j++ {
 			if p[j] != 0 {
@@ -203,10 +203,10 @@ func TestDeriveUniformBallX4(t *testing.T) {
 	var seed [32]byte
 	PolyDeriveUniformBallX4(
 		[4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]},
-		&seed,
+		seed[:],
 	)
 	for j := 0; j < 4; j++ {
-		PolyDeriveUniformBall(&p, &seed)
+		PolyDeriveUniformBall(&p, seed[:])
 		if ps[j] != p {
 			t.Fatalf("%d\n%v\n%v", j, ps[j], p)
 		}
@@ -219,7 +219,7 @@ func BenchmarkPolyDeriveUniformBall(b *testing.B) {
 	var w1 VecK
 	for i := 0; i < b.N; i++ {
 		w1[0][0] = uint32(i)
-		PolyDeriveUniformBall(&p, &seed)
+		PolyDeriveUniformBall(&p, seed[:])
 	}
 }
 
@@ -231,7 +231,7 @@ func BenchmarkPolyDeriveUniformBallX4(b *testing.B) {
 		w1[0][0] = uint32(i)
 		PolyDeriveUniformBallX4(
 			[4]*common.Poly{&p, &p, &p, &p},
-			&seed,
+			seed[:],
 		)
 	}
 }
diff --git a/sign/dilithium/mode5/internal/vec.go b/sign/dilithium/mode5/internal/vec.go
index f52973e45..d07d3b245 100644
--- a/sign/dilithium/mode5/internal/vec.go
+++ b/sign/dilithium/mode5/internal/vec.go
@@ -3,7 +3,7 @@
 package internal
 
 import (
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // A vector of L polynomials.
diff --git a/sign/dilithium/mode5aes.go b/sign/dilithium/mode5aes.go
index 258b8a825..0dfd3854f 100644
--- a/sign/dilithium/mode5aes.go
+++ b/sign/dilithium/mode5aes.go
@@ -6,8 +6,8 @@ import (
 	"fmt"
 	"io"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
 	"github.com/cloudflare/circl/sign/dilithium/mode5aes"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // implMode5AES implements the mode.Mode interface for Dilithium5-AES.
diff --git a/sign/dilithium/mode5aes/dilithium.go b/sign/dilithium/mode5aes/dilithium.go
index 2a0f05e7a..c0300f2e6 100644
--- a/sign/dilithium/mode5aes/dilithium.go
+++ b/sign/dilithium/mode5aes/dilithium.go
@@ -1,9 +1,11 @@
 // Code generated from modePkg.templ.go. DO NOT EDIT.
 
+
 // mode5aes implements the CRYSTALS-Dilithium signature scheme Dilithium5-AES
 // as submitted to round3 of the NIST PQC competition and described in
 //
 // https://pq-crystals.org/dilithium/data/dilithium-specification-round3-20210208.pdf
+
 package mode5aes
 
 import (
@@ -11,8 +13,10 @@ import (
 	"errors"
 	"io"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+
 	"github.com/cloudflare/circl/sign/dilithium/mode5aes/internal"
+
 )
 
 const (
diff --git a/sign/dilithium/mode5aes/internal/dilithium.go b/sign/dilithium/mode5aes/internal/dilithium.go
index 79a17d504..7869d0475 100644
--- a/sign/dilithium/mode5aes/internal/dilithium.go
+++ b/sign/dilithium/mode5aes/internal/dilithium.go
@@ -8,7 +8,7 @@ import (
 	"io"
 
 	"github.com/cloudflare/circl/internal/sha3"
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 const (
@@ -29,13 +29,13 @@ const (
 	Alpha = 2 * Gamma2
 
 	// Size of a packed private key
-	PrivateKeySize = 32 + 32 + 32 + PolyLeqEtaSize*(L+K) + common.PolyT0Size*K
+	PrivateKeySize = 32 + 32 + TRSize + PolyLeqEtaSize*(L+K) + common.PolyT0Size*K
 
 	// Size of a packed public key
 	PublicKeySize = 32 + common.PolyT1Size*K
 
 	// Size of a packed signature
-	SignatureSize = L*PolyLeGamma1Size + Omega + K + 32
+	SignatureSize = L*PolyLeGamma1Size + Omega + K + CTildeSize
 
 	// Size of packed w₁
 	PolyW1Size = (common.N * (common.QBits - Gamma1Bits)) / 8
@@ -49,7 +49,7 @@ type PublicKey struct {
 	// Cached values
 	t1p [common.PolyT1Size * K]byte
 	A   *Mat
-	tr  *[32]byte
+	tr  *[TRSize]byte
 }
 
 // PrivateKey is the type of Dilithium private keys.
@@ -59,7 +59,7 @@ type PrivateKey struct {
 	s1  VecL
 	s2  VecK
 	t0  VecK
-	tr  [32]byte
+	tr  [TRSize]byte
 
 	// Cached values
 	A   Mat  // ExpandA(ρ)
@@ -71,14 +71,14 @@ type PrivateKey struct {
 type unpackedSignature struct {
 	z    VecL
 	hint VecK
-	c    [32]byte
+	c    [CTildeSize]byte
 }
 
 // Packs the signature into buf.
 func (sig *unpackedSignature) Pack(buf []byte) {
 	copy(buf[:], sig.c[:])
-	sig.z.PackLeGamma1(buf[32:])
-	sig.hint.PackHint(buf[32+L*PolyLeGamma1Size:])
+	sig.z.PackLeGamma1(buf[CTildeSize:])
+	sig.hint.PackHint(buf[CTildeSize+L*PolyLeGamma1Size:])
 }
 
 // Sets sig to the signature encoded in the buffer.
@@ -89,11 +89,11 @@ func (sig *unpackedSignature) Unpack(buf []byte) bool {
 		return false
 	}
 	copy(sig.c[:], buf[:])
-	sig.z.UnpackLeGamma1(buf[32:])
+	sig.z.UnpackLeGamma1(buf[CTildeSize:])
 	if sig.z.Exceeds(Gamma1 - Beta) {
 		return false
 	}
-	if !sig.hint.UnpackHint(buf[32+L*PolyLeGamma1Size:]) {
+	if !sig.hint.UnpackHint(buf[CTildeSize+L*PolyLeGamma1Size:]) {
 		return false
 	}
 	return true
@@ -115,7 +115,7 @@ func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) {
 	pk.A.Derive(&pk.rho)
 
 	// tr = CRH(ρ ‖ t1) = CRH(pk)
-	pk.tr = new([32]byte)
+	pk.tr = new([TRSize]byte)
 	h := sha3.NewShake256()
 	_, _ = h.Write(buf[:])
 	_, _ = h.Read(pk.tr[:])
@@ -125,8 +125,8 @@ func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) {
 func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) {
 	copy(buf[:32], sk.rho[:])
 	copy(buf[32:64], sk.key[:])
-	copy(buf[64:96], sk.tr[:])
-	offset := 96
+	copy(buf[64:64+TRSize], sk.tr[:])
+	offset := 64 + TRSize
 	sk.s1.PackLeqEta(buf[offset:])
 	offset += PolyLeqEtaSize * L
 	sk.s2.PackLeqEta(buf[offset:])
@@ -138,8 +138,8 @@ func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) {
 func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) {
 	copy(sk.rho[:], buf[:32])
 	copy(sk.key[:], buf[32:64])
-	copy(sk.tr[:], buf[64:96])
-	offset := 96
+	copy(sk.tr[:], buf[64:64+TRSize])
+	offset := 64 + TRSize
 	sk.s1.UnpackLeqEta(buf[offset:])
 	offset += PolyLeqEtaSize * L
 	sk.s2.UnpackLeqEta(buf[offset:])
@@ -250,7 +250,7 @@ func Verify(pk *PublicKey, msg []byte, signature []byte) bool {
 	var zh VecL
 	var Az, Az2dct1, w1 VecK
 	var ch common.Poly
-	var cp [32]byte
+	var cp [CTildeSize]byte
 	var w1Packed [PolyW1Size * K]byte
 
 	// Note that Unpack() checked whether ‖z‖_∞ < γ₁ - β
@@ -279,7 +279,7 @@ func Verify(pk *PublicKey, msg []byte, signature []byte) bool {
 	// which is small enough for NTT().
 	Az2dct1.MulBy2toD(&pk.t1)
 	Az2dct1.NTT()
-	PolyDeriveUniformBall(&ch, &sig.c)
+	PolyDeriveUniformBall(&ch, sig.c[:32])
 	ch.NTT()
 	for i := 0; i < K; i++ {
 		Az2dct1[i].MulHat(&Az2dct1[i], &ch)
@@ -330,6 +330,11 @@ func SignTo(sk *PrivateKey, msg []byte, signature []byte) {
 	// ρ' = CRH(key ‖ μ)
 	h.Reset()
 	_, _ = h.Write(sk.key[:])
+	if NIST {
+		// We implement the deterministic variant  where rnd is all zeroes.
+		// TODO expose randomized variant?
+		_, _ = h.Write(make([]byte, 32))
+	}
 	_, _ = h.Write(mu[:])
 	_, _ = h.Read(rhop[:])
 
@@ -368,7 +373,7 @@ func SignTo(sk *PrivateKey, msg []byte, signature []byte) {
 		_, _ = h.Write(w1Packed[:])
 		_, _ = h.Read(sig.c[:])
 
-		PolyDeriveUniformBall(&ch, &sig.c)
+		PolyDeriveUniformBall(&ch, sig.c[:32])
 		ch.NTT()
 
 		// Ensure ‖ w₀ - c·s2 ‖_∞ < γ₂ - β.
diff --git a/sign/dilithium/mode5aes/internal/dilithium_test.go b/sign/dilithium/mode5aes/internal/dilithium_test.go
index ca347a831..825e7da08 100644
--- a/sign/dilithium/mode5aes/internal/dilithium_test.go
+++ b/sign/dilithium/mode5aes/internal/dilithium_test.go
@@ -6,7 +6,7 @@ import (
 	"encoding/binary"
 	"testing"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // Checks whether p is normalized.  Only used in tests.
diff --git a/sign/dilithium/mode5aes/internal/mat.go b/sign/dilithium/mode5aes/internal/mat.go
index cb473c149..ceaf634fa 100644
--- a/sign/dilithium/mode5aes/internal/mat.go
+++ b/sign/dilithium/mode5aes/internal/mat.go
@@ -3,7 +3,7 @@
 package internal
 
 import (
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // A k by l matrix of polynomials.
diff --git a/sign/dilithium/mode5aes/internal/pack.go b/sign/dilithium/mode5aes/internal/pack.go
index 0285dfd8e..1854b4197 100644
--- a/sign/dilithium/mode5aes/internal/pack.go
+++ b/sign/dilithium/mode5aes/internal/pack.go
@@ -3,7 +3,7 @@
 package internal
 
 import (
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // Writes p with norm less than or equal η into buf, which must be of
diff --git a/sign/dilithium/mode5aes/internal/pack_test.go b/sign/dilithium/mode5aes/internal/pack_test.go
index 24f568e4d..f952c6a09 100644
--- a/sign/dilithium/mode5aes/internal/pack_test.go
+++ b/sign/dilithium/mode5aes/internal/pack_test.go
@@ -5,7 +5,7 @@ package internal
 import (
 	"testing"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 func TestPolyPackLeqEta(t *testing.T) {
diff --git a/sign/dilithium/mode5aes/internal/params.go b/sign/dilithium/mode5aes/internal/params.go
index 419cb2a2b..340b6d73a 100644
--- a/sign/dilithium/mode5aes/internal/params.go
+++ b/sign/dilithium/mode5aes/internal/params.go
@@ -13,4 +13,7 @@ const (
 	Tau           = 60
 	Gamma1Bits    = 19
 	Gamma2        = 261888
+	NIST          = false
+	TRSize        = 32
+	CTildeSize    = 32
 )
diff --git a/sign/dilithium/mode5aes/internal/params_test.go b/sign/dilithium/mode5aes/internal/params_test.go
index a5e746f68..57e14f820 100644
--- a/sign/dilithium/mode5aes/internal/params_test.go
+++ b/sign/dilithium/mode5aes/internal/params_test.go
@@ -3,7 +3,7 @@ package internal
 import (
 	"testing"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // Tests specific to the current mode
diff --git a/sign/dilithium/mode5aes/internal/rounding.go b/sign/dilithium/mode5aes/internal/rounding.go
index 71360cb29..58123c090 100644
--- a/sign/dilithium/mode5aes/internal/rounding.go
+++ b/sign/dilithium/mode5aes/internal/rounding.go
@@ -3,7 +3,7 @@
 package internal
 
 import (
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // Splits 0 ≤ a < q into a₀ and a₁ with a = a₁*α + a₀ with -α/2 < a₀ ≤ α/2,
diff --git a/sign/dilithium/mode5aes/internal/rounding_test.go b/sign/dilithium/mode5aes/internal/rounding_test.go
index 5824f2656..ad653ca3f 100644
--- a/sign/dilithium/mode5aes/internal/rounding_test.go
+++ b/sign/dilithium/mode5aes/internal/rounding_test.go
@@ -6,7 +6,7 @@ import (
 	"flag"
 	"testing"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 var runVeryLongTest = flag.Bool("very-long", false, "runs very long tests")
diff --git a/sign/dilithium/mode5aes/internal/sample.go b/sign/dilithium/mode5aes/internal/sample.go
index c47185ada..62c261332 100644
--- a/sign/dilithium/mode5aes/internal/sample.go
+++ b/sign/dilithium/mode5aes/internal/sample.go
@@ -6,7 +6,7 @@ import (
 	"encoding/binary"
 
 	"github.com/cloudflare/circl/internal/sha3"
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 	"github.com/cloudflare/circl/simd/keccakf1600"
 )
 
@@ -246,12 +246,12 @@ func PolyDeriveUniformLeGamma1(p *common.Poly, seed *[64]byte, nonce uint16) {
 // Can only be called when DeriveX4Available is true.
 //
 // This function is currently not used (yet).
-func PolyDeriveUniformBallX4(ps [4]*common.Poly, seed *[32]byte) {
+func PolyDeriveUniformBallX4(ps [4]*common.Poly, seed []byte) {
 	var perm keccakf1600.StateX4
 	state := perm.Initialize(false)
 
 	// Absorb the seed in the four states
-	for i := 0; i < 4; i++ {
+	for i := 0; i < 32/8; i++ {
 		v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)])
 		for j := 0; j < 4; j++ {
 			state[i*4+j] = v
@@ -260,7 +260,7 @@ func PolyDeriveUniformBallX4(ps [4]*common.Poly, seed *[32]byte) {
 
 	// SHAKE256 domain separator and padding
 	for j := 0; j < 4; j++ {
-		state[4*4+j] ^= 0x1f
+		state[(32/8)*4+j] ^= 0x1f
 		state[16*4+j] ^= 0x80 << 56
 	}
 	perm.Permute()
@@ -327,7 +327,7 @@ func PolyDeriveUniformBallX4(ps [4]*common.Poly, seed *[32]byte) {
 // Samples p uniformly with τ non-zero coefficients in {q-1,1}.
 //
 // The polynomial p will be normalized.
-func PolyDeriveUniformBall(p *common.Poly, seed *[32]byte) {
+func PolyDeriveUniformBall(p *common.Poly, seed []byte) {
 	var buf [136]byte // SHAKE-256 rate is 136
 
 	h := sha3.NewShake256()
diff --git a/sign/dilithium/mode5aes/internal/sample_test.go b/sign/dilithium/mode5aes/internal/sample_test.go
index 1a0a4f72c..2059599eb 100644
--- a/sign/dilithium/mode5aes/internal/sample_test.go
+++ b/sign/dilithium/mode5aes/internal/sample_test.go
@@ -6,7 +6,7 @@ import (
 	"encoding/binary"
 	"testing"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 func TestVectorDeriveUniform(t *testing.T) {
@@ -155,7 +155,7 @@ func TestDeriveUniformBall(t *testing.T) {
 	var seed [32]byte
 	for i := 0; i < 100; i++ {
 		binary.LittleEndian.PutUint64(seed[:], uint64(i))
-		PolyDeriveUniformBall(&p, &seed)
+		PolyDeriveUniformBall(&p, seed[:])
 		nonzero := 0
 		for j := 0; j < common.N; j++ {
 			if p[j] != 0 {
@@ -203,10 +203,10 @@ func TestDeriveUniformBallX4(t *testing.T) {
 	var seed [32]byte
 	PolyDeriveUniformBallX4(
 		[4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]},
-		&seed,
+		seed[:],
 	)
 	for j := 0; j < 4; j++ {
-		PolyDeriveUniformBall(&p, &seed)
+		PolyDeriveUniformBall(&p, seed[:])
 		if ps[j] != p {
 			t.Fatalf("%d\n%v\n%v", j, ps[j], p)
 		}
@@ -219,7 +219,7 @@ func BenchmarkPolyDeriveUniformBall(b *testing.B) {
 	var w1 VecK
 	for i := 0; i < b.N; i++ {
 		w1[0][0] = uint32(i)
-		PolyDeriveUniformBall(&p, &seed)
+		PolyDeriveUniformBall(&p, seed[:])
 	}
 }
 
@@ -231,7 +231,7 @@ func BenchmarkPolyDeriveUniformBallX4(b *testing.B) {
 		w1[0][0] = uint32(i)
 		PolyDeriveUniformBallX4(
 			[4]*common.Poly{&p, &p, &p, &p},
-			&seed,
+			seed[:],
 		)
 	}
 }
diff --git a/sign/dilithium/mode5aes/internal/vec.go b/sign/dilithium/mode5aes/internal/vec.go
index f52973e45..d07d3b245 100644
--- a/sign/dilithium/mode5aes/internal/vec.go
+++ b/sign/dilithium/mode5aes/internal/vec.go
@@ -3,7 +3,7 @@
 package internal
 
 import (
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // A vector of L polynomials.
diff --git a/sign/dilithium/templates/mode.templ.go b/sign/dilithium/templates/mode.templ.go
index 8c76b2512..fb7930de9 100644
--- a/sign/dilithium/templates/mode.templ.go
+++ b/sign/dilithium/templates/mode.templ.go
@@ -9,15 +9,21 @@ package dilithium
 import (
 	"fmt"
 	"io"
-
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+{{ if .NIST }}
+	"github.com/cloudflare/circl/sign/mldsa/{{.Pkg}}"
+{{ else }}
 	"github.com/cloudflare/circl/sign/dilithium/{{.Pkg}}"
+{{- end }}
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
 )
 
 // {{.Impl}} implements the mode.Mode interface for {{.Name}}.
 type {{.Impl}} struct{}
-
+{{ if .NIST }}
+// {{.Mode}} is {{.Name}}.
+{{- else }}
 // {{.Mode}} is Dilithium in mode "{{.Name}}".
+{{- end }}
 var {{.Mode}} Mode = &{{.Impl}}{}
 
 func (m *{{.Impl}}) GenerateKey(rand io.Reader) (
diff --git a/sign/dilithium/templates/modePkg.templ.go b/sign/dilithium/templates/modePkg.templ.go
index 29dc73556..fbaa89746 100644
--- a/sign/dilithium/templates/modePkg.templ.go
+++ b/sign/dilithium/templates/modePkg.templ.go
@@ -4,10 +4,14 @@
 
 // Code generated from modePkg.templ.go. DO NOT EDIT.
 
+{{ if .NIST }}
+// {{.Pkg}} implements NIST signature scheme {{.Name}} as defined in FIPS204.
+{{ else }}
 // {{.Pkg}} implements the CRYSTALS-Dilithium signature scheme {{.Name}}
 // as submitted to round3 of the NIST PQC competition and described in
 //
 // https://pq-crystals.org/dilithium/data/dilithium-specification-round3-20210208.pdf
+{{ end }}
 package {{.Pkg}}
 
 import (
@@ -15,8 +19,12 @@ import (
 	"errors"
 	"io"
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+{{ if .NIST }}
+	"github.com/cloudflare/circl/sign/mldsa/{{.Pkg}}/internal"
+{{ else }}
 	"github.com/cloudflare/circl/sign/dilithium/{{.Pkg}}/internal"
+{{ end }}
 )
 
 const (
diff --git a/sign/dilithium/templates/params.templ.go b/sign/dilithium/templates/params.templ.go
index 1e0331c25..faeae3aac 100644
--- a/sign/dilithium/templates/params.templ.go
+++ b/sign/dilithium/templates/params.templ.go
@@ -17,4 +17,7 @@ const (
 	Tau           = {{.Tau}}
 	Gamma1Bits    = {{.Gamma1Bits}}
 	Gamma2        = {{.Gamma2}}
+	NIST          = {{.NIST}}
+	TRSize        = {{.TRSize}}
+	CTildeSize    = {{.CTildeSize}}
 )
diff --git a/sign/dilithium/internal/common/aes.go b/sign/internal/dilithium/aes.go
similarity index 98%
rename from sign/dilithium/internal/common/aes.go
rename to sign/internal/dilithium/aes.go
index f5de25425..895a20597 100644
--- a/sign/dilithium/internal/common/aes.go
+++ b/sign/internal/dilithium/aes.go
@@ -1,4 +1,4 @@
-package common
+package dilithium
 
 import (
 	"crypto/aes"
diff --git a/sign/dilithium/internal/common/amd64.go b/sign/internal/dilithium/amd64.go
similarity index 99%
rename from sign/dilithium/internal/common/amd64.go
rename to sign/internal/dilithium/amd64.go
index a58e4bf46..7941b26ab 100644
--- a/sign/dilithium/internal/common/amd64.go
+++ b/sign/internal/dilithium/amd64.go
@@ -1,7 +1,7 @@
 //go:build amd64
 // +build amd64
 
-package common
+package dilithium
 
 import (
 	"golang.org/x/sys/cpu"
diff --git a/sign/dilithium/internal/common/amd64.s b/sign/internal/dilithium/amd64.s
similarity index 100%
rename from sign/dilithium/internal/common/amd64.s
rename to sign/internal/dilithium/amd64.s
diff --git a/sign/dilithium/internal/common/asm/go.mod b/sign/internal/dilithium/asm/go.mod
similarity index 59%
rename from sign/dilithium/internal/common/asm/go.mod
rename to sign/internal/dilithium/asm/go.mod
index 5638957e6..41948fce3 100644
--- a/sign/dilithium/internal/common/asm/go.mod
+++ b/sign/internal/dilithium/asm/go.mod
@@ -1,4 +1,4 @@
-module github.com/cloudflare/circl/sign/dilithium/internal/common/asm
+module github.com/cloudflare/circl/sign/internal/dilithium/asm
 
 go 1.21
 
@@ -12,4 +12,4 @@ require (
 	golang.org/x/tools v0.17.0 // indirect
 )
 
-replace github.com/cloudflare/circl => ../../../../../
+replace github.com/cloudflare/circl => ../../../../
diff --git a/sign/dilithium/internal/common/asm/go.sum b/sign/internal/dilithium/asm/go.sum
similarity index 100%
rename from sign/dilithium/internal/common/asm/go.sum
rename to sign/internal/dilithium/asm/go.sum
diff --git a/sign/dilithium/internal/common/asm/src.go b/sign/internal/dilithium/asm/src.go
similarity index 99%
rename from sign/dilithium/internal/common/asm/src.go
rename to sign/internal/dilithium/asm/src.go
index 834efff93..8ff84c91a 100644
--- a/sign/dilithium/internal/common/asm/src.go
+++ b/sign/internal/dilithium/asm/src.go
@@ -1,4 +1,4 @@
-//go:generate go run src.go -out ../amd64.s -stubs ../stubs_amd64.go -pkg common
+//go:generate go run src.go -out ../amd64.s -stubs ../stubs_amd64.go -pkg dilithium
 
 // AVX2 optimized version of Poly.[Inv]NTT().  See the comments on the generic
 // implementation for details on the maths involved.
@@ -9,7 +9,7 @@ import (
 	. "github.com/mmcloughlin/avo/operand" // nolint:golint,stylecheck
 	. "github.com/mmcloughlin/avo/reg"     // nolint:golint,stylecheck
 
-	"github.com/cloudflare/circl/sign/dilithium/internal/common/params"
+	"github.com/cloudflare/circl/sign/internal/dilithium/params"
 )
 
 // XXX align Poly on 16 bytes such that we can use aligned moves
diff --git a/sign/dilithium/internal/common/field.go b/sign/internal/dilithium/field.go
similarity index 98%
rename from sign/dilithium/internal/common/field.go
rename to sign/internal/dilithium/field.go
index 2aab16ecb..c2fc6ca72 100644
--- a/sign/dilithium/internal/common/field.go
+++ b/sign/internal/dilithium/field.go
@@ -1,4 +1,4 @@
-package common
+package dilithium
 
 // Returns a y with y < 2q and y = x mod q.
 // Note that in general *not*: ReduceLe2Q(ReduceLe2Q(x)) == x.
diff --git a/sign/dilithium/internal/common/field_test.go b/sign/internal/dilithium/field_test.go
similarity index 98%
rename from sign/dilithium/internal/common/field_test.go
rename to sign/internal/dilithium/field_test.go
index f9864eabe..85db87960 100644
--- a/sign/dilithium/internal/common/field_test.go
+++ b/sign/internal/dilithium/field_test.go
@@ -1,4 +1,4 @@
-package common
+package dilithium
 
 import (
 	"crypto/rand"
diff --git a/sign/dilithium/internal/common/generic.go b/sign/internal/dilithium/generic.go
similarity index 99%
rename from sign/dilithium/internal/common/generic.go
rename to sign/internal/dilithium/generic.go
index f10545246..4f02272b6 100644
--- a/sign/dilithium/internal/common/generic.go
+++ b/sign/internal/dilithium/generic.go
@@ -1,7 +1,7 @@
 //go:build !amd64
 // +build !amd64
 
-package common
+package dilithium
 
 // Execute an in-place forward NTT on as.
 //
diff --git a/sign/dilithium/internal/common/ntt.go b/sign/internal/dilithium/ntt.go
similarity index 99%
rename from sign/dilithium/internal/common/ntt.go
rename to sign/internal/dilithium/ntt.go
index 6f5370ae0..1568ccb4b 100644
--- a/sign/dilithium/internal/common/ntt.go
+++ b/sign/internal/dilithium/ntt.go
@@ -1,4 +1,4 @@
-package common
+package dilithium
 
 // Zetas lists precomputed powers of the root of unity in Montgomery
 // representation used for the NTT:
diff --git a/sign/dilithium/internal/common/ntt_test.go b/sign/internal/dilithium/ntt_test.go
similarity index 98%
rename from sign/dilithium/internal/common/ntt_test.go
rename to sign/internal/dilithium/ntt_test.go
index 4524f245d..71d736a92 100644
--- a/sign/dilithium/internal/common/ntt_test.go
+++ b/sign/internal/dilithium/ntt_test.go
@@ -1,4 +1,4 @@
-package common
+package dilithium
 
 import "testing"
 
diff --git a/sign/dilithium/internal/common/pack.go b/sign/internal/dilithium/pack.go
similarity index 99%
rename from sign/dilithium/internal/common/pack.go
rename to sign/internal/dilithium/pack.go
index 6c366089c..4b952a004 100644
--- a/sign/dilithium/internal/common/pack.go
+++ b/sign/internal/dilithium/pack.go
@@ -1,4 +1,4 @@
-package common
+package dilithium
 
 // Sets p to the polynomial whose coefficients are less than 1024 encoded
 // into buf (which must be of size PolyT1Size).
diff --git a/sign/dilithium/internal/common/pack_test.go b/sign/internal/dilithium/pack_test.go
similarity index 96%
rename from sign/dilithium/internal/common/pack_test.go
rename to sign/internal/dilithium/pack_test.go
index 140d3f134..37d37ce46 100644
--- a/sign/dilithium/internal/common/pack_test.go
+++ b/sign/internal/dilithium/pack_test.go
@@ -1,4 +1,4 @@
-package common
+package dilithium
 
 import "testing"
 
diff --git a/sign/dilithium/internal/common/params.go b/sign/internal/dilithium/params.go
similarity index 79%
rename from sign/dilithium/internal/common/params.go
rename to sign/internal/dilithium/params.go
index 7713c6da9..f423217f0 100644
--- a/sign/dilithium/internal/common/params.go
+++ b/sign/internal/dilithium/params.go
@@ -1,7 +1,7 @@
-package common
+package dilithium
 
 import (
-	"github.com/cloudflare/circl/sign/dilithium/internal/common/params"
+	"github.com/cloudflare/circl/sign/internal/dilithium/params"
 )
 
 const (
diff --git a/sign/dilithium/internal/common/params/params.go b/sign/internal/dilithium/params/params.go
similarity index 100%
rename from sign/dilithium/internal/common/params/params.go
rename to sign/internal/dilithium/params/params.go
diff --git a/sign/dilithium/internal/common/poly.go b/sign/internal/dilithium/poly.go
similarity index 99%
rename from sign/dilithium/internal/common/poly.go
rename to sign/internal/dilithium/poly.go
index 7ac8e57da..96c0551b3 100644
--- a/sign/dilithium/internal/common/poly.go
+++ b/sign/internal/dilithium/poly.go
@@ -1,4 +1,4 @@
-package common
+package dilithium
 
 // An element of our base ring R which are polynomials over Z_q modulo
 // the equation Xᴺ = -1, where q=2²³ - 2¹³ + 1 and N=256.
diff --git a/sign/dilithium/internal/common/poly_test.go b/sign/internal/dilithium/poly_test.go
similarity index 99%
rename from sign/dilithium/internal/common/poly_test.go
rename to sign/internal/dilithium/poly_test.go
index 5601aa276..42e5fc46d 100644
--- a/sign/dilithium/internal/common/poly_test.go
+++ b/sign/internal/dilithium/poly_test.go
@@ -1,4 +1,4 @@
-package common
+package dilithium
 
 import "testing"
 
diff --git a/sign/dilithium/internal/common/stubs_amd64.go b/sign/internal/dilithium/stubs_amd64.go
similarity index 91%
rename from sign/dilithium/internal/common/stubs_amd64.go
rename to sign/internal/dilithium/stubs_amd64.go
index 97451507f..6ae5401ab 100644
--- a/sign/dilithium/internal/common/stubs_amd64.go
+++ b/sign/internal/dilithium/stubs_amd64.go
@@ -1,8 +1,8 @@
-// Code generated by command: go run src.go -out ../amd64.s -stubs ../stubs_amd64.go -pkg common. DO NOT EDIT.
+// Code generated by command: go run src.go -out ../amd64.s -stubs ../stubs_amd64.go -pkg dilithium. DO NOT EDIT.
 
 //go:build amd64
 
-package common
+package dilithium
 
 //go:noescape
 func nttAVX2(p *[256]uint32)
diff --git a/sign/mldsa/doc.go b/sign/mldsa/doc.go
new file mode 100644
index 000000000..d5dce5749
--- /dev/null
+++ b/sign/mldsa/doc.go
@@ -0,0 +1,2 @@
+// mldsa implements NIST post-quantum signature scheme ML-DSA.
+package mldsa
diff --git a/sign/mldsa/mldsa44/dilithium.go b/sign/mldsa/mldsa44/dilithium.go
new file mode 100644
index 000000000..71e2b7906
--- /dev/null
+++ b/sign/mldsa/mldsa44/dilithium.go
@@ -0,0 +1,182 @@
+// Code generated from modePkg.templ.go. DO NOT EDIT.
+
+
+// mldsa44 implements NIST signature scheme ML-DSA-44 as defined in FIPS204.
+
+package mldsa44
+
+import (
+	"crypto"
+	"errors"
+	"io"
+
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+
+	"github.com/cloudflare/circl/sign/mldsa/mldsa44/internal"
+
+)
+
+const (
+	// Size of seed for NewKeyFromSeed
+	SeedSize = common.SeedSize
+
+	// Size of a packed PublicKey
+	PublicKeySize = internal.PublicKeySize
+
+	// Size of a packed PrivateKey
+	PrivateKeySize = internal.PrivateKeySize
+
+	// Size of a signature
+	SignatureSize = internal.SignatureSize
+)
+
+// PublicKey is the type of ML-DSA-44 public key
+type PublicKey internal.PublicKey
+
+// PrivateKey is the type of ML-DSA-44 private key
+type PrivateKey internal.PrivateKey
+
+// GenerateKey generates a public/private key pair using entropy from rand.
+// If rand is nil, crypto/rand.Reader will be used.
+func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) {
+	pk, sk, err := internal.GenerateKey(rand)
+	return (*PublicKey)(pk), (*PrivateKey)(sk), err
+}
+
+// NewKeyFromSeed derives a public/private key pair using the given seed.
+func NewKeyFromSeed(seed *[SeedSize]byte) (*PublicKey, *PrivateKey) {
+	pk, sk := internal.NewKeyFromSeed(seed)
+	return (*PublicKey)(pk), (*PrivateKey)(sk)
+}
+
+// SignTo signs the given message and writes the signature into signature.
+// It will panic if signature is not of length at least SignatureSize.
+func SignTo(sk *PrivateKey, msg []byte, signature []byte) {
+	internal.SignTo(
+		(*internal.PrivateKey)(sk),
+		msg,
+		signature,
+	)
+}
+
+// Verify checks whether the given signature by pk on msg is valid.
+func Verify(pk *PublicKey, msg []byte, signature []byte) bool {
+	return internal.Verify(
+		(*internal.PublicKey)(pk),
+		msg,
+		signature,
+	)
+}
+
+// Sets pk to the public key encoded in buf.
+func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) {
+	(*internal.PublicKey)(pk).Unpack(buf)
+}
+
+// Sets sk to the private key encoded in buf.
+func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) {
+	(*internal.PrivateKey)(sk).Unpack(buf)
+}
+
+// Packs the public key into buf.
+func (pk *PublicKey) Pack(buf *[PublicKeySize]byte) {
+	(*internal.PublicKey)(pk).Pack(buf)
+}
+
+// Packs the private key into buf.
+func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) {
+	(*internal.PrivateKey)(sk).Pack(buf)
+}
+
+// Packs the public key.
+func (pk *PublicKey) Bytes() []byte {
+	var buf [PublicKeySize]byte
+	pk.Pack(&buf)
+	return buf[:]
+}
+
+// Packs the private key.
+func (sk *PrivateKey) Bytes() []byte {
+	var buf [PrivateKeySize]byte
+	sk.Pack(&buf)
+	return buf[:]
+}
+
+// Packs the public key.
+func (pk *PublicKey) MarshalBinary() ([]byte, error) {
+	return pk.Bytes(), nil
+}
+
+// Packs the private key.
+func (sk *PrivateKey) MarshalBinary() ([]byte, error) {
+	return sk.Bytes(), nil
+}
+
+// Unpacks the public key from data.
+func (pk *PublicKey) UnmarshalBinary(data []byte) error {
+	if len(data) != PublicKeySize {
+		return errors.New("packed public key must be of mldsa44.PublicKeySize bytes")
+	}
+	var buf [PublicKeySize]byte
+	copy(buf[:], data)
+	pk.Unpack(&buf)
+	return nil
+}
+
+// Unpacks the private key from data.
+func (sk *PrivateKey) UnmarshalBinary(data []byte) error {
+	if len(data) != PrivateKeySize {
+		return errors.New("packed private key must be of mldsa44.PrivateKeySize bytes")
+	}
+	var buf [PrivateKeySize]byte
+	copy(buf[:], data)
+	sk.Unpack(&buf)
+	return nil
+}
+
+// Sign signs the given message.
+//
+// opts.HashFunc() must return zero, which can be achieved by passing
+// crypto.Hash(0) for opts.  rand is ignored.  Will only return an error
+// if opts.HashFunc() is non-zero.
+//
+// This function is used to make PrivateKey implement the crypto.Signer
+// interface.  The package-level SignTo function might be more convenient
+// to use.
+func (sk *PrivateKey) Sign(rand io.Reader, msg []byte, opts crypto.SignerOpts) (
+	signature []byte, err error) {
+	var sig [SignatureSize]byte
+
+	if opts.HashFunc() != crypto.Hash(0) {
+		return nil, errors.New("dilithium: cannot sign hashed message")
+	}
+
+	SignTo(sk, msg, sig[:])
+	return sig[:], nil
+}
+
+// Computes the public key corresponding to this private key.
+//
+// Returns a *PublicKey.  The type crypto.PublicKey is used to make
+// PrivateKey implement the crypto.Signer interface.
+func (sk *PrivateKey) Public() crypto.PublicKey {
+	return (*PublicKey)((*internal.PrivateKey)(sk).Public())
+}
+
+// Equal returns whether the two private keys equal.
+func (sk *PrivateKey) Equal(other crypto.PrivateKey) bool {
+	castOther, ok := other.(*PrivateKey)
+	if !ok {
+		return false
+	}
+	return (*internal.PrivateKey)(sk).Equal((*internal.PrivateKey)(castOther))
+}
+
+// Equal returns whether the two public keys equal.
+func (pk *PublicKey) Equal(other crypto.PublicKey) bool {
+	castOther, ok := other.(*PublicKey)
+	if !ok {
+		return false
+	}
+	return (*internal.PublicKey)(pk).Equal((*internal.PublicKey)(castOther))
+}
diff --git a/sign/mldsa/mldsa44/internal/dilithium.go b/sign/mldsa/mldsa44/internal/dilithium.go
new file mode 100644
index 000000000..7869d0475
--- /dev/null
+++ b/sign/mldsa/mldsa44/internal/dilithium.go
@@ -0,0 +1,482 @@
+// Code generated from mode3/internal/dilithium.go by gen.go
+
+package internal
+
+import (
+	cryptoRand "crypto/rand"
+	"crypto/subtle"
+	"io"
+
+	"github.com/cloudflare/circl/internal/sha3"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+)
+
+const (
+	// Size of a packed polynomial of norm ≤η.
+	// (Note that the  formula is not valid in general.)
+	PolyLeqEtaSize = (common.N * DoubleEtaBits) / 8
+
+	// β = τη, the maximum size of c s₂.
+	Beta = Tau * Eta
+
+	// γ₁ range of y
+	Gamma1 = 1 << Gamma1Bits
+
+	// Size of packed polynomial of norm <γ₁ such as z
+	PolyLeGamma1Size = (Gamma1Bits + 1) * common.N / 8
+
+	// α = 2γ₂ parameter for decompose
+	Alpha = 2 * Gamma2
+
+	// Size of a packed private key
+	PrivateKeySize = 32 + 32 + TRSize + PolyLeqEtaSize*(L+K) + common.PolyT0Size*K
+
+	// Size of a packed public key
+	PublicKeySize = 32 + common.PolyT1Size*K
+
+	// Size of a packed signature
+	SignatureSize = L*PolyLeGamma1Size + Omega + K + CTildeSize
+
+	// Size of packed w₁
+	PolyW1Size = (common.N * (common.QBits - Gamma1Bits)) / 8
+)
+
+// PublicKey is the type of Dilithium public keys.
+type PublicKey struct {
+	rho [32]byte
+	t1  VecK
+
+	// Cached values
+	t1p [common.PolyT1Size * K]byte
+	A   *Mat
+	tr  *[TRSize]byte
+}
+
+// PrivateKey is the type of Dilithium private keys.
+type PrivateKey struct {
+	rho [32]byte
+	key [32]byte
+	s1  VecL
+	s2  VecK
+	t0  VecK
+	tr  [TRSize]byte
+
+	// Cached values
+	A   Mat  // ExpandA(ρ)
+	s1h VecL // NTT(s₁)
+	s2h VecK // NTT(s₂)
+	t0h VecK // NTT(t₀)
+}
+
+type unpackedSignature struct {
+	z    VecL
+	hint VecK
+	c    [CTildeSize]byte
+}
+
+// Packs the signature into buf.
+func (sig *unpackedSignature) Pack(buf []byte) {
+	copy(buf[:], sig.c[:])
+	sig.z.PackLeGamma1(buf[CTildeSize:])
+	sig.hint.PackHint(buf[CTildeSize+L*PolyLeGamma1Size:])
+}
+
+// Sets sig to the signature encoded in the buffer.
+//
+// Returns whether buf contains a properly packed signature.
+func (sig *unpackedSignature) Unpack(buf []byte) bool {
+	if len(buf) < SignatureSize {
+		return false
+	}
+	copy(sig.c[:], buf[:])
+	sig.z.UnpackLeGamma1(buf[CTildeSize:])
+	if sig.z.Exceeds(Gamma1 - Beta) {
+		return false
+	}
+	if !sig.hint.UnpackHint(buf[CTildeSize+L*PolyLeGamma1Size:]) {
+		return false
+	}
+	return true
+}
+
+// Packs the public key into buf.
+func (pk *PublicKey) Pack(buf *[PublicKeySize]byte) {
+	copy(buf[:32], pk.rho[:])
+	copy(buf[32:], pk.t1p[:])
+}
+
+// Sets pk to the public key encoded in buf.
+func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) {
+	copy(pk.rho[:], buf[:32])
+	copy(pk.t1p[:], buf[32:])
+
+	pk.t1.UnpackT1(pk.t1p[:])
+	pk.A = new(Mat)
+	pk.A.Derive(&pk.rho)
+
+	// tr = CRH(ρ ‖ t1) = CRH(pk)
+	pk.tr = new([TRSize]byte)
+	h := sha3.NewShake256()
+	_, _ = h.Write(buf[:])
+	_, _ = h.Read(pk.tr[:])
+}
+
+// Packs the private key into buf.
+func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) {
+	copy(buf[:32], sk.rho[:])
+	copy(buf[32:64], sk.key[:])
+	copy(buf[64:64+TRSize], sk.tr[:])
+	offset := 64 + TRSize
+	sk.s1.PackLeqEta(buf[offset:])
+	offset += PolyLeqEtaSize * L
+	sk.s2.PackLeqEta(buf[offset:])
+	offset += PolyLeqEtaSize * K
+	sk.t0.PackT0(buf[offset:])
+}
+
+// Sets sk to the private key encoded in buf.
+func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) {
+	copy(sk.rho[:], buf[:32])
+	copy(sk.key[:], buf[32:64])
+	copy(sk.tr[:], buf[64:64+TRSize])
+	offset := 64 + TRSize
+	sk.s1.UnpackLeqEta(buf[offset:])
+	offset += PolyLeqEtaSize * L
+	sk.s2.UnpackLeqEta(buf[offset:])
+	offset += PolyLeqEtaSize * K
+	sk.t0.UnpackT0(buf[offset:])
+
+	// Cached values
+	sk.A.Derive(&sk.rho)
+	sk.t0h = sk.t0
+	sk.t0h.NTT()
+	sk.s1h = sk.s1
+	sk.s1h.NTT()
+	sk.s2h = sk.s2
+	sk.s2h.NTT()
+}
+
+// GenerateKey generates a public/private key pair using entropy from rand.
+// If rand is nil, crypto/rand.Reader will be used.
+func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) {
+	var seed [32]byte
+	if rand == nil {
+		rand = cryptoRand.Reader
+	}
+	_, err := io.ReadFull(rand, seed[:])
+	if err != nil {
+		return nil, nil, err
+	}
+	pk, sk := NewKeyFromSeed(&seed)
+	return pk, sk, nil
+}
+
+// NewKeyFromSeed derives a public/private key pair using the given seed.
+func NewKeyFromSeed(seed *[common.SeedSize]byte) (*PublicKey, *PrivateKey) {
+	var eSeed [128]byte // expanded seed
+	var pk PublicKey
+	var sk PrivateKey
+	var sSeed [64]byte
+
+	h := sha3.NewShake256()
+	_, _ = h.Write(seed[:])
+	_, _ = h.Read(eSeed[:])
+
+	copy(pk.rho[:], eSeed[:32])
+	copy(sSeed[:], eSeed[32:96])
+	copy(sk.key[:], eSeed[96:])
+	copy(sk.rho[:], pk.rho[:])
+
+	sk.A.Derive(&pk.rho)
+
+	for i := uint16(0); i < L; i++ {
+		PolyDeriveUniformLeqEta(&sk.s1[i], &sSeed, i)
+	}
+
+	for i := uint16(0); i < K; i++ {
+		PolyDeriveUniformLeqEta(&sk.s2[i], &sSeed, i+L)
+	}
+
+	sk.s1h = sk.s1
+	sk.s1h.NTT()
+	sk.s2h = sk.s2
+	sk.s2h.NTT()
+
+	sk.computeT0andT1(&sk.t0, &pk.t1)
+
+	sk.t0h = sk.t0
+	sk.t0h.NTT()
+
+	// Complete public key far enough to be packed
+	pk.t1.PackT1(pk.t1p[:])
+	pk.A = &sk.A
+
+	// Finish private key
+	var packedPk [PublicKeySize]byte
+	pk.Pack(&packedPk)
+
+	// tr = CRH(ρ ‖ t1) = CRH(pk)
+	h.Reset()
+	_, _ = h.Write(packedPk[:])
+	_, _ = h.Read(sk.tr[:])
+
+	// Finish cache of public key
+	pk.tr = &sk.tr
+
+	return &pk, &sk
+}
+
+// Computes t0 and t1 from sk.s1h, sk.s2 and sk.A.
+func (sk *PrivateKey) computeT0andT1(t0, t1 *VecK) {
+	var t VecK
+
+	// Set t to A s₁ + s₂
+	for i := 0; i < K; i++ {
+		PolyDotHat(&t[i], &sk.A[i], &sk.s1h)
+		t[i].ReduceLe2Q()
+		t[i].InvNTT()
+	}
+	t.Add(&t, &sk.s2)
+	t.Normalize()
+
+	// Compute t₀, t₁ = Power2Round(t)
+	t.Power2Round(t0, t1)
+}
+
+// Verify checks whether the given signature by pk on msg is valid.
+func Verify(pk *PublicKey, msg []byte, signature []byte) bool {
+	var sig unpackedSignature
+	var mu [64]byte
+	var zh VecL
+	var Az, Az2dct1, w1 VecK
+	var ch common.Poly
+	var cp [CTildeSize]byte
+	var w1Packed [PolyW1Size * K]byte
+
+	// Note that Unpack() checked whether ‖z‖_∞ < γ₁ - β
+	// and ensured that there at most ω ones in pk.hint.
+	if !sig.Unpack(signature) {
+		return false
+	}
+
+	// μ = CRH(tr ‖ msg)
+	h := sha3.NewShake256()
+	_, _ = h.Write(pk.tr[:])
+	_, _ = h.Write(msg)
+	_, _ = h.Read(mu[:])
+
+	// Compute Az
+	zh = sig.z
+	zh.NTT()
+
+	for i := 0; i < K; i++ {
+		PolyDotHat(&Az[i], &pk.A[i], &zh)
+	}
+
+	// Next, we compute Az - 2ᵈ·c·t₁.
+	// Note that the coefficients of t₁ are bounded by 256 = 2⁹,
+	// so the coefficients of Az2dct1 will bounded by 2⁹⁺ᵈ = 2²³ < 2q,
+	// which is small enough for NTT().
+	Az2dct1.MulBy2toD(&pk.t1)
+	Az2dct1.NTT()
+	PolyDeriveUniformBall(&ch, sig.c[:32])
+	ch.NTT()
+	for i := 0; i < K; i++ {
+		Az2dct1[i].MulHat(&Az2dct1[i], &ch)
+	}
+	Az2dct1.Sub(&Az, &Az2dct1)
+	Az2dct1.ReduceLe2Q()
+	Az2dct1.InvNTT()
+	Az2dct1.NormalizeAssumingLe2Q()
+
+	// UseHint(pk.hint, Az - 2ᵈ·c·t₁)
+	//    = UseHint(pk.hint, w - c·s₂ + c·t₀)
+	//    = UseHint(pk.hint, r + c·t₀)
+	//    = r₁ = w₁.
+	w1.UseHint(&Az2dct1, &sig.hint)
+	w1.PackW1(w1Packed[:])
+
+	// c' = H(μ, w₁)
+	h.Reset()
+	_, _ = h.Write(mu[:])
+	_, _ = h.Write(w1Packed[:])
+	_, _ = h.Read(cp[:])
+
+	return sig.c == cp
+}
+
+// SignTo signs the given message and writes the signature into signature.
+//
+//nolint:funlen
+func SignTo(sk *PrivateKey, msg []byte, signature []byte) {
+	var mu, rhop [64]byte
+	var w1Packed [PolyW1Size * K]byte
+	var y, yh VecL
+	var w, w0, w1, w0mcs2, ct0, w0mcs2pct0 VecK
+	var ch common.Poly
+	var yNonce uint16
+	var sig unpackedSignature
+
+	if len(signature) < SignatureSize {
+		panic("Signature does not fit in that byteslice")
+	}
+
+	//  μ = CRH(tr ‖ msg)
+	h := sha3.NewShake256()
+	_, _ = h.Write(sk.tr[:])
+	_, _ = h.Write(msg)
+	_, _ = h.Read(mu[:])
+
+	// ρ' = CRH(key ‖ μ)
+	h.Reset()
+	_, _ = h.Write(sk.key[:])
+	if NIST {
+		// We implement the deterministic variant  where rnd is all zeroes.
+		// TODO expose randomized variant?
+		_, _ = h.Write(make([]byte, 32))
+	}
+	_, _ = h.Write(mu[:])
+	_, _ = h.Read(rhop[:])
+
+	// Main rejection loop
+	attempt := 0
+	for {
+		attempt++
+		if attempt >= 576 {
+			// Depending on the mode, one try has a chance between 1/7 and 1/4
+			// of succeeding.  Thus it is safe to say that 576 iterations
+			// are enough as (6/7)⁵⁷⁶ < 2⁻¹²⁸.
+			panic("This should only happen 1 in  2^{128}: something is wrong.")
+		}
+
+		// y = ExpandMask(ρ', key)
+		VecLDeriveUniformLeGamma1(&y, &rhop, yNonce)
+		yNonce += uint16(L)
+
+		// Set w to A y
+		yh = y
+		yh.NTT()
+		for i := 0; i < K; i++ {
+			PolyDotHat(&w[i], &sk.A[i], &yh)
+			w[i].ReduceLe2Q()
+			w[i].InvNTT()
+		}
+
+		// Decompose w into w₀ and w₁
+		w.NormalizeAssumingLe2Q()
+		w.Decompose(&w0, &w1)
+
+		// c~ = H(μ ‖ w₁)
+		w1.PackW1(w1Packed[:])
+		h.Reset()
+		_, _ = h.Write(mu[:])
+		_, _ = h.Write(w1Packed[:])
+		_, _ = h.Read(sig.c[:])
+
+		PolyDeriveUniformBall(&ch, sig.c[:32])
+		ch.NTT()
+
+		// Ensure ‖ w₀ - c·s2 ‖_∞ < γ₂ - β.
+		//
+		// By Lemma 3 of the specification this is equivalent to checking that
+		// both ‖ r₀ ‖_∞ < γ₂ - β and r₁ = w₁, for the decomposition
+		// w - c·s₂	 = r₁ α + r₀ as computed by decompose().
+		// See also §4.1 of the specification.
+		for i := 0; i < K; i++ {
+			w0mcs2[i].MulHat(&ch, &sk.s2h[i])
+			w0mcs2[i].InvNTT()
+		}
+		w0mcs2.Sub(&w0, &w0mcs2)
+		w0mcs2.Normalize()
+
+		if w0mcs2.Exceeds(Gamma2 - Beta) {
+			continue
+		}
+
+		// z = y + c·s₁
+		for i := 0; i < L; i++ {
+			sig.z[i].MulHat(&ch, &sk.s1h[i])
+			sig.z[i].InvNTT()
+		}
+		sig.z.Add(&sig.z, &y)
+		sig.z.Normalize()
+
+		// Ensure  ‖z‖_∞ < γ₁ - β
+		if sig.z.Exceeds(Gamma1 - Beta) {
+			continue
+		}
+
+		// Compute c·t₀
+		for i := 0; i < K; i++ {
+			ct0[i].MulHat(&ch, &sk.t0h[i])
+			ct0[i].InvNTT()
+		}
+		ct0.NormalizeAssumingLe2Q()
+
+		// Ensure ‖c·t₀‖_∞ < γ₂.
+		if ct0.Exceeds(Gamma2) {
+			continue
+		}
+
+		// Create the hint to be able to reconstruct w₁ from w - c·s₂ + c·t0.
+		// Note that we're not using makeHint() in the obvious way as we
+		// do not know whether ‖ sc·s₂ - c·t₀ ‖_∞ < γ₂.  Instead we note
+		// that our makeHint() is actually the same as a makeHint for a
+		// different decomposition:
+		//
+		// Earlier we ensured indirectly with a check that r₁ = w₁ where
+		// r = w - c·s₂.  Hence r₀ = r - r₁ α = w - c·s₂ - w₁ α = w₀ - c·s₂.
+		// Thus  MakeHint(w₀ - c·s₂ + c·t₀, w₁) = MakeHint(r0 + c·t₀, r₁)
+		// and UseHint(w - c·s₂ + c·t₀, w₁) = UseHint(r + c·t₀, r₁).
+		// As we just ensured that ‖ c·t₀ ‖_∞ < γ₂ our usage is correct.
+		w0mcs2pct0.Add(&w0mcs2, &ct0)
+		w0mcs2pct0.NormalizeAssumingLe2Q()
+		hintPop := sig.hint.MakeHint(&w0mcs2pct0, &w1)
+		if hintPop > Omega {
+			continue
+		}
+
+		break
+	}
+
+	sig.Pack(signature[:])
+}
+
+// Computes the public key corresponding to this private key.
+func (sk *PrivateKey) Public() *PublicKey {
+	var t0 VecK
+	pk := &PublicKey{
+		rho: sk.rho,
+		A:   &sk.A,
+		tr:  &sk.tr,
+	}
+	sk.computeT0andT1(&t0, &pk.t1)
+	pk.t1.PackT1(pk.t1p[:])
+	return pk
+}
+
+// Equal returns whether the two public keys are equal
+func (pk *PublicKey) Equal(other *PublicKey) bool {
+	return pk.rho == other.rho && pk.t1 == other.t1
+}
+
+// Equal returns whether the two private keys are equal
+func (sk *PrivateKey) Equal(other *PrivateKey) bool {
+	ret := (subtle.ConstantTimeCompare(sk.rho[:], other.rho[:]) &
+		subtle.ConstantTimeCompare(sk.key[:], other.key[:]) &
+		subtle.ConstantTimeCompare(sk.tr[:], other.tr[:]))
+
+	acc := uint32(0)
+	for i := 0; i < L; i++ {
+		for j := 0; j < common.N; j++ {
+			acc |= sk.s1[i][j] ^ other.s1[i][j]
+		}
+	}
+	for i := 0; i < K; i++ {
+		for j := 0; j < common.N; j++ {
+			acc |= sk.s2[i][j] ^ other.s2[i][j]
+			acc |= sk.t0[i][j] ^ other.t0[i][j]
+		}
+	}
+	return (ret & subtle.ConstantTimeEq(int32(acc), 0)) == 1
+}
diff --git a/sign/mldsa/mldsa44/internal/dilithium_test.go b/sign/mldsa/mldsa44/internal/dilithium_test.go
new file mode 100644
index 000000000..825e7da08
--- /dev/null
+++ b/sign/mldsa/mldsa44/internal/dilithium_test.go
@@ -0,0 +1,144 @@
+// Code generated from mode3/internal/dilithium_test.go by gen.go
+
+package internal
+
+import (
+	"encoding/binary"
+	"testing"
+
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+)
+
+// Checks whether p is normalized.  Only used in tests.
+func PolyNormalized(p *common.Poly) bool {
+	p2 := *p
+	p2.Normalize()
+	return p2 == *p
+}
+
+func BenchmarkSkUnpack(b *testing.B) {
+	var buf [PrivateKeySize]byte
+	var sk PrivateKey
+	for i := 0; i < b.N; i++ {
+		sk.Unpack(&buf)
+	}
+}
+
+func BenchmarkPkUnpack(b *testing.B) {
+	var buf [PublicKeySize]byte
+	var pk PublicKey
+	for i := 0; i < b.N; i++ {
+		pk.Unpack(&buf)
+	}
+}
+
+func BenchmarkVerify(b *testing.B) {
+	// Note that the expansion of the matrix A is done at Unpacking/Keygen
+	// instead of at the moment of verification (as in the reference
+	// implementation.)
+	var seed [32]byte
+	var msg [8]byte
+	var sig [SignatureSize]byte
+	pk, sk := NewKeyFromSeed(&seed)
+	SignTo(sk, msg[:], sig[:])
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		// We should generate a new signature for every verify attempt,
+		// as this influences the time a little bit.  This difference, however,
+		// is small and generating a new signature in between creates a lot
+		// pressure on the allocator which makes an accurate measurement hard.
+		Verify(pk, msg[:], sig[:])
+	}
+}
+
+func BenchmarkSign(b *testing.B) {
+	// Note that the expansion of the matrix A is done at Unpacking/Keygen
+	// instead of at the moment of signing (as in the reference implementation.)
+	var seed [32]byte
+	var msg [8]byte
+	var sig [SignatureSize]byte
+	_, sk := NewKeyFromSeed(&seed)
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		binary.LittleEndian.PutUint64(msg[:], uint64(i))
+		SignTo(sk, msg[:], sig[:])
+	}
+}
+
+func BenchmarkGenerateKey(b *testing.B) {
+	var seed [32]byte
+	for i := 0; i < b.N; i++ {
+		binary.LittleEndian.PutUint64(seed[:], uint64(i))
+		NewKeyFromSeed(&seed)
+	}
+}
+
+func BenchmarkPublicFromPrivate(b *testing.B) {
+	var seed [32]byte
+	for i := 0; i < b.N; i++ {
+		b.StopTimer()
+		binary.LittleEndian.PutUint64(seed[:], uint64(i))
+		_, sk := NewKeyFromSeed(&seed)
+		b.StartTimer()
+		sk.Public()
+	}
+}
+
+func TestSignThenVerifyAndPkSkPacking(t *testing.T) {
+	var seed [common.SeedSize]byte
+	var sig [SignatureSize]byte
+	var msg [8]byte
+	var pkb [PublicKeySize]byte
+	var skb [PrivateKeySize]byte
+	var pk2 PublicKey
+	var sk2 PrivateKey
+	for i := uint64(0); i < 100; i++ {
+		binary.LittleEndian.PutUint64(seed[:], i)
+		pk, sk := NewKeyFromSeed(&seed)
+		if !sk.Equal(sk) {
+			t.Fatal()
+		}
+		for j := uint64(0); j < 10; j++ {
+			binary.LittleEndian.PutUint64(msg[:], j)
+			SignTo(sk, msg[:], sig[:])
+			if !Verify(pk, msg[:], sig[:]) {
+				t.Fatal()
+			}
+		}
+		pk.Pack(&pkb)
+		pk2.Unpack(&pkb)
+		if !pk.Equal(&pk2) {
+			t.Fatal()
+		}
+		sk.Pack(&skb)
+		sk2.Unpack(&skb)
+		if !sk.Equal(&sk2) {
+			t.Fatal()
+		}
+	}
+}
+
+func TestPublicFromPrivate(t *testing.T) {
+	var seed [common.SeedSize]byte
+	for i := uint64(0); i < 100; i++ {
+		binary.LittleEndian.PutUint64(seed[:], i)
+		pk, sk := NewKeyFromSeed(&seed)
+		pk2 := sk.Public()
+		if !pk.Equal(pk2) {
+			t.Fatal()
+		}
+	}
+}
+
+func TestGamma1Size(t *testing.T) {
+	var expected int
+	switch Gamma1Bits {
+	case 17:
+		expected = 576
+	case 19:
+		expected = 640
+	}
+	if expected != PolyLeGamma1Size {
+		t.Fatal()
+	}
+}
diff --git a/sign/mldsa/mldsa44/internal/mat.go b/sign/mldsa/mldsa44/internal/mat.go
new file mode 100644
index 000000000..ceaf634fa
--- /dev/null
+++ b/sign/mldsa/mldsa44/internal/mat.go
@@ -0,0 +1,59 @@
+// Code generated from mode3/internal/mat.go by gen.go
+
+package internal
+
+import (
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+)
+
+// A k by l matrix of polynomials.
+type Mat [K]VecL
+
+// Expands the given seed to a complete matrix.
+//
+// This function is called ExpandA in the specification.
+func (m *Mat) Derive(seed *[32]byte) {
+	if !DeriveX4Available {
+		for i := uint16(0); i < K; i++ {
+			for j := uint16(0); j < L; j++ {
+				PolyDeriveUniform(&m[i][j], seed, (i<<8)+j)
+			}
+		}
+		return
+	}
+
+	idx := 0
+	var nonces [4]uint16
+	var ps [4]*common.Poly
+	for i := uint16(0); i < K; i++ {
+		for j := uint16(0); j < L; j++ {
+			nonces[idx] = (i << 8) + j
+			ps[idx] = &m[i][j]
+			idx++
+			if idx == 4 {
+				idx = 0
+				PolyDeriveUniformX4(ps, seed, nonces)
+			}
+		}
+	}
+	if idx != 0 {
+		for i := idx; i < 4; i++ {
+			ps[i] = nil
+		}
+		PolyDeriveUniformX4(ps, seed, nonces)
+	}
+}
+
+// Set p to the inner product of a and b using pointwise multiplication.
+//
+// Assumes a and b are in Montgomery form and their coefficients are
+// pairwise sufficiently small to multiply, see Poly.MulHat().  Resulting
+// coefficients are bounded by 2Lq.
+func PolyDotHat(p *common.Poly, a, b *VecL) {
+	var t common.Poly
+	*p = common.Poly{} // zero p
+	for i := 0; i < L; i++ {
+		t.MulHat(&a[i], &b[i])
+		p.Add(&t, p)
+	}
+}
diff --git a/sign/mldsa/mldsa44/internal/pack.go b/sign/mldsa/mldsa44/internal/pack.go
new file mode 100644
index 000000000..1854b4197
--- /dev/null
+++ b/sign/mldsa/mldsa44/internal/pack.go
@@ -0,0 +1,270 @@
+// Code generated from mode3/internal/pack.go by gen.go
+
+package internal
+
+import (
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+)
+
+// Writes p with norm less than or equal η into buf, which must be of
+// size PolyLeqEtaSize.
+//
+// Assumes coefficients of p are not normalized, but in [q-η,q+η].
+func PolyPackLeqEta(p *common.Poly, buf []byte) {
+	if DoubleEtaBits == 4 { // compiler eliminates branch
+		j := 0
+		for i := 0; i < PolyLeqEtaSize; i++ {
+			buf[i] = (byte(common.Q+Eta-p[j]) |
+				byte(common.Q+Eta-p[j+1])<<4)
+			j += 2
+		}
+	} else if DoubleEtaBits == 3 {
+		j := 0
+		for i := 0; i < PolyLeqEtaSize; i += 3 {
+			buf[i] = (byte(common.Q+Eta-p[j]) |
+				(byte(common.Q+Eta-p[j+1]) << 3) |
+				(byte(common.Q+Eta-p[j+2]) << 6))
+			buf[i+1] = ((byte(common.Q+Eta-p[j+2]) >> 2) |
+				(byte(common.Q+Eta-p[j+3]) << 1) |
+				(byte(common.Q+Eta-p[j+4]) << 4) |
+				(byte(common.Q+Eta-p[j+5]) << 7))
+			buf[i+2] = ((byte(common.Q+Eta-p[j+5]) >> 1) |
+				(byte(common.Q+Eta-p[j+6]) << 2) |
+				(byte(common.Q+Eta-p[j+7]) << 5))
+			j += 8
+		}
+	} else {
+		panic("eta not supported")
+	}
+}
+
+// Sets p to the polynomial of norm less than or equal η encoded in the
+// given buffer of size PolyLeqEtaSize.
+//
+// Output coefficients of p are not normalized, but in [q-η,q+η] provided
+// buf was created using PackLeqEta.
+//
+// Beware, for arbitrary buf the coefficients of p might end up in
+// the interval [q-2^b,q+2^b] where b is the least b with η≤2^b.
+func PolyUnpackLeqEta(p *common.Poly, buf []byte) {
+	if DoubleEtaBits == 4 { // compiler eliminates branch
+		j := 0
+		for i := 0; i < PolyLeqEtaSize; i++ {
+			p[j] = common.Q + Eta - uint32(buf[i]&15)
+			p[j+1] = common.Q + Eta - uint32(buf[i]>>4)
+			j += 2
+		}
+	} else if DoubleEtaBits == 3 {
+		j := 0
+		for i := 0; i < PolyLeqEtaSize; i += 3 {
+			p[j] = common.Q + Eta - uint32(buf[i]&7)
+			p[j+1] = common.Q + Eta - uint32((buf[i]>>3)&7)
+			p[j+2] = common.Q + Eta - uint32((buf[i]>>6)|((buf[i+1]<<2)&7))
+			p[j+3] = common.Q + Eta - uint32((buf[i+1]>>1)&7)
+			p[j+4] = common.Q + Eta - uint32((buf[i+1]>>4)&7)
+			p[j+5] = common.Q + Eta - uint32((buf[i+1]>>7)|((buf[i+2]<<1)&7))
+			p[j+6] = common.Q + Eta - uint32((buf[i+2]>>2)&7)
+			p[j+7] = common.Q + Eta - uint32((buf[i+2]>>5)&7)
+			j += 8
+		}
+	} else {
+		panic("eta not supported")
+	}
+}
+
+// Writes v with coefficients in {0, 1} of which at most ω non-zero
+// to buf, which must have length ω+k.
+func (v *VecK) PackHint(buf []byte) {
+	// The packed hint starts with the indices of the non-zero coefficients
+	// For instance:
+	//
+	//    (x⁵⁶ + x¹⁰⁰, x²⁵⁵, 0, x² + x²³, x¹)
+	//
+	// Yields
+	//
+	//  56, 100, 255, 2, 23, 1
+	//
+	// Then we pad with zeroes until we have a list of ω items:
+	// //  56, 100, 255, 2, 23, 1, 0, 0, ..., 0
+	//
+	// Then we finish with a list of the switch-over-indices in this
+	// list between polynomials, so:
+	//
+	//  56, 100, 255, 2, 23, 1, 0, 0, ..., 0, 2, 3, 3, 5, 6
+
+	off := uint8(0)
+	for i := 0; i < K; i++ {
+		for j := uint16(0); j < common.N; j++ {
+			if v[i][j] != 0 {
+				buf[off] = uint8(j)
+				off++
+			}
+		}
+		buf[Omega+i] = off
+	}
+	for ; off < Omega; off++ {
+		buf[off] = 0
+	}
+}
+
+// Sets v to the vector encoded using VecK.PackHint()
+//
+// Returns whether unpacking was successful.
+func (v *VecK) UnpackHint(buf []byte) bool {
+	// A priori, there would be several reasonable ways to encode the same
+	// hint vector.  We take care to only allow only one encoding, to ensure
+	// "strong unforgeability".
+	//
+	// See PackHint() source for description of the encoding.
+	*v = VecK{}         // zero v
+	prevSOP := uint8(0) // previous switch-over-point
+	for i := 0; i < K; i++ {
+		SOP := buf[Omega+i]
+		if SOP < prevSOP || SOP > Omega {
+			return false // ensures switch-over-points are increasing
+		}
+		for j := prevSOP; j < SOP; j++ {
+			if j > prevSOP && buf[j] <= buf[j-1] {
+				return false // ensures indices are increasing (within a poly)
+			}
+			v[i][buf[j]] = 1
+		}
+		prevSOP = SOP
+	}
+	for j := prevSOP; j < Omega; j++ {
+		if buf[j] != 0 {
+			return false // ensures padding indices are zero
+		}
+	}
+
+	return true
+}
+
+// Sets p to the polynomial packed into buf by PolyPackLeGamma1.
+//
+// p will be normalized.
+func PolyUnpackLeGamma1(p *common.Poly, buf []byte) {
+	if Gamma1Bits == 17 {
+		j := 0
+		for i := 0; i < PolyLeGamma1Size; i += 9 {
+			p0 := uint32(buf[i]) | (uint32(buf[i+1]) << 8) |
+				(uint32(buf[i+2]&0x3) << 16)
+			p1 := uint32(buf[i+2]>>2) | (uint32(buf[i+3]) << 6) |
+				(uint32(buf[i+4]&0xf) << 14)
+			p2 := uint32(buf[i+4]>>4) | (uint32(buf[i+5]) << 4) |
+				(uint32(buf[i+6]&0x3f) << 12)
+			p3 := uint32(buf[i+6]>>6) | (uint32(buf[i+7]) << 2) |
+				(uint32(buf[i+8]) << 10)
+
+			// coefficients in [0,…,2γ₁)
+			p0 = Gamma1 - p0 // (-γ₁,…,γ₁]
+			p1 = Gamma1 - p1
+			p2 = Gamma1 - p2
+			p3 = Gamma1 - p3
+
+			p0 += uint32(int32(p0)>>31) & common.Q // normalize
+			p1 += uint32(int32(p1)>>31) & common.Q
+			p2 += uint32(int32(p2)>>31) & common.Q
+			p3 += uint32(int32(p3)>>31) & common.Q
+
+			p[j] = p0
+			p[j+1] = p1
+			p[j+2] = p2
+			p[j+3] = p3
+
+			j += 4
+		}
+	} else if Gamma1Bits == 19 {
+		j := 0
+		for i := 0; i < PolyLeGamma1Size; i += 5 {
+			p0 := uint32(buf[i]) | (uint32(buf[i+1]) << 8) |
+				(uint32(buf[i+2]&0xf) << 16)
+			p1 := uint32(buf[i+2]>>4) | (uint32(buf[i+3]) << 4) |
+				(uint32(buf[i+4]) << 12)
+
+			p0 = Gamma1 - p0
+			p1 = Gamma1 - p1
+
+			p0 += uint32(int32(p0)>>31) & common.Q
+			p1 += uint32(int32(p1)>>31) & common.Q
+
+			p[j] = p0
+			p[j+1] = p1
+
+			j += 2
+		}
+	} else {
+		panic("γ₁ not supported")
+	}
+}
+
+// Writes p whose coefficients are in (-γ₁,γ₁] into buf
+// which has to be of length PolyLeGamma1Size.
+//
+// Assumes p is normalized.
+func PolyPackLeGamma1(p *common.Poly, buf []byte) {
+	if Gamma1Bits == 17 {
+		j := 0
+		// coefficients in [0,…,γ₁] ∪ (q-γ₁,…,q)
+		for i := 0; i < PolyLeGamma1Size; i += 9 {
+			p0 := Gamma1 - p[j]                    // [0,…,γ₁] ∪ (γ₁-q,…,2γ₁-q)
+			p0 += uint32(int32(p0)>>31) & common.Q // [0,…,2γ₁)
+			p1 := Gamma1 - p[j+1]
+			p1 += uint32(int32(p1)>>31) & common.Q
+			p2 := Gamma1 - p[j+2]
+			p2 += uint32(int32(p2)>>31) & common.Q
+			p3 := Gamma1 - p[j+3]
+			p3 += uint32(int32(p3)>>31) & common.Q
+
+			buf[i+0] = byte(p0)
+			buf[i+1] = byte(p0 >> 8)
+			buf[i+2] = byte(p0>>16) | byte(p1<<2)
+			buf[i+3] = byte(p1 >> 6)
+			buf[i+4] = byte(p1>>14) | byte(p2<<4)
+			buf[i+5] = byte(p2 >> 4)
+			buf[i+6] = byte(p2>>12) | byte(p3<<6)
+			buf[i+7] = byte(p3 >> 2)
+			buf[i+8] = byte(p3 >> 10)
+
+			j += 4
+		}
+	} else if Gamma1Bits == 19 {
+		j := 0
+		for i := 0; i < PolyLeGamma1Size; i += 5 {
+			// Coefficients are in [0, γ₁] ∪ (Q-γ₁, Q)
+			p0 := Gamma1 - p[j]
+			p0 += uint32(int32(p0)>>31) & common.Q
+			p1 := Gamma1 - p[j+1]
+			p1 += uint32(int32(p1)>>31) & common.Q
+
+			buf[i+0] = byte(p0)
+			buf[i+1] = byte(p0 >> 8)
+			buf[i+2] = byte(p0>>16) | byte(p1<<4)
+			buf[i+3] = byte(p1 >> 4)
+			buf[i+4] = byte(p1 >> 12)
+
+			j += 2
+		}
+	} else {
+		panic("γ₁ not supported")
+	}
+}
+
+// Pack w₁ into buf, which must be of length PolyW1Size.
+//
+// Assumes w₁ is normalized.
+func PolyPackW1(p *common.Poly, buf []byte) {
+	if Gamma1Bits == 19 {
+		p.PackLe16(buf)
+	} else if Gamma1Bits == 17 {
+		j := 0
+		for i := 0; i < PolyW1Size; i += 3 {
+			buf[i] = byte(p[j]) | byte(p[j+1]<<6)
+			buf[i+1] = byte(p[j+1]>>2) | byte(p[j+2]<<4)
+			buf[i+2] = byte(p[j+2]>>4) | byte(p[j+3]<<2)
+			j += 4
+		}
+	} else {
+		panic("unsupported γ₁")
+	}
+}
diff --git a/sign/mldsa/mldsa44/internal/pack_test.go b/sign/mldsa/mldsa44/internal/pack_test.go
new file mode 100644
index 000000000..f952c6a09
--- /dev/null
+++ b/sign/mldsa/mldsa44/internal/pack_test.go
@@ -0,0 +1,93 @@
+// Code generated from mode3/internal/pack_test.go by gen.go
+
+package internal
+
+import (
+	"testing"
+
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+)
+
+func TestPolyPackLeqEta(t *testing.T) {
+	var p1, p2 common.Poly
+	var seed [64]byte
+	var buf [PolyLeqEtaSize]byte
+
+	for i := uint16(0); i < 100; i++ {
+		// Note that DeriveUniformLeqEta sets p to the right kind of
+		// unnormalized vector.
+		PolyDeriveUniformLeqEta(&p1, &seed, i)
+		for j := 0; j < PolyLeqEtaSize; j++ {
+			if p1[j] < common.Q-Eta || p1[j] > common.Q+Eta {
+				t.Fatalf("DerveUniformLeqEta out of bounds")
+			}
+		}
+		PolyPackLeqEta(&p1, buf[:])
+		PolyUnpackLeqEta(&p2, buf[:])
+		if p1 != p2 {
+			t.Fatalf("%v != %v", p1, p2)
+		}
+	}
+}
+
+func TestPolyPackT1(t *testing.T) {
+	var p1, p2 common.Poly
+	var seed [32]byte
+	var buf [common.PolyT1Size]byte
+
+	for i := uint16(0); i < 100; i++ {
+		PolyDeriveUniform(&p1, &seed, i)
+		p1.Normalize()
+		for j := 0; j < common.N; j++ {
+			p1[j] &= 0x1ff
+		}
+		p1.PackT1(buf[:])
+		p2.UnpackT1(buf[:])
+		if p1 != p2 {
+			t.Fatalf("%v != %v", p1, p2)
+		}
+	}
+}
+
+func TestPolyPackT0(t *testing.T) {
+	var p, p0, p1, p2 common.Poly
+	var seed [32]byte
+	var buf [common.PolyT0Size]byte
+
+	for i := uint16(0); i < 100; i++ {
+		PolyDeriveUniform(&p, &seed, i)
+		p.Normalize()
+		p.Power2Round(&p0, &p1)
+
+		p0.PackT0(buf[:])
+		p2.UnpackT0(buf[:])
+		if p0 != p2 {
+			t.Fatalf("%v !=\n%v", p0, p2)
+		}
+	}
+}
+
+func BenchmarkUnpackLeGamma1(b *testing.B) {
+	var p common.Poly
+	var buf [PolyLeGamma1Size]byte
+	for i := 0; i < b.N; i++ {
+		PolyUnpackLeGamma1(&p, buf[:])
+	}
+}
+
+func TestPolyPackLeGamma1(t *testing.T) {
+	var p0, p1 common.Poly
+	var seed [64]byte
+	var buf [PolyLeGamma1Size]byte
+
+	for i := uint16(0); i < 100; i++ {
+		PolyDeriveUniformLeGamma1(&p0, &seed, i)
+		p0.Normalize()
+
+		PolyPackLeGamma1(&p0, buf[:])
+		PolyUnpackLeGamma1(&p1, buf[:])
+		if p0 != p1 {
+			t.Fatalf("%v != %v", p0, p1)
+		}
+	}
+}
diff --git a/sign/mldsa/mldsa44/internal/params.go b/sign/mldsa/mldsa44/internal/params.go
new file mode 100644
index 000000000..fec07cbbe
--- /dev/null
+++ b/sign/mldsa/mldsa44/internal/params.go
@@ -0,0 +1,19 @@
+// Code generated from params.templ.go. DO NOT EDIT.
+
+package internal
+
+const (
+	Name          = "ML-DSA-44"
+	UseAES        = false
+	K             = 4
+	L             = 4
+	Eta           = 2
+	DoubleEtaBits = 3
+	Omega         = 80
+	Tau           = 39
+	Gamma1Bits    = 17
+	Gamma2        = 95232
+	NIST          = true
+	TRSize        = 64
+	CTildeSize    = 32
+)
diff --git a/sign/mldsa/mldsa44/internal/rounding.go b/sign/mldsa/mldsa44/internal/rounding.go
new file mode 100644
index 000000000..58123c090
--- /dev/null
+++ b/sign/mldsa/mldsa44/internal/rounding.go
@@ -0,0 +1,142 @@
+// Code generated from mode3/internal/rounding.go by gen.go
+
+package internal
+
+import (
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+)
+
+// Splits 0 ≤ a < q into a₀ and a₁ with a = a₁*α + a₀ with -α/2 < a₀ ≤ α/2,
+// except for when we would have a₁ = (q-1)/α in which case a₁=0 is taken
+// and -α/2 ≤ a₀ < 0.  Returns a₀ + q.  Note 0 ≤ a₁ < (q-1)/α.
+// Recall α = 2γ₂.
+func decompose(a uint32) (a0plusQ, a1 uint32) {
+	// a₁ = ⌈a / 128⌉
+	a1 = (a + 127) >> 7
+
+	if Alpha == 523776 {
+		// 1025/2²² is close enough to 1/4092 so that a₁
+		// becomes a/α rounded down.
+		a1 = ((a1*1025 + (1 << 21)) >> 22)
+
+		// For the corner-case a₁ = (q-1)/α = 16, we have to set a₁=0.
+		a1 &= 15
+	} else if Alpha == 190464 {
+		// 1488/2²⁴ is close enough to 1/1488 so that a₁
+		// becomes a/α rounded down.
+		a1 = ((a1 * 11275) + (1 << 23)) >> 24
+
+		// For the corner-case a₁ = (q-1)/α = 44, we have to set a₁=0.
+		a1 ^= uint32(int32(43-a1)>>31) & a1
+	} else {
+		panic("unsupported α")
+	}
+
+	a0plusQ = a - a1*Alpha
+
+	// In the corner-case, when we set a₁=0, we will incorrectly
+	// have a₀ > (q-1)/2 and we'll need to subtract q.  As we
+	// return a₀ + q, that comes down to adding q if a₀ < (q-1)/2.
+	a0plusQ += uint32(int32(a0plusQ-(common.Q-1)/2)>>31) & common.Q
+
+	return
+}
+
+// Assume 0 ≤ r, f < Q with ‖f‖_∞ ≤ α/2.  Decompose r as r = r1*α + r0 as
+// computed by decompose().  Write r' := r - f (mod Q).  Now, decompose
+// r'=r-f again as  r' = r'1*α + r'0 using decompose().  As f is small, we
+// have r'1 = r1 + h, where h ∈ {-1, 0, 1}.  makeHint() computes |h|
+// given z0 := r0 - f (mod Q) and r1.  With |h|, which is called the hint,
+// we can reconstruct r1 using only r' = r - f, which is done by useHint().
+// To wit:
+//
+//	useHint( r - f, makeHint( r0 - f, r1 ) ) = r1.
+//
+// Assumes 0 ≤ z0 < Q.
+func makeHint(z0, r1 uint32) uint32 {
+	// If -α/2 < r0 - f ≤ α/2, then r1*α + r0 - f is a valid decomposition of r'
+	// with the restrictions of decompose() and so r'1 = r1.  So the hint
+	// should be 0. This is covered by the first two inequalities.
+	// There is one other case: if r0 - f = -α/2, then r1*α + r0 - f is also
+	// a valid decomposition if r1 = 0.  In the other cases a one is carried
+	// and the hint should be 1.
+	if z0 <= Gamma2 || z0 > common.Q-Gamma2 || (z0 == common.Q-Gamma2 && r1 == 0) {
+		return 0
+	}
+	return 1
+}
+
+// Uses the hint created by makeHint() to reconstruct r1 from r'=r-f; see
+// documentation of makeHint() for context.
+// Assumes 0 ≤ r' < Q.
+func useHint(rp uint32, hint uint32) uint32 {
+	rp0plusQ, rp1 := decompose(rp)
+	if hint == 0 {
+		return rp1
+	}
+	if rp0plusQ > common.Q {
+		return (rp1 + 1) & 15
+	}
+	return (rp1 - 1) & 15
+}
+
+// Sets p to the hint polynomial for p0 the modified low bits and p1
+// the unmodified high bits --- see makeHint().
+//
+// Returns the number of ones in the hint polynomial.
+func PolyMakeHint(p, p0, p1 *common.Poly) (pop uint32) {
+	for i := 0; i < common.N; i++ {
+		h := makeHint(p0[i], p1[i])
+		pop += h
+		p[i] = h
+	}
+	return
+}
+
+// Computes corrections to the high bits of the polynomial q according
+// to the hints in h and sets p to the corrected high bits.  Returns p.
+func PolyUseHint(p, q, hint *common.Poly) {
+	var q0PlusQ common.Poly
+
+	// See useHint() and makeHint() for an explanation.  We reimplement it
+	// here so that we can call Poly.Decompose(), which might be way faster
+	// than calling decompose() in a loop (for instance when having AVX2.)
+
+	PolyDecompose(q, &q0PlusQ, p)
+
+	for i := 0; i < common.N; i++ {
+		if hint[i] == 0 {
+			continue
+		}
+		if Gamma2 == 261888 {
+			if q0PlusQ[i] > common.Q {
+				p[i] = (p[i] + 1) & 15
+			} else {
+				p[i] = (p[i] - 1) & 15
+			}
+		} else if Gamma2 == 95232 {
+			if q0PlusQ[i] > common.Q {
+				if p[i] == 43 {
+					p[i] = 0
+				} else {
+					p[i]++
+				}
+			} else {
+				if p[i] == 0 {
+					p[i] = 43
+				} else {
+					p[i]--
+				}
+			}
+		} else {
+			panic("unsupported γ₂")
+		}
+	}
+}
+
+// Splits each of the coefficients of p using decompose.
+func PolyDecompose(p, p0PlusQ, p1 *common.Poly) {
+	for i := 0; i < common.N; i++ {
+		p0PlusQ[i], p1[i] = decompose(p[i])
+	}
+}
diff --git a/sign/mldsa/mldsa44/internal/rounding_test.go b/sign/mldsa/mldsa44/internal/rounding_test.go
new file mode 100644
index 000000000..ad653ca3f
--- /dev/null
+++ b/sign/mldsa/mldsa44/internal/rounding_test.go
@@ -0,0 +1,81 @@
+// Code generated from mode3/internal/rounding_test.go by gen.go
+
+package internal
+
+import (
+	"flag"
+	"testing"
+
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+)
+
+var runVeryLongTest = flag.Bool("very-long", false, "runs very long tests")
+
+func TestDecompose(t *testing.T) {
+	for a := uint32(0); a < common.Q; a++ {
+		a0PlusQ, a1 := decompose(a)
+		a0 := int32(a0PlusQ) - int32(common.Q)
+		recombined := a0 + int32(Alpha*a1)
+		if a1 == 0 && recombined < 0 {
+			recombined += common.Q
+			if -(Alpha/2) > a0 || a0 >= 0 {
+				t.Fatalf("decompose(%v): a0 out of bounds", a)
+			}
+		} else {
+			if (-(Alpha / 2) >= a0) || (a0 > Alpha/2) {
+				t.Fatalf("decompose(%v): a0 out of bounds", a)
+			}
+		}
+		if int32(a) != recombined {
+			t.Fatalf("decompose(%v) doesn't recombine %v %v", a, a0, a1)
+		}
+	}
+}
+
+func TestMakeHint(t *testing.T) {
+	if !*runVeryLongTest {
+		t.SkipNow()
+	}
+	for w := uint32(0); w < common.Q; w++ {
+		w0, w1 := decompose(w)
+		for fn := uint32(0); fn <= Gamma2; fn++ {
+			fsign := false
+			for {
+				var f uint32
+				if fsign {
+					if fn == 0 {
+						break
+					}
+					f = common.Q - fn
+				} else {
+					f = fn
+				}
+
+				hint := makeHint(common.ReduceLe2Q(w0+common.Q-f), w1)
+				w1p := useHint(common.ReduceLe2Q(w+common.Q-f), hint)
+				if w1p != w1 {
+					t.Fatal()
+				}
+
+				if fsign {
+					break
+				}
+				fsign = true
+			}
+		}
+	}
+}
+
+func BenchmarkDecompose(b *testing.B) {
+	var p, p0, p1 common.Poly
+	for i := 0; i < b.N; i++ {
+		PolyDecompose(&p, &p0, &p1)
+	}
+}
+
+func BenchmarkMakeHint(b *testing.B) {
+	var p, p0, p1 common.Poly
+	for i := 0; i < b.N; i++ {
+		PolyMakeHint(&p, &p0, &p1)
+	}
+}
diff --git a/sign/mldsa/mldsa44/internal/sample.go b/sign/mldsa/mldsa44/internal/sample.go
new file mode 100644
index 000000000..62c261332
--- /dev/null
+++ b/sign/mldsa/mldsa44/internal/sample.go
@@ -0,0 +1,370 @@
+// Code generated from mode3/internal/sample.go by gen.go
+
+package internal
+
+import (
+	"encoding/binary"
+
+	"github.com/cloudflare/circl/internal/sha3"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+	"github.com/cloudflare/circl/simd/keccakf1600"
+)
+
+// DeriveX4Available indicates whether the system supports the quick fourway
+// sampling variants like PolyDeriveUniformX4.
+var DeriveX4Available = keccakf1600.IsEnabledX4() && !UseAES
+
+// For each i, sample ps[i] uniformly from the given seed and nonces[i].
+// ps[i] may be nil and is ignored in that case.
+//
+// Can only be called when DeriveX4Available is true.
+func PolyDeriveUniformX4(ps [4]*common.Poly, seed *[32]byte, nonces [4]uint16) {
+	var perm keccakf1600.StateX4
+	state := perm.Initialize(false)
+
+	// Absorb the seed in the four states
+	for i := 0; i < 4; i++ {
+		v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)])
+		for j := 0; j < 4; j++ {
+			state[i*4+j] = v
+		}
+	}
+
+	// Absorb the nonces, the SHAKE128 domain separator (0b1111), the
+	// start of the padding (0b...001) and the end of the padding 0b100...
+	// Recall that the rate of SHAKE128 is 168 --- i.e. 21 uint64s.
+	for j := 0; j < 4; j++ {
+		state[4*4+j] = uint64(nonces[j]) | (0x1f << 16)
+		state[20*4+j] = 0x80 << 56
+	}
+
+	var idx [4]int // indices into ps
+	for j := 0; j < 4; j++ {
+		if ps[j] == nil {
+			idx[j] = common.N // mark nil polynomial as completed
+		}
+	}
+
+	done := false
+	for !done {
+		// Applies KeccaK-f[1600] to state to get the next 21 uint64s of each
+		// of the four SHAKE128 streams.
+		perm.Permute()
+
+		done = true
+
+	PolyLoop:
+		for j := 0; j < 4; j++ {
+			if idx[j] == common.N {
+				continue
+			}
+			for i := 0; i < 7; i++ {
+				var t [8]uint32
+				t[0] = uint32(state[i*3*4+j] & 0x7fffff)
+				t[1] = uint32((state[i*3*4+j] >> 24) & 0x7fffff)
+				t[2] = uint32((state[i*3*4+j] >> 48) |
+					((state[(i*3+1)*4+j] & 0x7f) << 16))
+				t[3] = uint32((state[(i*3+1)*4+j] >> 8) & 0x7fffff)
+				t[4] = uint32((state[(i*3+1)*4+j] >> 32) & 0x7fffff)
+				t[5] = uint32((state[(i*3+1)*4+j] >> 56) |
+					((state[(i*3+2)*4+j] & 0x7fff) << 8))
+				t[6] = uint32((state[(i*3+2)*4+j] >> 16) & 0x7fffff)
+				t[7] = uint32((state[(i*3+2)*4+j] >> 40) & 0x7fffff)
+
+				for k := 0; k < 8; k++ {
+					if t[k] < common.Q {
+						ps[j][idx[j]] = t[k]
+						idx[j]++
+						if idx[j] == common.N {
+							continue PolyLoop
+						}
+					}
+				}
+			}
+			done = false
+		}
+	}
+}
+
+// Sample p uniformly from the given seed and nonce.
+//
+// p will be normalized.
+func PolyDeriveUniform(p *common.Poly, seed *[32]byte, nonce uint16) {
+	var i, length int
+	var buf [12 * 16]byte // fits 168B SHAKE-128 rate and 12 16B AES blocks
+
+	if UseAES {
+		length = 12 * 16
+	} else {
+		length = 168
+	}
+
+	sample := func() {
+		// Note that 3 divides into 168 and 12*16, so we use up buf completely.
+		for j := 0; j < length && i < common.N; j += 3 {
+			t := (uint32(buf[j]) | (uint32(buf[j+1]) << 8) |
+				(uint32(buf[j+2]) << 16)) & 0x7fffff
+
+			// We use rejection sampling
+			if t < common.Q {
+				p[i] = t
+				i++
+			}
+		}
+	}
+
+	if UseAES {
+		h := common.NewAesStream128(seed, nonce)
+
+		for i < common.N {
+			h.SqueezeInto(buf[:length])
+			sample()
+		}
+	} else {
+		var iv [32 + 2]byte // 32 byte seed + uint16 nonce
+		h := sha3.NewShake128()
+		copy(iv[:32], seed[:])
+		iv[32] = uint8(nonce)
+		iv[33] = uint8(nonce >> 8)
+		_, _ = h.Write(iv[:])
+
+		for i < common.N {
+			_, _ = h.Read(buf[:168])
+			sample()
+		}
+	}
+}
+
+// Sample p uniformly with coefficients of norm less than or equal η,
+// using the given seed and nonce.
+//
+// p will not be normalized, but will have coefficients in [q-η,q+η].
+func PolyDeriveUniformLeqEta(p *common.Poly, seed *[64]byte, nonce uint16) {
+	// Assumes 2 < η < 8.
+	var i, length int
+	var buf [9 * 16]byte // fits 136B SHAKE-256 rate and 9 16B AES blocks
+
+	if UseAES {
+		length = 9 * 16
+	} else {
+		length = 136
+	}
+
+	sample := func() {
+		// We use rejection sampling
+		for j := 0; j < length && i < common.N; j++ {
+			t1 := uint32(buf[j]) & 15
+			t2 := uint32(buf[j]) >> 4
+			if Eta == 2 { // branch is eliminated by compiler
+				if t1 <= 14 {
+					t1 -= ((205 * t1) >> 10) * 5 // reduce mod  5
+					p[i] = common.Q + Eta - t1
+					i++
+				}
+				if t2 <= 14 && i < common.N {
+					t2 -= ((205 * t2) >> 10) * 5 // reduce mod 5
+					p[i] = common.Q + Eta - t2
+					i++
+				}
+			} else if Eta == 4 {
+				if t1 <= 2*Eta {
+					p[i] = common.Q + Eta - t1
+					i++
+				}
+				if t2 <= 2*Eta && i < common.N {
+					p[i] = common.Q + Eta - t2
+					i++
+				}
+			} else {
+				panic("unsupported η")
+			}
+		}
+	}
+
+	if UseAES {
+		h := common.NewAesStream256(seed, nonce)
+
+		for i < common.N {
+			h.SqueezeInto(buf[:length])
+			sample()
+		}
+	} else {
+		var iv [64 + 2]byte // 64 byte seed + uint16 nonce
+
+		h := sha3.NewShake256()
+		copy(iv[:64], seed[:])
+		iv[64] = uint8(nonce)
+		iv[65] = uint8(nonce >> 8)
+
+		// 136 is SHAKE-256 rate
+		_, _ = h.Write(iv[:])
+
+		for i < common.N {
+			_, _ = h.Read(buf[:136])
+			sample()
+		}
+	}
+}
+
+// Sample v[i] uniformly with coefficients in (-γ₁,…,γ₁]  using the
+// given seed and nonce+i
+//
+// p will be normalized.
+func VecLDeriveUniformLeGamma1(v *VecL, seed *[64]byte, nonce uint16) {
+	for i := 0; i < L; i++ {
+		PolyDeriveUniformLeGamma1(&v[i], seed, nonce+uint16(i))
+	}
+}
+
+// Sample p uniformly with coefficients in (-γ₁,…,γK1s] using the
+// given seed and nonce.
+//
+// p will be normalized.
+func PolyDeriveUniformLeGamma1(p *common.Poly, seed *[64]byte, nonce uint16) {
+	var buf [PolyLeGamma1Size]byte
+
+	if UseAES {
+		h := common.NewAesStream256(seed, nonce)
+		h.SqueezeInto(buf[:])
+	} else {
+		var iv [66]byte
+		h := sha3.NewShake256()
+		copy(iv[:64], seed[:])
+		iv[64] = uint8(nonce)
+		iv[65] = uint8(nonce >> 8)
+		_, _ = h.Write(iv[:])
+		_, _ = h.Read(buf[:])
+	}
+
+	PolyUnpackLeGamma1(p, buf[:])
+}
+
+// For each i, sample ps[i] uniformly with τ non-zero coefficients in {q-1,1}
+// using the given seed and w1[i].  ps[i] may be nil and is ignored
+// in that case.  ps[i] will be normalized.
+//
+// Can only be called when DeriveX4Available is true.
+//
+// This function is currently not used (yet).
+func PolyDeriveUniformBallX4(ps [4]*common.Poly, seed []byte) {
+	var perm keccakf1600.StateX4
+	state := perm.Initialize(false)
+
+	// Absorb the seed in the four states
+	for i := 0; i < 32/8; i++ {
+		v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)])
+		for j := 0; j < 4; j++ {
+			state[i*4+j] = v
+		}
+	}
+
+	// SHAKE256 domain separator and padding
+	for j := 0; j < 4; j++ {
+		state[(32/8)*4+j] ^= 0x1f
+		state[16*4+j] ^= 0x80 << 56
+	}
+	perm.Permute()
+
+	var signs [4]uint64
+	var idx [4]uint16 // indices into ps
+
+	for j := 0; j < 4; j++ {
+		if ps[j] != nil {
+			signs[j] = state[j]
+			*ps[j] = common.Poly{} // zero ps[j]
+			idx[j] = common.N - Tau
+		} else {
+			idx[j] = common.N // mark as completed
+		}
+	}
+
+	stateOffset := 1
+	for {
+		done := true
+
+	PolyLoop:
+		for j := 0; j < 4; j++ {
+			if idx[j] == common.N {
+				continue
+			}
+
+			for i := stateOffset; i < 17; i++ {
+				var bs [8]byte
+				binary.LittleEndian.PutUint64(bs[:], state[4*i+j])
+				for k := 0; k < 8; k++ {
+					b := uint16(bs[k])
+
+					if b > idx[j] {
+						continue
+					}
+
+					ps[j][idx[j]] = ps[j][b]
+					ps[j][b] = 1
+					// Takes least significant bit of signs and uses it for the sign.
+					// Note 1 ^ (1 | (Q-1)) = Q-1.
+					ps[j][b] ^= uint32((-(signs[j] & 1)) & (1 | (common.Q - 1)))
+					signs[j] >>= 1
+
+					idx[j]++
+					if idx[j] == common.N {
+						continue PolyLoop
+					}
+				}
+			}
+
+			done = false
+		}
+
+		if done {
+			break
+		}
+
+		perm.Permute()
+		stateOffset = 0
+	}
+}
+
+// Samples p uniformly with τ non-zero coefficients in {q-1,1}.
+//
+// The polynomial p will be normalized.
+func PolyDeriveUniformBall(p *common.Poly, seed []byte) {
+	var buf [136]byte // SHAKE-256 rate is 136
+
+	h := sha3.NewShake256()
+	_, _ = h.Write(seed[:])
+	_, _ = h.Read(buf[:])
+
+	// Essentially we generate a sequence of τ ones or minus ones,
+	// prepend 196 zeroes and shuffle the concatenation using the
+	// usual algorithm (Fisher--Yates.)
+	signs := binary.LittleEndian.Uint64(buf[:])
+	bufOff := 8 // offset into buf
+
+	*p = common.Poly{} // zero p
+	for i := uint16(common.N - Tau); i < common.N; i++ {
+		var b uint16
+
+		// Find location of where to move the new coefficient to using
+		// rejection sampling.
+		for {
+			if bufOff >= 136 {
+				_, _ = h.Read(buf[:])
+				bufOff = 0
+			}
+
+			b = uint16(buf[bufOff])
+			bufOff++
+
+			if b <= i {
+				break
+			}
+		}
+
+		p[i] = p[b]
+		p[b] = 1
+		// Takes least significant bit of signs and uses it for the sign.
+		// Note 1 ^ (1 | (Q-1)) = Q-1.
+		p[b] ^= uint32((-(signs & 1)) & (1 | (common.Q - 1)))
+		signs >>= 1
+	}
+}
diff --git a/sign/mldsa/mldsa44/internal/sample_test.go b/sign/mldsa/mldsa44/internal/sample_test.go
new file mode 100644
index 000000000..2059599eb
--- /dev/null
+++ b/sign/mldsa/mldsa44/internal/sample_test.go
@@ -0,0 +1,266 @@
+// Code generated from mode3/internal/sample_test.go by gen.go
+
+package internal
+
+import (
+	"encoding/binary"
+	"testing"
+
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+)
+
+func TestVectorDeriveUniform(t *testing.T) {
+	var p, p2 common.Poly
+	var seed [32]byte
+	if UseAES {
+		p2 = common.Poly{
+			6724291, 310295, 6949524, 4464039, 1482136, 2522903,
+			7025059, 3006320, 7286364, 7516512, 3361305, 1955529,
+			4765954, 1725325, 6933066, 4299100, 6625173, 4272792,
+			583034, 4971409, 2259140, 7715362, 3975394, 2341624,
+			5481174, 8150082, 365246, 5491939, 1083120, 7517301,
+			3104783, 2475292, 184149, 6425226, 4591622, 5964030,
+			4729604, 5471092, 1828227, 1082044, 2516245, 1692580,
+			3274844, 5443294, 7256740, 4989638, 3191250, 7479519,
+			5124211, 5603858, 1230692, 2513454, 2828034, 4254312,
+			1512596, 5245430, 5517392, 2814840, 932545, 6826733,
+			3511094, 4075348, 3233981, 7268882, 2913733, 4870249,
+			4123492, 8124406, 4016949, 5478752, 2750895, 603525,
+			5724798, 3985430, 3483012, 6434230, 3136996, 8297976,
+			4107616, 7307748, 6962904, 7544473, 1193110, 3448595,
+			4814773, 5607932, 8221314, 1054046, 1541208, 1866050,
+			8227412, 2925778, 5293953, 2065416, 4972769, 3616283,
+			7990594, 1105530, 7121836, 1170740, 7417431, 633146,
+			253820, 7235019, 3539504, 6807707, 451390, 5481526,
+			2859902, 1063061, 4579730, 7126652, 7033767, 4294814,
+			1414604, 7620048, 1953268, 8304556, 1156814, 1182881,
+			5311519, 3057534, 5277666, 682843, 2070398, 2874278,
+			4859533, 6376664, 6694074, 1590242, 2620706, 8331066,
+			5643845, 5037538, 2891516, 7004879, 3754327, 5031296,
+			5463118, 2420870, 8116529, 5517696, 7435129, 3873963,
+			710407, 713806, 175647, 4274571, 2655021, 7319503,
+			3027243, 7129679, 4213435, 2429323, 4643873, 4568526,
+			649664, 1720514, 6497260, 2683517, 7672754, 7105190,
+			3148405, 5898369, 5667677, 8050874, 1587139, 7315260,
+			4337416, 2202680, 2338714, 557467, 6752058, 2469794,
+			485071, 1617604, 3590498, 2151466, 2005823, 7727956,
+			7776292, 6783433, 6787146, 1732833, 3596857, 7436284,
+			4483349, 4970142, 4472608, 6478342, 1236215, 5695744,
+			2280717, 2889355, 3233946, 5187812, 978685, 5177364,
+			2922353, 4824807, 5302883, 6739803, 8092453, 5883903,
+			816553, 6041174, 8317591, 1459178, 5332455, 1835058,
+			1368601, 2820950, 3479224, 2589540, 7992934, 3421045,
+			4657128, 8292902, 4153567, 3553988, 7830320, 6722913,
+			2555309, 4149801, 8328975, 1560545, 7757473, 3106458,
+			4310856, 7135453, 3481032, 652626, 1841361, 8126828,
+			6250018, 300536, 7380070, 8174419, 1418793, 6208185,
+			3906256, 6679016, 1605701, 3561489, 5819724, 5746996,
+			8044214, 7087187, 7102330, 4962927, 4253983, 7108567,
+			4119736, 6584065, 441634, 6941656,
+		}
+	} else {
+		p2 = common.Poly{
+			2901364, 562527, 5258502, 3885002, 4190126, 4460268, 6884052,
+			3514511, 5383040, 213206, 2155865, 5179607, 3551954, 2312357,
+			6066350, 8126097, 1179080, 4787182, 6552182, 6713644,
+			1561067, 7626063, 7859743, 5052321, 7032876, 7815031, 157938,
+			1865184, 490802, 5717642, 3451902, 7000218, 3743250, 1677431,
+			1875427, 5596150, 671623, 3819041, 6247594, 1014875, 4933545,
+			7122446, 6682963, 3388398, 3335295, 943002, 1145083, 3113071,
+			105967, 1916675, 7474561, 1107006, 700548, 2147909, 1603855,
+			5049181, 437882, 6118899, 5656914, 6731065, 3066622, 865453,
+			5427634, 981549, 4650873, 861291, 4003872, 5104220, 6171453,
+			3723302, 7426315, 6137283, 4874820, 6052561, 53441, 5032874,
+			5614778, 2248550, 1756499, 8280764, 8263880, 7600081,
+			5118374, 795344, 7543392, 6869925, 1841187, 4181568, 584562,
+			7483939, 4938664, 6863397, 5126354, 5218129, 6236086,
+			4149293, 379169, 4368487, 7490569, 3409215, 1580463, 3081737,
+			1278732, 7109719, 7371700, 2097931, 399836, 1700274, 7188595,
+			6830029, 1548850, 6593138, 6849097, 1518037, 2859442,
+			7772265, 7325153, 3281191, 7856131, 4995056, 4684325,
+			1351194, 8223904, 6817307, 2484146, 131782, 397032, 7436778,
+			7973479, 3171829, 5624626, 3540123, 7150120, 8313283,
+			3604714, 1043574, 117692, 7797783, 7909392, 903315, 7335342,
+			7501562, 5826142, 2709813, 8245473, 2369045, 2782257,
+			5762833, 6474114, 6862031, 424522, 594248, 2626630, 7659983,
+			5642869, 4075194, 1592129, 245547, 5271031, 3205046, 982375,
+			267873, 1286496, 7230481, 3208972, 7485411, 676111, 4944500,
+			2959742, 5934456, 1414847, 6067948, 1709895, 4648315, 126008,
+			8258986, 2183134, 2302072, 4674924, 4306056, 7465311,
+			6500270, 4247428, 4016815, 4973426, 294287, 2456847, 3289700,
+			2732169, 1159447, 5569724, 140001, 3237977, 8007761, 5874533,
+			255652, 3119586, 2102434, 6248250, 8152822, 8006066, 7708625,
+			6997719, 6260212, 6186962, 6636650, 7836834, 7998017,
+			2061516, 1197591, 1706544, 733027, 2392907, 2700000, 8254598,
+			4488002, 160495, 2985325, 2036837, 2703633, 6406550, 3579947,
+			6195178, 5552390, 6804584, 6305468, 5731980, 6095195,
+			3323409, 1322661, 6690942, 3374630, 5615167, 479044, 3136054,
+			4380418, 2833144, 7829577, 1770522, 6056687, 240415, 14780,
+			3740517, 5224226, 3547288, 2083124, 4699398, 3654239,
+			5624978, 585593, 3655369, 2281739, 3338565, 1908093, 7784706,
+			4352830,
+		}
+	}
+	for i := 0; i < 32; i++ {
+		seed[i] = byte(i)
+	}
+	PolyDeriveUniform(&p, &seed, 30000)
+	if p != p2 {
+		t.Fatalf("%v != %v", p, p2)
+	}
+}
+
+func TestDeriveUniform(t *testing.T) {
+	var p common.Poly
+	var seed [32]byte
+	for i := 0; i < 100; i++ {
+		binary.LittleEndian.PutUint64(seed[:], uint64(i))
+		PolyDeriveUniform(&p, &seed, uint16(i))
+		if !PolyNormalized(&p) {
+			t.Fatal()
+		}
+	}
+}
+
+func TestDeriveUniformLeqEta(t *testing.T) {
+	var p common.Poly
+	var seed [64]byte
+	for i := 0; i < 100; i++ {
+		binary.LittleEndian.PutUint64(seed[:], uint64(i))
+		PolyDeriveUniformLeqEta(&p, &seed, uint16(i))
+		for j := 0; j < common.N; j++ {
+			if p[j] < common.Q-Eta || p[j] > common.Q+Eta {
+				t.Fatal()
+			}
+		}
+	}
+}
+
+func TestDeriveUniformLeGamma1(t *testing.T) {
+	var p common.Poly
+	var seed [64]byte
+	for i := 0; i < 100; i++ {
+		binary.LittleEndian.PutUint64(seed[:], uint64(i))
+		PolyDeriveUniformLeGamma1(&p, &seed, uint16(i))
+		for j := 0; j < common.N; j++ {
+			if (p[j] > Gamma1 && p[j] <= common.Q-Gamma1) || p[j] >= common.Q {
+				t.Fatal()
+			}
+		}
+	}
+}
+
+func TestDeriveUniformBall(t *testing.T) {
+	var p common.Poly
+	var seed [32]byte
+	for i := 0; i < 100; i++ {
+		binary.LittleEndian.PutUint64(seed[:], uint64(i))
+		PolyDeriveUniformBall(&p, seed[:])
+		nonzero := 0
+		for j := 0; j < common.N; j++ {
+			if p[j] != 0 {
+				if p[j] != 1 && p[j] != common.Q-1 {
+					t.Fatal()
+				}
+				nonzero++
+			}
+		}
+		if nonzero != Tau {
+			t.Fatal()
+		}
+	}
+}
+
+func TestDeriveUniformX4(t *testing.T) {
+	if !DeriveX4Available {
+		t.SkipNow()
+	}
+	var ps [4]common.Poly
+	var p common.Poly
+	var seed [32]byte
+	nonces := [4]uint16{12345, 54321, 13532, 37377}
+
+	for i := 0; i < len(seed); i++ {
+		seed[i] = byte(i)
+	}
+
+	PolyDeriveUniformX4([4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]}, &seed,
+		nonces)
+	for i := 0; i < 4; i++ {
+		PolyDeriveUniform(&p, &seed, nonces[i])
+		if ps[i] != p {
+			t.Fatal()
+		}
+	}
+}
+
+func TestDeriveUniformBallX4(t *testing.T) {
+	if !DeriveX4Available {
+		t.SkipNow()
+	}
+	var ps [4]common.Poly
+	var p common.Poly
+	var seed [32]byte
+	PolyDeriveUniformBallX4(
+		[4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]},
+		seed[:],
+	)
+	for j := 0; j < 4; j++ {
+		PolyDeriveUniformBall(&p, seed[:])
+		if ps[j] != p {
+			t.Fatalf("%d\n%v\n%v", j, ps[j], p)
+		}
+	}
+}
+
+func BenchmarkPolyDeriveUniformBall(b *testing.B) {
+	var seed [32]byte
+	var p common.Poly
+	var w1 VecK
+	for i := 0; i < b.N; i++ {
+		w1[0][0] = uint32(i)
+		PolyDeriveUniformBall(&p, seed[:])
+	}
+}
+
+func BenchmarkPolyDeriveUniformBallX4(b *testing.B) {
+	var seed [32]byte
+	var p common.Poly
+	var w1 VecK
+	for i := 0; i < b.N; i++ {
+		w1[0][0] = uint32(i)
+		PolyDeriveUniformBallX4(
+			[4]*common.Poly{&p, &p, &p, &p},
+			seed[:],
+		)
+	}
+}
+
+func BenchmarkPolyDeriveUniform(b *testing.B) {
+	var seed [32]byte
+	var p common.Poly
+	for i := 0; i < b.N; i++ {
+		PolyDeriveUniform(&p, &seed, uint16(i))
+	}
+}
+
+func BenchmarkPolyDeriveUniformX4(b *testing.B) {
+	if !DeriveX4Available {
+		b.SkipNow()
+	}
+	var seed [32]byte
+	var p [4]common.Poly
+	for i := 0; i < b.N; i++ {
+		nonce := uint16(4 * i)
+		PolyDeriveUniformX4([4]*common.Poly{&p[0], &p[1], &p[2], &p[3]},
+			&seed, [4]uint16{nonce, nonce + 1, nonce + 2, nonce + 3})
+	}
+}
+
+func BenchmarkPolyDeriveUniformLeGamma1(b *testing.B) {
+	var seed [64]byte
+	var p common.Poly
+	for i := 0; i < b.N; i++ {
+		PolyDeriveUniformLeGamma1(&p, &seed, uint16(i))
+	}
+}
diff --git a/sign/mldsa/mldsa44/internal/vec.go b/sign/mldsa/mldsa44/internal/vec.go
new file mode 100644
index 000000000..d07d3b245
--- /dev/null
+++ b/sign/mldsa/mldsa44/internal/vec.go
@@ -0,0 +1,281 @@
+// Code generated from mode3/internal/vec.go by gen.go
+
+package internal
+
+import (
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+)
+
+// A vector of L polynomials.
+type VecL [L]common.Poly
+
+// A vector of K polynomials.
+type VecK [K]common.Poly
+
+// Normalize the polynomials in this vector.
+func (v *VecL) Normalize() {
+	for i := 0; i < L; i++ {
+		v[i].Normalize()
+	}
+}
+
+// Normalize the polynomials in this vector assuming their coefficients
+// are already bounded by 2q.
+func (v *VecL) NormalizeAssumingLe2Q() {
+	for i := 0; i < L; i++ {
+		v[i].NormalizeAssumingLe2Q()
+	}
+}
+
+// Sets v to w + u.  Does not normalize.
+func (v *VecL) Add(w, u *VecL) {
+	for i := 0; i < L; i++ {
+		v[i].Add(&w[i], &u[i])
+	}
+}
+
+// Applies NTT componentwise. See Poly.NTT() for details.
+func (v *VecL) NTT() {
+	for i := 0; i < L; i++ {
+		v[i].NTT()
+	}
+}
+
+// Checks whether any of the coefficients exceeds the given bound in supnorm
+//
+// Requires the vector to be normalized.
+func (v *VecL) Exceeds(bound uint32) bool {
+	for i := 0; i < L; i++ {
+		if v[i].Exceeds(bound) {
+			return true
+		}
+	}
+	return false
+}
+
+// Applies Poly.Power2Round componentwise.
+//
+// Requires the vector to be normalized.
+func (v *VecL) Power2Round(v0PlusQ, v1 *VecL) {
+	for i := 0; i < L; i++ {
+		v[i].Power2Round(&v0PlusQ[i], &v1[i])
+	}
+}
+
+// Applies Poly.Decompose componentwise.
+//
+// Requires the vector to be normalized.
+func (v *VecL) Decompose(v0PlusQ, v1 *VecL) {
+	for i := 0; i < L; i++ {
+		PolyDecompose(&v[i], &v0PlusQ[i], &v1[i])
+	}
+}
+
+// Sequentially packs each polynomial using Poly.PackLeqEta().
+func (v *VecL) PackLeqEta(buf []byte) {
+	offset := 0
+	for i := 0; i < L; i++ {
+		PolyPackLeqEta(&v[i], buf[offset:])
+		offset += PolyLeqEtaSize
+	}
+}
+
+// Sets v to the polynomials packed in buf using VecL.PackLeqEta().
+func (v *VecL) UnpackLeqEta(buf []byte) {
+	offset := 0
+	for i := 0; i < L; i++ {
+		PolyUnpackLeqEta(&v[i], buf[offset:])
+		offset += PolyLeqEtaSize
+	}
+}
+
+// Sequentially packs each polynomial using PolyPackLeGamma1().
+func (v *VecL) PackLeGamma1(buf []byte) {
+	offset := 0
+	for i := 0; i < L; i++ {
+		PolyPackLeGamma1(&v[i], buf[offset:])
+		offset += PolyLeGamma1Size
+	}
+}
+
+// Sets v to the polynomials packed in buf using VecL.PackLeGamma1().
+func (v *VecL) UnpackLeGamma1(buf []byte) {
+	offset := 0
+	for i := 0; i < L; i++ {
+		PolyUnpackLeGamma1(&v[i], buf[offset:])
+		offset += PolyLeGamma1Size
+	}
+}
+
+// Normalize the polynomials in this vector.
+func (v *VecK) Normalize() {
+	for i := 0; i < K; i++ {
+		v[i].Normalize()
+	}
+}
+
+// Normalize the polynomials in this vector assuming their coefficients
+// are already bounded by 2q.
+func (v *VecK) NormalizeAssumingLe2Q() {
+	for i := 0; i < K; i++ {
+		v[i].NormalizeAssumingLe2Q()
+	}
+}
+
+// Sets v to w + u.  Does not normalize.
+func (v *VecK) Add(w, u *VecK) {
+	for i := 0; i < K; i++ {
+		v[i].Add(&w[i], &u[i])
+	}
+}
+
+// Checks whether any of the coefficients exceeds the given bound in supnorm
+//
+// Requires the vector to be normalized.
+func (v *VecK) Exceeds(bound uint32) bool {
+	for i := 0; i < K; i++ {
+		if v[i].Exceeds(bound) {
+			return true
+		}
+	}
+	return false
+}
+
+// Applies Poly.Power2Round componentwise.
+//
+// Requires the vector to be normalized.
+func (v *VecK) Power2Round(v0PlusQ, v1 *VecK) {
+	for i := 0; i < K; i++ {
+		v[i].Power2Round(&v0PlusQ[i], &v1[i])
+	}
+}
+
+// Applies Poly.Decompose componentwise.
+//
+// Requires the vector to be normalized.
+func (v *VecK) Decompose(v0PlusQ, v1 *VecK) {
+	for i := 0; i < K; i++ {
+		PolyDecompose(&v[i], &v0PlusQ[i], &v1[i])
+	}
+}
+
+// Sets v to the hint vector for v0 the modified low bits and v1
+// the unmodified high bits --- see makeHint().
+//
+// Returns the number of ones in the hint vector.
+func (v *VecK) MakeHint(v0, v1 *VecK) (pop uint32) {
+	for i := 0; i < K; i++ {
+		pop += PolyMakeHint(&v[i], &v0[i], &v1[i])
+	}
+	return
+}
+
+// Computes corrections to the high bits of the polynomials in the vector
+// w using the hints in h and sets v to the corrected high bits.  Returns v.
+// See useHint().
+func (v *VecK) UseHint(q, hint *VecK) *VecK {
+	for i := 0; i < K; i++ {
+		PolyUseHint(&v[i], &q[i], &hint[i])
+	}
+	return v
+}
+
+// Sequentially packs each polynomial using Poly.PackT1().
+func (v *VecK) PackT1(buf []byte) {
+	offset := 0
+	for i := 0; i < K; i++ {
+		v[i].PackT1(buf[offset:])
+		offset += common.PolyT1Size
+	}
+}
+
+// Sets v to the vector packed into buf by PackT1().
+func (v *VecK) UnpackT1(buf []byte) {
+	offset := 0
+	for i := 0; i < K; i++ {
+		v[i].UnpackT1(buf[offset:])
+		offset += common.PolyT1Size
+	}
+}
+
+// Sequentially packs each polynomial using Poly.PackT0().
+func (v *VecK) PackT0(buf []byte) {
+	offset := 0
+	for i := 0; i < K; i++ {
+		v[i].PackT0(buf[offset:])
+		offset += common.PolyT0Size
+	}
+}
+
+// Sets v to the vector packed into buf by PackT0().
+func (v *VecK) UnpackT0(buf []byte) {
+	offset := 0
+	for i := 0; i < K; i++ {
+		v[i].UnpackT0(buf[offset:])
+		offset += common.PolyT0Size
+	}
+}
+
+// Sequentially packs each polynomial using Poly.PackLeqEta().
+func (v *VecK) PackLeqEta(buf []byte) {
+	offset := 0
+	for i := 0; i < K; i++ {
+		PolyPackLeqEta(&v[i], buf[offset:])
+		offset += PolyLeqEtaSize
+	}
+}
+
+// Sets v to the polynomials packed in buf using VecK.PackLeqEta().
+func (v *VecK) UnpackLeqEta(buf []byte) {
+	offset := 0
+	for i := 0; i < K; i++ {
+		PolyUnpackLeqEta(&v[i], buf[offset:])
+		offset += PolyLeqEtaSize
+	}
+}
+
+// Applies NTT componentwise. See Poly.NTT() for details.
+func (v *VecK) NTT() {
+	for i := 0; i < K; i++ {
+		v[i].NTT()
+	}
+}
+
+// Sequentially packs each polynomial using PolyPackW1().
+func (v *VecK) PackW1(buf []byte) {
+	offset := 0
+	for i := 0; i < K; i++ {
+		PolyPackW1(&v[i], buf[offset:])
+		offset += PolyW1Size
+	}
+}
+
+// Sets v to a - b.
+//
+// Warning: assumes coefficients of the polynomials of  b are less than 2q.
+func (v *VecK) Sub(a, b *VecK) {
+	for i := 0; i < K; i++ {
+		v[i].Sub(&a[i], &b[i])
+	}
+}
+
+// Sets v to 2ᵈ w without reducing.
+func (v *VecK) MulBy2toD(w *VecK) {
+	for i := 0; i < K; i++ {
+		v[i].MulBy2toD(&w[i])
+	}
+}
+
+// Applies InvNTT componentwise. See Poly.InvNTT() for details.
+func (v *VecK) InvNTT() {
+	for i := 0; i < K; i++ {
+		v[i].InvNTT()
+	}
+}
+
+// Applies Poly.ReduceLe2Q() componentwise.
+func (v *VecK) ReduceLe2Q() {
+	for i := 0; i < K; i++ {
+		v[i].ReduceLe2Q()
+	}
+}
diff --git a/sign/mldsa/mldsa65/dilithium.go b/sign/mldsa/mldsa65/dilithium.go
new file mode 100644
index 000000000..9411e84a7
--- /dev/null
+++ b/sign/mldsa/mldsa65/dilithium.go
@@ -0,0 +1,182 @@
+// Code generated from modePkg.templ.go. DO NOT EDIT.
+
+
+// mldsa65 implements NIST signature scheme ML-DSA-65 as defined in FIPS204.
+
+package mldsa65
+
+import (
+	"crypto"
+	"errors"
+	"io"
+
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+
+	"github.com/cloudflare/circl/sign/mldsa/mldsa65/internal"
+
+)
+
+const (
+	// Size of seed for NewKeyFromSeed
+	SeedSize = common.SeedSize
+
+	// Size of a packed PublicKey
+	PublicKeySize = internal.PublicKeySize
+
+	// Size of a packed PrivateKey
+	PrivateKeySize = internal.PrivateKeySize
+
+	// Size of a signature
+	SignatureSize = internal.SignatureSize
+)
+
+// PublicKey is the type of ML-DSA-65 public key
+type PublicKey internal.PublicKey
+
+// PrivateKey is the type of ML-DSA-65 private key
+type PrivateKey internal.PrivateKey
+
+// GenerateKey generates a public/private key pair using entropy from rand.
+// If rand is nil, crypto/rand.Reader will be used.
+func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) {
+	pk, sk, err := internal.GenerateKey(rand)
+	return (*PublicKey)(pk), (*PrivateKey)(sk), err
+}
+
+// NewKeyFromSeed derives a public/private key pair using the given seed.
+func NewKeyFromSeed(seed *[SeedSize]byte) (*PublicKey, *PrivateKey) {
+	pk, sk := internal.NewKeyFromSeed(seed)
+	return (*PublicKey)(pk), (*PrivateKey)(sk)
+}
+
+// SignTo signs the given message and writes the signature into signature.
+// It will panic if signature is not of length at least SignatureSize.
+func SignTo(sk *PrivateKey, msg []byte, signature []byte) {
+	internal.SignTo(
+		(*internal.PrivateKey)(sk),
+		msg,
+		signature,
+	)
+}
+
+// Verify checks whether the given signature by pk on msg is valid.
+func Verify(pk *PublicKey, msg []byte, signature []byte) bool {
+	return internal.Verify(
+		(*internal.PublicKey)(pk),
+		msg,
+		signature,
+	)
+}
+
+// Sets pk to the public key encoded in buf.
+func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) {
+	(*internal.PublicKey)(pk).Unpack(buf)
+}
+
+// Sets sk to the private key encoded in buf.
+func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) {
+	(*internal.PrivateKey)(sk).Unpack(buf)
+}
+
+// Packs the public key into buf.
+func (pk *PublicKey) Pack(buf *[PublicKeySize]byte) {
+	(*internal.PublicKey)(pk).Pack(buf)
+}
+
+// Packs the private key into buf.
+func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) {
+	(*internal.PrivateKey)(sk).Pack(buf)
+}
+
+// Packs the public key.
+func (pk *PublicKey) Bytes() []byte {
+	var buf [PublicKeySize]byte
+	pk.Pack(&buf)
+	return buf[:]
+}
+
+// Packs the private key.
+func (sk *PrivateKey) Bytes() []byte {
+	var buf [PrivateKeySize]byte
+	sk.Pack(&buf)
+	return buf[:]
+}
+
+// Packs the public key.
+func (pk *PublicKey) MarshalBinary() ([]byte, error) {
+	return pk.Bytes(), nil
+}
+
+// Packs the private key.
+func (sk *PrivateKey) MarshalBinary() ([]byte, error) {
+	return sk.Bytes(), nil
+}
+
+// Unpacks the public key from data.
+func (pk *PublicKey) UnmarshalBinary(data []byte) error {
+	if len(data) != PublicKeySize {
+		return errors.New("packed public key must be of mldsa65.PublicKeySize bytes")
+	}
+	var buf [PublicKeySize]byte
+	copy(buf[:], data)
+	pk.Unpack(&buf)
+	return nil
+}
+
+// Unpacks the private key from data.
+func (sk *PrivateKey) UnmarshalBinary(data []byte) error {
+	if len(data) != PrivateKeySize {
+		return errors.New("packed private key must be of mldsa65.PrivateKeySize bytes")
+	}
+	var buf [PrivateKeySize]byte
+	copy(buf[:], data)
+	sk.Unpack(&buf)
+	return nil
+}
+
+// Sign signs the given message.
+//
+// opts.HashFunc() must return zero, which can be achieved by passing
+// crypto.Hash(0) for opts.  rand is ignored.  Will only return an error
+// if opts.HashFunc() is non-zero.
+//
+// This function is used to make PrivateKey implement the crypto.Signer
+// interface.  The package-level SignTo function might be more convenient
+// to use.
+func (sk *PrivateKey) Sign(rand io.Reader, msg []byte, opts crypto.SignerOpts) (
+	signature []byte, err error) {
+	var sig [SignatureSize]byte
+
+	if opts.HashFunc() != crypto.Hash(0) {
+		return nil, errors.New("dilithium: cannot sign hashed message")
+	}
+
+	SignTo(sk, msg, sig[:])
+	return sig[:], nil
+}
+
+// Computes the public key corresponding to this private key.
+//
+// Returns a *PublicKey.  The type crypto.PublicKey is used to make
+// PrivateKey implement the crypto.Signer interface.
+func (sk *PrivateKey) Public() crypto.PublicKey {
+	return (*PublicKey)((*internal.PrivateKey)(sk).Public())
+}
+
+// Equal returns whether the two private keys equal.
+func (sk *PrivateKey) Equal(other crypto.PrivateKey) bool {
+	castOther, ok := other.(*PrivateKey)
+	if !ok {
+		return false
+	}
+	return (*internal.PrivateKey)(sk).Equal((*internal.PrivateKey)(castOther))
+}
+
+// Equal returns whether the two public keys equal.
+func (pk *PublicKey) Equal(other crypto.PublicKey) bool {
+	castOther, ok := other.(*PublicKey)
+	if !ok {
+		return false
+	}
+	return (*internal.PublicKey)(pk).Equal((*internal.PublicKey)(castOther))
+}
diff --git a/sign/mldsa/mldsa65/internal/dilithium.go b/sign/mldsa/mldsa65/internal/dilithium.go
new file mode 100644
index 000000000..7869d0475
--- /dev/null
+++ b/sign/mldsa/mldsa65/internal/dilithium.go
@@ -0,0 +1,482 @@
+// Code generated from mode3/internal/dilithium.go by gen.go
+
+package internal
+
+import (
+	cryptoRand "crypto/rand"
+	"crypto/subtle"
+	"io"
+
+	"github.com/cloudflare/circl/internal/sha3"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+)
+
+const (
+	// Size of a packed polynomial of norm ≤η.
+	// (Note that the  formula is not valid in general.)
+	PolyLeqEtaSize = (common.N * DoubleEtaBits) / 8
+
+	// β = τη, the maximum size of c s₂.
+	Beta = Tau * Eta
+
+	// γ₁ range of y
+	Gamma1 = 1 << Gamma1Bits
+
+	// Size of packed polynomial of norm <γ₁ such as z
+	PolyLeGamma1Size = (Gamma1Bits + 1) * common.N / 8
+
+	// α = 2γ₂ parameter for decompose
+	Alpha = 2 * Gamma2
+
+	// Size of a packed private key
+	PrivateKeySize = 32 + 32 + TRSize + PolyLeqEtaSize*(L+K) + common.PolyT0Size*K
+
+	// Size of a packed public key
+	PublicKeySize = 32 + common.PolyT1Size*K
+
+	// Size of a packed signature
+	SignatureSize = L*PolyLeGamma1Size + Omega + K + CTildeSize
+
+	// Size of packed w₁
+	PolyW1Size = (common.N * (common.QBits - Gamma1Bits)) / 8
+)
+
+// PublicKey is the type of Dilithium public keys.
+type PublicKey struct {
+	rho [32]byte
+	t1  VecK
+
+	// Cached values
+	t1p [common.PolyT1Size * K]byte
+	A   *Mat
+	tr  *[TRSize]byte
+}
+
+// PrivateKey is the type of Dilithium private keys.
+type PrivateKey struct {
+	rho [32]byte
+	key [32]byte
+	s1  VecL
+	s2  VecK
+	t0  VecK
+	tr  [TRSize]byte
+
+	// Cached values
+	A   Mat  // ExpandA(ρ)
+	s1h VecL // NTT(s₁)
+	s2h VecK // NTT(s₂)
+	t0h VecK // NTT(t₀)
+}
+
+type unpackedSignature struct {
+	z    VecL
+	hint VecK
+	c    [CTildeSize]byte
+}
+
+// Packs the signature into buf.
+func (sig *unpackedSignature) Pack(buf []byte) {
+	copy(buf[:], sig.c[:])
+	sig.z.PackLeGamma1(buf[CTildeSize:])
+	sig.hint.PackHint(buf[CTildeSize+L*PolyLeGamma1Size:])
+}
+
+// Sets sig to the signature encoded in the buffer.
+//
+// Returns whether buf contains a properly packed signature.
+func (sig *unpackedSignature) Unpack(buf []byte) bool {
+	if len(buf) < SignatureSize {
+		return false
+	}
+	copy(sig.c[:], buf[:])
+	sig.z.UnpackLeGamma1(buf[CTildeSize:])
+	if sig.z.Exceeds(Gamma1 - Beta) {
+		return false
+	}
+	if !sig.hint.UnpackHint(buf[CTildeSize+L*PolyLeGamma1Size:]) {
+		return false
+	}
+	return true
+}
+
+// Packs the public key into buf.
+func (pk *PublicKey) Pack(buf *[PublicKeySize]byte) {
+	copy(buf[:32], pk.rho[:])
+	copy(buf[32:], pk.t1p[:])
+}
+
+// Sets pk to the public key encoded in buf.
+func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) {
+	copy(pk.rho[:], buf[:32])
+	copy(pk.t1p[:], buf[32:])
+
+	pk.t1.UnpackT1(pk.t1p[:])
+	pk.A = new(Mat)
+	pk.A.Derive(&pk.rho)
+
+	// tr = CRH(ρ ‖ t1) = CRH(pk)
+	pk.tr = new([TRSize]byte)
+	h := sha3.NewShake256()
+	_, _ = h.Write(buf[:])
+	_, _ = h.Read(pk.tr[:])
+}
+
+// Packs the private key into buf.
+func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) {
+	copy(buf[:32], sk.rho[:])
+	copy(buf[32:64], sk.key[:])
+	copy(buf[64:64+TRSize], sk.tr[:])
+	offset := 64 + TRSize
+	sk.s1.PackLeqEta(buf[offset:])
+	offset += PolyLeqEtaSize * L
+	sk.s2.PackLeqEta(buf[offset:])
+	offset += PolyLeqEtaSize * K
+	sk.t0.PackT0(buf[offset:])
+}
+
+// Sets sk to the private key encoded in buf.
+func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) {
+	copy(sk.rho[:], buf[:32])
+	copy(sk.key[:], buf[32:64])
+	copy(sk.tr[:], buf[64:64+TRSize])
+	offset := 64 + TRSize
+	sk.s1.UnpackLeqEta(buf[offset:])
+	offset += PolyLeqEtaSize * L
+	sk.s2.UnpackLeqEta(buf[offset:])
+	offset += PolyLeqEtaSize * K
+	sk.t0.UnpackT0(buf[offset:])
+
+	// Cached values
+	sk.A.Derive(&sk.rho)
+	sk.t0h = sk.t0
+	sk.t0h.NTT()
+	sk.s1h = sk.s1
+	sk.s1h.NTT()
+	sk.s2h = sk.s2
+	sk.s2h.NTT()
+}
+
+// GenerateKey generates a public/private key pair using entropy from rand.
+// If rand is nil, crypto/rand.Reader will be used.
+func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) {
+	var seed [32]byte
+	if rand == nil {
+		rand = cryptoRand.Reader
+	}
+	_, err := io.ReadFull(rand, seed[:])
+	if err != nil {
+		return nil, nil, err
+	}
+	pk, sk := NewKeyFromSeed(&seed)
+	return pk, sk, nil
+}
+
+// NewKeyFromSeed derives a public/private key pair using the given seed.
+func NewKeyFromSeed(seed *[common.SeedSize]byte) (*PublicKey, *PrivateKey) {
+	var eSeed [128]byte // expanded seed
+	var pk PublicKey
+	var sk PrivateKey
+	var sSeed [64]byte
+
+	h := sha3.NewShake256()
+	_, _ = h.Write(seed[:])
+	_, _ = h.Read(eSeed[:])
+
+	copy(pk.rho[:], eSeed[:32])
+	copy(sSeed[:], eSeed[32:96])
+	copy(sk.key[:], eSeed[96:])
+	copy(sk.rho[:], pk.rho[:])
+
+	sk.A.Derive(&pk.rho)
+
+	for i := uint16(0); i < L; i++ {
+		PolyDeriveUniformLeqEta(&sk.s1[i], &sSeed, i)
+	}
+
+	for i := uint16(0); i < K; i++ {
+		PolyDeriveUniformLeqEta(&sk.s2[i], &sSeed, i+L)
+	}
+
+	sk.s1h = sk.s1
+	sk.s1h.NTT()
+	sk.s2h = sk.s2
+	sk.s2h.NTT()
+
+	sk.computeT0andT1(&sk.t0, &pk.t1)
+
+	sk.t0h = sk.t0
+	sk.t0h.NTT()
+
+	// Complete public key far enough to be packed
+	pk.t1.PackT1(pk.t1p[:])
+	pk.A = &sk.A
+
+	// Finish private key
+	var packedPk [PublicKeySize]byte
+	pk.Pack(&packedPk)
+
+	// tr = CRH(ρ ‖ t1) = CRH(pk)
+	h.Reset()
+	_, _ = h.Write(packedPk[:])
+	_, _ = h.Read(sk.tr[:])
+
+	// Finish cache of public key
+	pk.tr = &sk.tr
+
+	return &pk, &sk
+}
+
+// Computes t0 and t1 from sk.s1h, sk.s2 and sk.A.
+func (sk *PrivateKey) computeT0andT1(t0, t1 *VecK) {
+	var t VecK
+
+	// Set t to A s₁ + s₂
+	for i := 0; i < K; i++ {
+		PolyDotHat(&t[i], &sk.A[i], &sk.s1h)
+		t[i].ReduceLe2Q()
+		t[i].InvNTT()
+	}
+	t.Add(&t, &sk.s2)
+	t.Normalize()
+
+	// Compute t₀, t₁ = Power2Round(t)
+	t.Power2Round(t0, t1)
+}
+
+// Verify checks whether the given signature by pk on msg is valid.
+func Verify(pk *PublicKey, msg []byte, signature []byte) bool {
+	var sig unpackedSignature
+	var mu [64]byte
+	var zh VecL
+	var Az, Az2dct1, w1 VecK
+	var ch common.Poly
+	var cp [CTildeSize]byte
+	var w1Packed [PolyW1Size * K]byte
+
+	// Note that Unpack() checked whether ‖z‖_∞ < γ₁ - β
+	// and ensured that there at most ω ones in pk.hint.
+	if !sig.Unpack(signature) {
+		return false
+	}
+
+	// μ = CRH(tr ‖ msg)
+	h := sha3.NewShake256()
+	_, _ = h.Write(pk.tr[:])
+	_, _ = h.Write(msg)
+	_, _ = h.Read(mu[:])
+
+	// Compute Az
+	zh = sig.z
+	zh.NTT()
+
+	for i := 0; i < K; i++ {
+		PolyDotHat(&Az[i], &pk.A[i], &zh)
+	}
+
+	// Next, we compute Az - 2ᵈ·c·t₁.
+	// Note that the coefficients of t₁ are bounded by 256 = 2⁹,
+	// so the coefficients of Az2dct1 will bounded by 2⁹⁺ᵈ = 2²³ < 2q,
+	// which is small enough for NTT().
+	Az2dct1.MulBy2toD(&pk.t1)
+	Az2dct1.NTT()
+	PolyDeriveUniformBall(&ch, sig.c[:32])
+	ch.NTT()
+	for i := 0; i < K; i++ {
+		Az2dct1[i].MulHat(&Az2dct1[i], &ch)
+	}
+	Az2dct1.Sub(&Az, &Az2dct1)
+	Az2dct1.ReduceLe2Q()
+	Az2dct1.InvNTT()
+	Az2dct1.NormalizeAssumingLe2Q()
+
+	// UseHint(pk.hint, Az - 2ᵈ·c·t₁)
+	//    = UseHint(pk.hint, w - c·s₂ + c·t₀)
+	//    = UseHint(pk.hint, r + c·t₀)
+	//    = r₁ = w₁.
+	w1.UseHint(&Az2dct1, &sig.hint)
+	w1.PackW1(w1Packed[:])
+
+	// c' = H(μ, w₁)
+	h.Reset()
+	_, _ = h.Write(mu[:])
+	_, _ = h.Write(w1Packed[:])
+	_, _ = h.Read(cp[:])
+
+	return sig.c == cp
+}
+
+// SignTo signs the given message and writes the signature into signature.
+//
+//nolint:funlen
+func SignTo(sk *PrivateKey, msg []byte, signature []byte) {
+	var mu, rhop [64]byte
+	var w1Packed [PolyW1Size * K]byte
+	var y, yh VecL
+	var w, w0, w1, w0mcs2, ct0, w0mcs2pct0 VecK
+	var ch common.Poly
+	var yNonce uint16
+	var sig unpackedSignature
+
+	if len(signature) < SignatureSize {
+		panic("Signature does not fit in that byteslice")
+	}
+
+	//  μ = CRH(tr ‖ msg)
+	h := sha3.NewShake256()
+	_, _ = h.Write(sk.tr[:])
+	_, _ = h.Write(msg)
+	_, _ = h.Read(mu[:])
+
+	// ρ' = CRH(key ‖ μ)
+	h.Reset()
+	_, _ = h.Write(sk.key[:])
+	if NIST {
+		// We implement the deterministic variant  where rnd is all zeroes.
+		// TODO expose randomized variant?
+		_, _ = h.Write(make([]byte, 32))
+	}
+	_, _ = h.Write(mu[:])
+	_, _ = h.Read(rhop[:])
+
+	// Main rejection loop
+	attempt := 0
+	for {
+		attempt++
+		if attempt >= 576 {
+			// Depending on the mode, one try has a chance between 1/7 and 1/4
+			// of succeeding.  Thus it is safe to say that 576 iterations
+			// are enough as (6/7)⁵⁷⁶ < 2⁻¹²⁸.
+			panic("This should only happen 1 in  2^{128}: something is wrong.")
+		}
+
+		// y = ExpandMask(ρ', key)
+		VecLDeriveUniformLeGamma1(&y, &rhop, yNonce)
+		yNonce += uint16(L)
+
+		// Set w to A y
+		yh = y
+		yh.NTT()
+		for i := 0; i < K; i++ {
+			PolyDotHat(&w[i], &sk.A[i], &yh)
+			w[i].ReduceLe2Q()
+			w[i].InvNTT()
+		}
+
+		// Decompose w into w₀ and w₁
+		w.NormalizeAssumingLe2Q()
+		w.Decompose(&w0, &w1)
+
+		// c~ = H(μ ‖ w₁)
+		w1.PackW1(w1Packed[:])
+		h.Reset()
+		_, _ = h.Write(mu[:])
+		_, _ = h.Write(w1Packed[:])
+		_, _ = h.Read(sig.c[:])
+
+		PolyDeriveUniformBall(&ch, sig.c[:32])
+		ch.NTT()
+
+		// Ensure ‖ w₀ - c·s2 ‖_∞ < γ₂ - β.
+		//
+		// By Lemma 3 of the specification this is equivalent to checking that
+		// both ‖ r₀ ‖_∞ < γ₂ - β and r₁ = w₁, for the decomposition
+		// w - c·s₂	 = r₁ α + r₀ as computed by decompose().
+		// See also §4.1 of the specification.
+		for i := 0; i < K; i++ {
+			w0mcs2[i].MulHat(&ch, &sk.s2h[i])
+			w0mcs2[i].InvNTT()
+		}
+		w0mcs2.Sub(&w0, &w0mcs2)
+		w0mcs2.Normalize()
+
+		if w0mcs2.Exceeds(Gamma2 - Beta) {
+			continue
+		}
+
+		// z = y + c·s₁
+		for i := 0; i < L; i++ {
+			sig.z[i].MulHat(&ch, &sk.s1h[i])
+			sig.z[i].InvNTT()
+		}
+		sig.z.Add(&sig.z, &y)
+		sig.z.Normalize()
+
+		// Ensure  ‖z‖_∞ < γ₁ - β
+		if sig.z.Exceeds(Gamma1 - Beta) {
+			continue
+		}
+
+		// Compute c·t₀
+		for i := 0; i < K; i++ {
+			ct0[i].MulHat(&ch, &sk.t0h[i])
+			ct0[i].InvNTT()
+		}
+		ct0.NormalizeAssumingLe2Q()
+
+		// Ensure ‖c·t₀‖_∞ < γ₂.
+		if ct0.Exceeds(Gamma2) {
+			continue
+		}
+
+		// Create the hint to be able to reconstruct w₁ from w - c·s₂ + c·t0.
+		// Note that we're not using makeHint() in the obvious way as we
+		// do not know whether ‖ sc·s₂ - c·t₀ ‖_∞ < γ₂.  Instead we note
+		// that our makeHint() is actually the same as a makeHint for a
+		// different decomposition:
+		//
+		// Earlier we ensured indirectly with a check that r₁ = w₁ where
+		// r = w - c·s₂.  Hence r₀ = r - r₁ α = w - c·s₂ - w₁ α = w₀ - c·s₂.
+		// Thus  MakeHint(w₀ - c·s₂ + c·t₀, w₁) = MakeHint(r0 + c·t₀, r₁)
+		// and UseHint(w - c·s₂ + c·t₀, w₁) = UseHint(r + c·t₀, r₁).
+		// As we just ensured that ‖ c·t₀ ‖_∞ < γ₂ our usage is correct.
+		w0mcs2pct0.Add(&w0mcs2, &ct0)
+		w0mcs2pct0.NormalizeAssumingLe2Q()
+		hintPop := sig.hint.MakeHint(&w0mcs2pct0, &w1)
+		if hintPop > Omega {
+			continue
+		}
+
+		break
+	}
+
+	sig.Pack(signature[:])
+}
+
+// Computes the public key corresponding to this private key.
+func (sk *PrivateKey) Public() *PublicKey {
+	var t0 VecK
+	pk := &PublicKey{
+		rho: sk.rho,
+		A:   &sk.A,
+		tr:  &sk.tr,
+	}
+	sk.computeT0andT1(&t0, &pk.t1)
+	pk.t1.PackT1(pk.t1p[:])
+	return pk
+}
+
+// Equal returns whether the two public keys are equal
+func (pk *PublicKey) Equal(other *PublicKey) bool {
+	return pk.rho == other.rho && pk.t1 == other.t1
+}
+
+// Equal returns whether the two private keys are equal
+func (sk *PrivateKey) Equal(other *PrivateKey) bool {
+	ret := (subtle.ConstantTimeCompare(sk.rho[:], other.rho[:]) &
+		subtle.ConstantTimeCompare(sk.key[:], other.key[:]) &
+		subtle.ConstantTimeCompare(sk.tr[:], other.tr[:]))
+
+	acc := uint32(0)
+	for i := 0; i < L; i++ {
+		for j := 0; j < common.N; j++ {
+			acc |= sk.s1[i][j] ^ other.s1[i][j]
+		}
+	}
+	for i := 0; i < K; i++ {
+		for j := 0; j < common.N; j++ {
+			acc |= sk.s2[i][j] ^ other.s2[i][j]
+			acc |= sk.t0[i][j] ^ other.t0[i][j]
+		}
+	}
+	return (ret & subtle.ConstantTimeEq(int32(acc), 0)) == 1
+}
diff --git a/sign/mldsa/mldsa65/internal/dilithium_test.go b/sign/mldsa/mldsa65/internal/dilithium_test.go
new file mode 100644
index 000000000..825e7da08
--- /dev/null
+++ b/sign/mldsa/mldsa65/internal/dilithium_test.go
@@ -0,0 +1,144 @@
+// Code generated from mode3/internal/dilithium_test.go by gen.go
+
+package internal
+
+import (
+	"encoding/binary"
+	"testing"
+
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+)
+
+// Checks whether p is normalized.  Only used in tests.
+func PolyNormalized(p *common.Poly) bool {
+	p2 := *p
+	p2.Normalize()
+	return p2 == *p
+}
+
+func BenchmarkSkUnpack(b *testing.B) {
+	var buf [PrivateKeySize]byte
+	var sk PrivateKey
+	for i := 0; i < b.N; i++ {
+		sk.Unpack(&buf)
+	}
+}
+
+func BenchmarkPkUnpack(b *testing.B) {
+	var buf [PublicKeySize]byte
+	var pk PublicKey
+	for i := 0; i < b.N; i++ {
+		pk.Unpack(&buf)
+	}
+}
+
+func BenchmarkVerify(b *testing.B) {
+	// Note that the expansion of the matrix A is done at Unpacking/Keygen
+	// instead of at the moment of verification (as in the reference
+	// implementation.)
+	var seed [32]byte
+	var msg [8]byte
+	var sig [SignatureSize]byte
+	pk, sk := NewKeyFromSeed(&seed)
+	SignTo(sk, msg[:], sig[:])
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		// We should generate a new signature for every verify attempt,
+		// as this influences the time a little bit.  This difference, however,
+		// is small and generating a new signature in between creates a lot
+		// pressure on the allocator which makes an accurate measurement hard.
+		Verify(pk, msg[:], sig[:])
+	}
+}
+
+func BenchmarkSign(b *testing.B) {
+	// Note that the expansion of the matrix A is done at Unpacking/Keygen
+	// instead of at the moment of signing (as in the reference implementation.)
+	var seed [32]byte
+	var msg [8]byte
+	var sig [SignatureSize]byte
+	_, sk := NewKeyFromSeed(&seed)
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		binary.LittleEndian.PutUint64(msg[:], uint64(i))
+		SignTo(sk, msg[:], sig[:])
+	}
+}
+
+func BenchmarkGenerateKey(b *testing.B) {
+	var seed [32]byte
+	for i := 0; i < b.N; i++ {
+		binary.LittleEndian.PutUint64(seed[:], uint64(i))
+		NewKeyFromSeed(&seed)
+	}
+}
+
+func BenchmarkPublicFromPrivate(b *testing.B) {
+	var seed [32]byte
+	for i := 0; i < b.N; i++ {
+		b.StopTimer()
+		binary.LittleEndian.PutUint64(seed[:], uint64(i))
+		_, sk := NewKeyFromSeed(&seed)
+		b.StartTimer()
+		sk.Public()
+	}
+}
+
+func TestSignThenVerifyAndPkSkPacking(t *testing.T) {
+	var seed [common.SeedSize]byte
+	var sig [SignatureSize]byte
+	var msg [8]byte
+	var pkb [PublicKeySize]byte
+	var skb [PrivateKeySize]byte
+	var pk2 PublicKey
+	var sk2 PrivateKey
+	for i := uint64(0); i < 100; i++ {
+		binary.LittleEndian.PutUint64(seed[:], i)
+		pk, sk := NewKeyFromSeed(&seed)
+		if !sk.Equal(sk) {
+			t.Fatal()
+		}
+		for j := uint64(0); j < 10; j++ {
+			binary.LittleEndian.PutUint64(msg[:], j)
+			SignTo(sk, msg[:], sig[:])
+			if !Verify(pk, msg[:], sig[:]) {
+				t.Fatal()
+			}
+		}
+		pk.Pack(&pkb)
+		pk2.Unpack(&pkb)
+		if !pk.Equal(&pk2) {
+			t.Fatal()
+		}
+		sk.Pack(&skb)
+		sk2.Unpack(&skb)
+		if !sk.Equal(&sk2) {
+			t.Fatal()
+		}
+	}
+}
+
+func TestPublicFromPrivate(t *testing.T) {
+	var seed [common.SeedSize]byte
+	for i := uint64(0); i < 100; i++ {
+		binary.LittleEndian.PutUint64(seed[:], i)
+		pk, sk := NewKeyFromSeed(&seed)
+		pk2 := sk.Public()
+		if !pk.Equal(pk2) {
+			t.Fatal()
+		}
+	}
+}
+
+func TestGamma1Size(t *testing.T) {
+	var expected int
+	switch Gamma1Bits {
+	case 17:
+		expected = 576
+	case 19:
+		expected = 640
+	}
+	if expected != PolyLeGamma1Size {
+		t.Fatal()
+	}
+}
diff --git a/sign/mldsa/mldsa65/internal/mat.go b/sign/mldsa/mldsa65/internal/mat.go
new file mode 100644
index 000000000..ceaf634fa
--- /dev/null
+++ b/sign/mldsa/mldsa65/internal/mat.go
@@ -0,0 +1,59 @@
+// Code generated from mode3/internal/mat.go by gen.go
+
+package internal
+
+import (
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+)
+
+// A k by l matrix of polynomials.
+type Mat [K]VecL
+
+// Expands the given seed to a complete matrix.
+//
+// This function is called ExpandA in the specification.
+func (m *Mat) Derive(seed *[32]byte) {
+	if !DeriveX4Available {
+		for i := uint16(0); i < K; i++ {
+			for j := uint16(0); j < L; j++ {
+				PolyDeriveUniform(&m[i][j], seed, (i<<8)+j)
+			}
+		}
+		return
+	}
+
+	idx := 0
+	var nonces [4]uint16
+	var ps [4]*common.Poly
+	for i := uint16(0); i < K; i++ {
+		for j := uint16(0); j < L; j++ {
+			nonces[idx] = (i << 8) + j
+			ps[idx] = &m[i][j]
+			idx++
+			if idx == 4 {
+				idx = 0
+				PolyDeriveUniformX4(ps, seed, nonces)
+			}
+		}
+	}
+	if idx != 0 {
+		for i := idx; i < 4; i++ {
+			ps[i] = nil
+		}
+		PolyDeriveUniformX4(ps, seed, nonces)
+	}
+}
+
+// Set p to the inner product of a and b using pointwise multiplication.
+//
+// Assumes a and b are in Montgomery form and their coefficients are
+// pairwise sufficiently small to multiply, see Poly.MulHat().  Resulting
+// coefficients are bounded by 2Lq.
+func PolyDotHat(p *common.Poly, a, b *VecL) {
+	var t common.Poly
+	*p = common.Poly{} // zero p
+	for i := 0; i < L; i++ {
+		t.MulHat(&a[i], &b[i])
+		p.Add(&t, p)
+	}
+}
diff --git a/sign/mldsa/mldsa65/internal/pack.go b/sign/mldsa/mldsa65/internal/pack.go
new file mode 100644
index 000000000..1854b4197
--- /dev/null
+++ b/sign/mldsa/mldsa65/internal/pack.go
@@ -0,0 +1,270 @@
+// Code generated from mode3/internal/pack.go by gen.go
+
+package internal
+
+import (
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+)
+
+// Writes p with norm less than or equal η into buf, which must be of
+// size PolyLeqEtaSize.
+//
+// Assumes coefficients of p are not normalized, but in [q-η,q+η].
+func PolyPackLeqEta(p *common.Poly, buf []byte) {
+	if DoubleEtaBits == 4 { // compiler eliminates branch
+		j := 0
+		for i := 0; i < PolyLeqEtaSize; i++ {
+			buf[i] = (byte(common.Q+Eta-p[j]) |
+				byte(common.Q+Eta-p[j+1])<<4)
+			j += 2
+		}
+	} else if DoubleEtaBits == 3 {
+		j := 0
+		for i := 0; i < PolyLeqEtaSize; i += 3 {
+			buf[i] = (byte(common.Q+Eta-p[j]) |
+				(byte(common.Q+Eta-p[j+1]) << 3) |
+				(byte(common.Q+Eta-p[j+2]) << 6))
+			buf[i+1] = ((byte(common.Q+Eta-p[j+2]) >> 2) |
+				(byte(common.Q+Eta-p[j+3]) << 1) |
+				(byte(common.Q+Eta-p[j+4]) << 4) |
+				(byte(common.Q+Eta-p[j+5]) << 7))
+			buf[i+2] = ((byte(common.Q+Eta-p[j+5]) >> 1) |
+				(byte(common.Q+Eta-p[j+6]) << 2) |
+				(byte(common.Q+Eta-p[j+7]) << 5))
+			j += 8
+		}
+	} else {
+		panic("eta not supported")
+	}
+}
+
+// Sets p to the polynomial of norm less than or equal η encoded in the
+// given buffer of size PolyLeqEtaSize.
+//
+// Output coefficients of p are not normalized, but in [q-η,q+η] provided
+// buf was created using PackLeqEta.
+//
+// Beware, for arbitrary buf the coefficients of p might end up in
+// the interval [q-2^b,q+2^b] where b is the least b with η≤2^b.
+func PolyUnpackLeqEta(p *common.Poly, buf []byte) {
+	if DoubleEtaBits == 4 { // compiler eliminates branch
+		j := 0
+		for i := 0; i < PolyLeqEtaSize; i++ {
+			p[j] = common.Q + Eta - uint32(buf[i]&15)
+			p[j+1] = common.Q + Eta - uint32(buf[i]>>4)
+			j += 2
+		}
+	} else if DoubleEtaBits == 3 {
+		j := 0
+		for i := 0; i < PolyLeqEtaSize; i += 3 {
+			p[j] = common.Q + Eta - uint32(buf[i]&7)
+			p[j+1] = common.Q + Eta - uint32((buf[i]>>3)&7)
+			p[j+2] = common.Q + Eta - uint32((buf[i]>>6)|((buf[i+1]<<2)&7))
+			p[j+3] = common.Q + Eta - uint32((buf[i+1]>>1)&7)
+			p[j+4] = common.Q + Eta - uint32((buf[i+1]>>4)&7)
+			p[j+5] = common.Q + Eta - uint32((buf[i+1]>>7)|((buf[i+2]<<1)&7))
+			p[j+6] = common.Q + Eta - uint32((buf[i+2]>>2)&7)
+			p[j+7] = common.Q + Eta - uint32((buf[i+2]>>5)&7)
+			j += 8
+		}
+	} else {
+		panic("eta not supported")
+	}
+}
+
+// Writes v with coefficients in {0, 1} of which at most ω non-zero
+// to buf, which must have length ω+k.
+func (v *VecK) PackHint(buf []byte) {
+	// The packed hint starts with the indices of the non-zero coefficients
+	// For instance:
+	//
+	//    (x⁵⁶ + x¹⁰⁰, x²⁵⁵, 0, x² + x²³, x¹)
+	//
+	// Yields
+	//
+	//  56, 100, 255, 2, 23, 1
+	//
+	// Then we pad with zeroes until we have a list of ω items:
+	// //  56, 100, 255, 2, 23, 1, 0, 0, ..., 0
+	//
+	// Then we finish with a list of the switch-over-indices in this
+	// list between polynomials, so:
+	//
+	//  56, 100, 255, 2, 23, 1, 0, 0, ..., 0, 2, 3, 3, 5, 6
+
+	off := uint8(0)
+	for i := 0; i < K; i++ {
+		for j := uint16(0); j < common.N; j++ {
+			if v[i][j] != 0 {
+				buf[off] = uint8(j)
+				off++
+			}
+		}
+		buf[Omega+i] = off
+	}
+	for ; off < Omega; off++ {
+		buf[off] = 0
+	}
+}
+
+// Sets v to the vector encoded using VecK.PackHint()
+//
+// Returns whether unpacking was successful.
+func (v *VecK) UnpackHint(buf []byte) bool {
+	// A priori, there would be several reasonable ways to encode the same
+	// hint vector.  We take care to only allow only one encoding, to ensure
+	// "strong unforgeability".
+	//
+	// See PackHint() source for description of the encoding.
+	*v = VecK{}         // zero v
+	prevSOP := uint8(0) // previous switch-over-point
+	for i := 0; i < K; i++ {
+		SOP := buf[Omega+i]
+		if SOP < prevSOP || SOP > Omega {
+			return false // ensures switch-over-points are increasing
+		}
+		for j := prevSOP; j < SOP; j++ {
+			if j > prevSOP && buf[j] <= buf[j-1] {
+				return false // ensures indices are increasing (within a poly)
+			}
+			v[i][buf[j]] = 1
+		}
+		prevSOP = SOP
+	}
+	for j := prevSOP; j < Omega; j++ {
+		if buf[j] != 0 {
+			return false // ensures padding indices are zero
+		}
+	}
+
+	return true
+}
+
+// Sets p to the polynomial packed into buf by PolyPackLeGamma1.
+//
+// p will be normalized.
+func PolyUnpackLeGamma1(p *common.Poly, buf []byte) {
+	if Gamma1Bits == 17 {
+		j := 0
+		for i := 0; i < PolyLeGamma1Size; i += 9 {
+			p0 := uint32(buf[i]) | (uint32(buf[i+1]) << 8) |
+				(uint32(buf[i+2]&0x3) << 16)
+			p1 := uint32(buf[i+2]>>2) | (uint32(buf[i+3]) << 6) |
+				(uint32(buf[i+4]&0xf) << 14)
+			p2 := uint32(buf[i+4]>>4) | (uint32(buf[i+5]) << 4) |
+				(uint32(buf[i+6]&0x3f) << 12)
+			p3 := uint32(buf[i+6]>>6) | (uint32(buf[i+7]) << 2) |
+				(uint32(buf[i+8]) << 10)
+
+			// coefficients in [0,…,2γ₁)
+			p0 = Gamma1 - p0 // (-γ₁,…,γ₁]
+			p1 = Gamma1 - p1
+			p2 = Gamma1 - p2
+			p3 = Gamma1 - p3
+
+			p0 += uint32(int32(p0)>>31) & common.Q // normalize
+			p1 += uint32(int32(p1)>>31) & common.Q
+			p2 += uint32(int32(p2)>>31) & common.Q
+			p3 += uint32(int32(p3)>>31) & common.Q
+
+			p[j] = p0
+			p[j+1] = p1
+			p[j+2] = p2
+			p[j+3] = p3
+
+			j += 4
+		}
+	} else if Gamma1Bits == 19 {
+		j := 0
+		for i := 0; i < PolyLeGamma1Size; i += 5 {
+			p0 := uint32(buf[i]) | (uint32(buf[i+1]) << 8) |
+				(uint32(buf[i+2]&0xf) << 16)
+			p1 := uint32(buf[i+2]>>4) | (uint32(buf[i+3]) << 4) |
+				(uint32(buf[i+4]) << 12)
+
+			p0 = Gamma1 - p0
+			p1 = Gamma1 - p1
+
+			p0 += uint32(int32(p0)>>31) & common.Q
+			p1 += uint32(int32(p1)>>31) & common.Q
+
+			p[j] = p0
+			p[j+1] = p1
+
+			j += 2
+		}
+	} else {
+		panic("γ₁ not supported")
+	}
+}
+
+// Writes p whose coefficients are in (-γ₁,γ₁] into buf
+// which has to be of length PolyLeGamma1Size.
+//
+// Assumes p is normalized.
+func PolyPackLeGamma1(p *common.Poly, buf []byte) {
+	if Gamma1Bits == 17 {
+		j := 0
+		// coefficients in [0,…,γ₁] ∪ (q-γ₁,…,q)
+		for i := 0; i < PolyLeGamma1Size; i += 9 {
+			p0 := Gamma1 - p[j]                    // [0,…,γ₁] ∪ (γ₁-q,…,2γ₁-q)
+			p0 += uint32(int32(p0)>>31) & common.Q // [0,…,2γ₁)
+			p1 := Gamma1 - p[j+1]
+			p1 += uint32(int32(p1)>>31) & common.Q
+			p2 := Gamma1 - p[j+2]
+			p2 += uint32(int32(p2)>>31) & common.Q
+			p3 := Gamma1 - p[j+3]
+			p3 += uint32(int32(p3)>>31) & common.Q
+
+			buf[i+0] = byte(p0)
+			buf[i+1] = byte(p0 >> 8)
+			buf[i+2] = byte(p0>>16) | byte(p1<<2)
+			buf[i+3] = byte(p1 >> 6)
+			buf[i+4] = byte(p1>>14) | byte(p2<<4)
+			buf[i+5] = byte(p2 >> 4)
+			buf[i+6] = byte(p2>>12) | byte(p3<<6)
+			buf[i+7] = byte(p3 >> 2)
+			buf[i+8] = byte(p3 >> 10)
+
+			j += 4
+		}
+	} else if Gamma1Bits == 19 {
+		j := 0
+		for i := 0; i < PolyLeGamma1Size; i += 5 {
+			// Coefficients are in [0, γ₁] ∪ (Q-γ₁, Q)
+			p0 := Gamma1 - p[j]
+			p0 += uint32(int32(p0)>>31) & common.Q
+			p1 := Gamma1 - p[j+1]
+			p1 += uint32(int32(p1)>>31) & common.Q
+
+			buf[i+0] = byte(p0)
+			buf[i+1] = byte(p0 >> 8)
+			buf[i+2] = byte(p0>>16) | byte(p1<<4)
+			buf[i+3] = byte(p1 >> 4)
+			buf[i+4] = byte(p1 >> 12)
+
+			j += 2
+		}
+	} else {
+		panic("γ₁ not supported")
+	}
+}
+
+// Pack w₁ into buf, which must be of length PolyW1Size.
+//
+// Assumes w₁ is normalized.
+func PolyPackW1(p *common.Poly, buf []byte) {
+	if Gamma1Bits == 19 {
+		p.PackLe16(buf)
+	} else if Gamma1Bits == 17 {
+		j := 0
+		for i := 0; i < PolyW1Size; i += 3 {
+			buf[i] = byte(p[j]) | byte(p[j+1]<<6)
+			buf[i+1] = byte(p[j+1]>>2) | byte(p[j+2]<<4)
+			buf[i+2] = byte(p[j+2]>>4) | byte(p[j+3]<<2)
+			j += 4
+		}
+	} else {
+		panic("unsupported γ₁")
+	}
+}
diff --git a/sign/mldsa/mldsa65/internal/pack_test.go b/sign/mldsa/mldsa65/internal/pack_test.go
new file mode 100644
index 000000000..f952c6a09
--- /dev/null
+++ b/sign/mldsa/mldsa65/internal/pack_test.go
@@ -0,0 +1,93 @@
+// Code generated from mode3/internal/pack_test.go by gen.go
+
+package internal
+
+import (
+	"testing"
+
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+)
+
+func TestPolyPackLeqEta(t *testing.T) {
+	var p1, p2 common.Poly
+	var seed [64]byte
+	var buf [PolyLeqEtaSize]byte
+
+	for i := uint16(0); i < 100; i++ {
+		// Note that DeriveUniformLeqEta sets p to the right kind of
+		// unnormalized vector.
+		PolyDeriveUniformLeqEta(&p1, &seed, i)
+		for j := 0; j < PolyLeqEtaSize; j++ {
+			if p1[j] < common.Q-Eta || p1[j] > common.Q+Eta {
+				t.Fatalf("DerveUniformLeqEta out of bounds")
+			}
+		}
+		PolyPackLeqEta(&p1, buf[:])
+		PolyUnpackLeqEta(&p2, buf[:])
+		if p1 != p2 {
+			t.Fatalf("%v != %v", p1, p2)
+		}
+	}
+}
+
+func TestPolyPackT1(t *testing.T) {
+	var p1, p2 common.Poly
+	var seed [32]byte
+	var buf [common.PolyT1Size]byte
+
+	for i := uint16(0); i < 100; i++ {
+		PolyDeriveUniform(&p1, &seed, i)
+		p1.Normalize()
+		for j := 0; j < common.N; j++ {
+			p1[j] &= 0x1ff
+		}
+		p1.PackT1(buf[:])
+		p2.UnpackT1(buf[:])
+		if p1 != p2 {
+			t.Fatalf("%v != %v", p1, p2)
+		}
+	}
+}
+
+func TestPolyPackT0(t *testing.T) {
+	var p, p0, p1, p2 common.Poly
+	var seed [32]byte
+	var buf [common.PolyT0Size]byte
+
+	for i := uint16(0); i < 100; i++ {
+		PolyDeriveUniform(&p, &seed, i)
+		p.Normalize()
+		p.Power2Round(&p0, &p1)
+
+		p0.PackT0(buf[:])
+		p2.UnpackT0(buf[:])
+		if p0 != p2 {
+			t.Fatalf("%v !=\n%v", p0, p2)
+		}
+	}
+}
+
+func BenchmarkUnpackLeGamma1(b *testing.B) {
+	var p common.Poly
+	var buf [PolyLeGamma1Size]byte
+	for i := 0; i < b.N; i++ {
+		PolyUnpackLeGamma1(&p, buf[:])
+	}
+}
+
+func TestPolyPackLeGamma1(t *testing.T) {
+	var p0, p1 common.Poly
+	var seed [64]byte
+	var buf [PolyLeGamma1Size]byte
+
+	for i := uint16(0); i < 100; i++ {
+		PolyDeriveUniformLeGamma1(&p0, &seed, i)
+		p0.Normalize()
+
+		PolyPackLeGamma1(&p0, buf[:])
+		PolyUnpackLeGamma1(&p1, buf[:])
+		if p0 != p1 {
+			t.Fatalf("%v != %v", p0, p1)
+		}
+	}
+}
diff --git a/sign/mldsa/mldsa65/internal/params.go b/sign/mldsa/mldsa65/internal/params.go
new file mode 100644
index 000000000..c7872fc11
--- /dev/null
+++ b/sign/mldsa/mldsa65/internal/params.go
@@ -0,0 +1,19 @@
+// Code generated from params.templ.go. DO NOT EDIT.
+
+package internal
+
+const (
+	Name          = "ML-DSA-65"
+	UseAES        = false
+	K             = 6
+	L             = 5
+	Eta           = 4
+	DoubleEtaBits = 4
+	Omega         = 55
+	Tau           = 49
+	Gamma1Bits    = 19
+	Gamma2        = 261888
+	NIST          = true
+	TRSize        = 64
+	CTildeSize    = 48
+)
diff --git a/sign/mldsa/mldsa65/internal/rounding.go b/sign/mldsa/mldsa65/internal/rounding.go
new file mode 100644
index 000000000..58123c090
--- /dev/null
+++ b/sign/mldsa/mldsa65/internal/rounding.go
@@ -0,0 +1,142 @@
+// Code generated from mode3/internal/rounding.go by gen.go
+
+package internal
+
+import (
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+)
+
+// Splits 0 ≤ a < q into a₀ and a₁ with a = a₁*α + a₀ with -α/2 < a₀ ≤ α/2,
+// except for when we would have a₁ = (q-1)/α in which case a₁=0 is taken
+// and -α/2 ≤ a₀ < 0.  Returns a₀ + q.  Note 0 ≤ a₁ < (q-1)/α.
+// Recall α = 2γ₂.
+func decompose(a uint32) (a0plusQ, a1 uint32) {
+	// a₁ = ⌈a / 128⌉
+	a1 = (a + 127) >> 7
+
+	if Alpha == 523776 {
+		// 1025/2²² is close enough to 1/4092 so that a₁
+		// becomes a/α rounded down.
+		a1 = ((a1*1025 + (1 << 21)) >> 22)
+
+		// For the corner-case a₁ = (q-1)/α = 16, we have to set a₁=0.
+		a1 &= 15
+	} else if Alpha == 190464 {
+		// 1488/2²⁴ is close enough to 1/1488 so that a₁
+		// becomes a/α rounded down.
+		a1 = ((a1 * 11275) + (1 << 23)) >> 24
+
+		// For the corner-case a₁ = (q-1)/α = 44, we have to set a₁=0.
+		a1 ^= uint32(int32(43-a1)>>31) & a1
+	} else {
+		panic("unsupported α")
+	}
+
+	a0plusQ = a - a1*Alpha
+
+	// In the corner-case, when we set a₁=0, we will incorrectly
+	// have a₀ > (q-1)/2 and we'll need to subtract q.  As we
+	// return a₀ + q, that comes down to adding q if a₀ < (q-1)/2.
+	a0plusQ += uint32(int32(a0plusQ-(common.Q-1)/2)>>31) & common.Q
+
+	return
+}
+
+// Assume 0 ≤ r, f < Q with ‖f‖_∞ ≤ α/2.  Decompose r as r = r1*α + r0 as
+// computed by decompose().  Write r' := r - f (mod Q).  Now, decompose
+// r'=r-f again as  r' = r'1*α + r'0 using decompose().  As f is small, we
+// have r'1 = r1 + h, where h ∈ {-1, 0, 1}.  makeHint() computes |h|
+// given z0 := r0 - f (mod Q) and r1.  With |h|, which is called the hint,
+// we can reconstruct r1 using only r' = r - f, which is done by useHint().
+// To wit:
+//
+//	useHint( r - f, makeHint( r0 - f, r1 ) ) = r1.
+//
+// Assumes 0 ≤ z0 < Q.
+func makeHint(z0, r1 uint32) uint32 {
+	// If -α/2 < r0 - f ≤ α/2, then r1*α + r0 - f is a valid decomposition of r'
+	// with the restrictions of decompose() and so r'1 = r1.  So the hint
+	// should be 0. This is covered by the first two inequalities.
+	// There is one other case: if r0 - f = -α/2, then r1*α + r0 - f is also
+	// a valid decomposition if r1 = 0.  In the other cases a one is carried
+	// and the hint should be 1.
+	if z0 <= Gamma2 || z0 > common.Q-Gamma2 || (z0 == common.Q-Gamma2 && r1 == 0) {
+		return 0
+	}
+	return 1
+}
+
+// Uses the hint created by makeHint() to reconstruct r1 from r'=r-f; see
+// documentation of makeHint() for context.
+// Assumes 0 ≤ r' < Q.
+func useHint(rp uint32, hint uint32) uint32 {
+	rp0plusQ, rp1 := decompose(rp)
+	if hint == 0 {
+		return rp1
+	}
+	if rp0plusQ > common.Q {
+		return (rp1 + 1) & 15
+	}
+	return (rp1 - 1) & 15
+}
+
+// Sets p to the hint polynomial for p0 the modified low bits and p1
+// the unmodified high bits --- see makeHint().
+//
+// Returns the number of ones in the hint polynomial.
+func PolyMakeHint(p, p0, p1 *common.Poly) (pop uint32) {
+	for i := 0; i < common.N; i++ {
+		h := makeHint(p0[i], p1[i])
+		pop += h
+		p[i] = h
+	}
+	return
+}
+
+// Computes corrections to the high bits of the polynomial q according
+// to the hints in h and sets p to the corrected high bits.  Returns p.
+func PolyUseHint(p, q, hint *common.Poly) {
+	var q0PlusQ common.Poly
+
+	// See useHint() and makeHint() for an explanation.  We reimplement it
+	// here so that we can call Poly.Decompose(), which might be way faster
+	// than calling decompose() in a loop (for instance when having AVX2.)
+
+	PolyDecompose(q, &q0PlusQ, p)
+
+	for i := 0; i < common.N; i++ {
+		if hint[i] == 0 {
+			continue
+		}
+		if Gamma2 == 261888 {
+			if q0PlusQ[i] > common.Q {
+				p[i] = (p[i] + 1) & 15
+			} else {
+				p[i] = (p[i] - 1) & 15
+			}
+		} else if Gamma2 == 95232 {
+			if q0PlusQ[i] > common.Q {
+				if p[i] == 43 {
+					p[i] = 0
+				} else {
+					p[i]++
+				}
+			} else {
+				if p[i] == 0 {
+					p[i] = 43
+				} else {
+					p[i]--
+				}
+			}
+		} else {
+			panic("unsupported γ₂")
+		}
+	}
+}
+
+// Splits each of the coefficients of p using decompose.
+func PolyDecompose(p, p0PlusQ, p1 *common.Poly) {
+	for i := 0; i < common.N; i++ {
+		p0PlusQ[i], p1[i] = decompose(p[i])
+	}
+}
diff --git a/sign/mldsa/mldsa65/internal/rounding_test.go b/sign/mldsa/mldsa65/internal/rounding_test.go
new file mode 100644
index 000000000..ad653ca3f
--- /dev/null
+++ b/sign/mldsa/mldsa65/internal/rounding_test.go
@@ -0,0 +1,81 @@
+// Code generated from mode3/internal/rounding_test.go by gen.go
+
+package internal
+
+import (
+	"flag"
+	"testing"
+
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+)
+
+var runVeryLongTest = flag.Bool("very-long", false, "runs very long tests")
+
+func TestDecompose(t *testing.T) {
+	for a := uint32(0); a < common.Q; a++ {
+		a0PlusQ, a1 := decompose(a)
+		a0 := int32(a0PlusQ) - int32(common.Q)
+		recombined := a0 + int32(Alpha*a1)
+		if a1 == 0 && recombined < 0 {
+			recombined += common.Q
+			if -(Alpha/2) > a0 || a0 >= 0 {
+				t.Fatalf("decompose(%v): a0 out of bounds", a)
+			}
+		} else {
+			if (-(Alpha / 2) >= a0) || (a0 > Alpha/2) {
+				t.Fatalf("decompose(%v): a0 out of bounds", a)
+			}
+		}
+		if int32(a) != recombined {
+			t.Fatalf("decompose(%v) doesn't recombine %v %v", a, a0, a1)
+		}
+	}
+}
+
+func TestMakeHint(t *testing.T) {
+	if !*runVeryLongTest {
+		t.SkipNow()
+	}
+	for w := uint32(0); w < common.Q; w++ {
+		w0, w1 := decompose(w)
+		for fn := uint32(0); fn <= Gamma2; fn++ {
+			fsign := false
+			for {
+				var f uint32
+				if fsign {
+					if fn == 0 {
+						break
+					}
+					f = common.Q - fn
+				} else {
+					f = fn
+				}
+
+				hint := makeHint(common.ReduceLe2Q(w0+common.Q-f), w1)
+				w1p := useHint(common.ReduceLe2Q(w+common.Q-f), hint)
+				if w1p != w1 {
+					t.Fatal()
+				}
+
+				if fsign {
+					break
+				}
+				fsign = true
+			}
+		}
+	}
+}
+
+func BenchmarkDecompose(b *testing.B) {
+	var p, p0, p1 common.Poly
+	for i := 0; i < b.N; i++ {
+		PolyDecompose(&p, &p0, &p1)
+	}
+}
+
+func BenchmarkMakeHint(b *testing.B) {
+	var p, p0, p1 common.Poly
+	for i := 0; i < b.N; i++ {
+		PolyMakeHint(&p, &p0, &p1)
+	}
+}
diff --git a/sign/mldsa/mldsa65/internal/sample.go b/sign/mldsa/mldsa65/internal/sample.go
new file mode 100644
index 000000000..62c261332
--- /dev/null
+++ b/sign/mldsa/mldsa65/internal/sample.go
@@ -0,0 +1,370 @@
+// Code generated from mode3/internal/sample.go by gen.go
+
+package internal
+
+import (
+	"encoding/binary"
+
+	"github.com/cloudflare/circl/internal/sha3"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+	"github.com/cloudflare/circl/simd/keccakf1600"
+)
+
+// DeriveX4Available indicates whether the system supports the quick fourway
+// sampling variants like PolyDeriveUniformX4.
+var DeriveX4Available = keccakf1600.IsEnabledX4() && !UseAES
+
+// For each i, sample ps[i] uniformly from the given seed and nonces[i].
+// ps[i] may be nil and is ignored in that case.
+//
+// Can only be called when DeriveX4Available is true.
+func PolyDeriveUniformX4(ps [4]*common.Poly, seed *[32]byte, nonces [4]uint16) {
+	var perm keccakf1600.StateX4
+	state := perm.Initialize(false)
+
+	// Absorb the seed in the four states
+	for i := 0; i < 4; i++ {
+		v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)])
+		for j := 0; j < 4; j++ {
+			state[i*4+j] = v
+		}
+	}
+
+	// Absorb the nonces, the SHAKE128 domain separator (0b1111), the
+	// start of the padding (0b...001) and the end of the padding 0b100...
+	// Recall that the rate of SHAKE128 is 168 --- i.e. 21 uint64s.
+	for j := 0; j < 4; j++ {
+		state[4*4+j] = uint64(nonces[j]) | (0x1f << 16)
+		state[20*4+j] = 0x80 << 56
+	}
+
+	var idx [4]int // indices into ps
+	for j := 0; j < 4; j++ {
+		if ps[j] == nil {
+			idx[j] = common.N // mark nil polynomial as completed
+		}
+	}
+
+	done := false
+	for !done {
+		// Applies KeccaK-f[1600] to state to get the next 21 uint64s of each
+		// of the four SHAKE128 streams.
+		perm.Permute()
+
+		done = true
+
+	PolyLoop:
+		for j := 0; j < 4; j++ {
+			if idx[j] == common.N {
+				continue
+			}
+			for i := 0; i < 7; i++ {
+				var t [8]uint32
+				t[0] = uint32(state[i*3*4+j] & 0x7fffff)
+				t[1] = uint32((state[i*3*4+j] >> 24) & 0x7fffff)
+				t[2] = uint32((state[i*3*4+j] >> 48) |
+					((state[(i*3+1)*4+j] & 0x7f) << 16))
+				t[3] = uint32((state[(i*3+1)*4+j] >> 8) & 0x7fffff)
+				t[4] = uint32((state[(i*3+1)*4+j] >> 32) & 0x7fffff)
+				t[5] = uint32((state[(i*3+1)*4+j] >> 56) |
+					((state[(i*3+2)*4+j] & 0x7fff) << 8))
+				t[6] = uint32((state[(i*3+2)*4+j] >> 16) & 0x7fffff)
+				t[7] = uint32((state[(i*3+2)*4+j] >> 40) & 0x7fffff)
+
+				for k := 0; k < 8; k++ {
+					if t[k] < common.Q {
+						ps[j][idx[j]] = t[k]
+						idx[j]++
+						if idx[j] == common.N {
+							continue PolyLoop
+						}
+					}
+				}
+			}
+			done = false
+		}
+	}
+}
+
+// Sample p uniformly from the given seed and nonce.
+//
+// p will be normalized.
+func PolyDeriveUniform(p *common.Poly, seed *[32]byte, nonce uint16) {
+	var i, length int
+	var buf [12 * 16]byte // fits 168B SHAKE-128 rate and 12 16B AES blocks
+
+	if UseAES {
+		length = 12 * 16
+	} else {
+		length = 168
+	}
+
+	sample := func() {
+		// Note that 3 divides into 168 and 12*16, so we use up buf completely.
+		for j := 0; j < length && i < common.N; j += 3 {
+			t := (uint32(buf[j]) | (uint32(buf[j+1]) << 8) |
+				(uint32(buf[j+2]) << 16)) & 0x7fffff
+
+			// We use rejection sampling
+			if t < common.Q {
+				p[i] = t
+				i++
+			}
+		}
+	}
+
+	if UseAES {
+		h := common.NewAesStream128(seed, nonce)
+
+		for i < common.N {
+			h.SqueezeInto(buf[:length])
+			sample()
+		}
+	} else {
+		var iv [32 + 2]byte // 32 byte seed + uint16 nonce
+		h := sha3.NewShake128()
+		copy(iv[:32], seed[:])
+		iv[32] = uint8(nonce)
+		iv[33] = uint8(nonce >> 8)
+		_, _ = h.Write(iv[:])
+
+		for i < common.N {
+			_, _ = h.Read(buf[:168])
+			sample()
+		}
+	}
+}
+
+// Sample p uniformly with coefficients of norm less than or equal η,
+// using the given seed and nonce.
+//
+// p will not be normalized, but will have coefficients in [q-η,q+η].
+func PolyDeriveUniformLeqEta(p *common.Poly, seed *[64]byte, nonce uint16) {
+	// Assumes 2 < η < 8.
+	var i, length int
+	var buf [9 * 16]byte // fits 136B SHAKE-256 rate and 9 16B AES blocks
+
+	if UseAES {
+		length = 9 * 16
+	} else {
+		length = 136
+	}
+
+	sample := func() {
+		// We use rejection sampling
+		for j := 0; j < length && i < common.N; j++ {
+			t1 := uint32(buf[j]) & 15
+			t2 := uint32(buf[j]) >> 4
+			if Eta == 2 { // branch is eliminated by compiler
+				if t1 <= 14 {
+					t1 -= ((205 * t1) >> 10) * 5 // reduce mod  5
+					p[i] = common.Q + Eta - t1
+					i++
+				}
+				if t2 <= 14 && i < common.N {
+					t2 -= ((205 * t2) >> 10) * 5 // reduce mod 5
+					p[i] = common.Q + Eta - t2
+					i++
+				}
+			} else if Eta == 4 {
+				if t1 <= 2*Eta {
+					p[i] = common.Q + Eta - t1
+					i++
+				}
+				if t2 <= 2*Eta && i < common.N {
+					p[i] = common.Q + Eta - t2
+					i++
+				}
+			} else {
+				panic("unsupported η")
+			}
+		}
+	}
+
+	if UseAES {
+		h := common.NewAesStream256(seed, nonce)
+
+		for i < common.N {
+			h.SqueezeInto(buf[:length])
+			sample()
+		}
+	} else {
+		var iv [64 + 2]byte // 64 byte seed + uint16 nonce
+
+		h := sha3.NewShake256()
+		copy(iv[:64], seed[:])
+		iv[64] = uint8(nonce)
+		iv[65] = uint8(nonce >> 8)
+
+		// 136 is SHAKE-256 rate
+		_, _ = h.Write(iv[:])
+
+		for i < common.N {
+			_, _ = h.Read(buf[:136])
+			sample()
+		}
+	}
+}
+
+// Sample v[i] uniformly with coefficients in (-γ₁,…,γ₁]  using the
+// given seed and nonce+i
+//
+// p will be normalized.
+func VecLDeriveUniformLeGamma1(v *VecL, seed *[64]byte, nonce uint16) {
+	for i := 0; i < L; i++ {
+		PolyDeriveUniformLeGamma1(&v[i], seed, nonce+uint16(i))
+	}
+}
+
+// Sample p uniformly with coefficients in (-γ₁,…,γK1s] using the
+// given seed and nonce.
+//
+// p will be normalized.
+func PolyDeriveUniformLeGamma1(p *common.Poly, seed *[64]byte, nonce uint16) {
+	var buf [PolyLeGamma1Size]byte
+
+	if UseAES {
+		h := common.NewAesStream256(seed, nonce)
+		h.SqueezeInto(buf[:])
+	} else {
+		var iv [66]byte
+		h := sha3.NewShake256()
+		copy(iv[:64], seed[:])
+		iv[64] = uint8(nonce)
+		iv[65] = uint8(nonce >> 8)
+		_, _ = h.Write(iv[:])
+		_, _ = h.Read(buf[:])
+	}
+
+	PolyUnpackLeGamma1(p, buf[:])
+}
+
+// For each i, sample ps[i] uniformly with τ non-zero coefficients in {q-1,1}
+// using the given seed and w1[i].  ps[i] may be nil and is ignored
+// in that case.  ps[i] will be normalized.
+//
+// Can only be called when DeriveX4Available is true.
+//
+// This function is currently not used (yet).
+func PolyDeriveUniformBallX4(ps [4]*common.Poly, seed []byte) {
+	var perm keccakf1600.StateX4
+	state := perm.Initialize(false)
+
+	// Absorb the seed in the four states
+	for i := 0; i < 32/8; i++ {
+		v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)])
+		for j := 0; j < 4; j++ {
+			state[i*4+j] = v
+		}
+	}
+
+	// SHAKE256 domain separator and padding
+	for j := 0; j < 4; j++ {
+		state[(32/8)*4+j] ^= 0x1f
+		state[16*4+j] ^= 0x80 << 56
+	}
+	perm.Permute()
+
+	var signs [4]uint64
+	var idx [4]uint16 // indices into ps
+
+	for j := 0; j < 4; j++ {
+		if ps[j] != nil {
+			signs[j] = state[j]
+			*ps[j] = common.Poly{} // zero ps[j]
+			idx[j] = common.N - Tau
+		} else {
+			idx[j] = common.N // mark as completed
+		}
+	}
+
+	stateOffset := 1
+	for {
+		done := true
+
+	PolyLoop:
+		for j := 0; j < 4; j++ {
+			if idx[j] == common.N {
+				continue
+			}
+
+			for i := stateOffset; i < 17; i++ {
+				var bs [8]byte
+				binary.LittleEndian.PutUint64(bs[:], state[4*i+j])
+				for k := 0; k < 8; k++ {
+					b := uint16(bs[k])
+
+					if b > idx[j] {
+						continue
+					}
+
+					ps[j][idx[j]] = ps[j][b]
+					ps[j][b] = 1
+					// Takes least significant bit of signs and uses it for the sign.
+					// Note 1 ^ (1 | (Q-1)) = Q-1.
+					ps[j][b] ^= uint32((-(signs[j] & 1)) & (1 | (common.Q - 1)))
+					signs[j] >>= 1
+
+					idx[j]++
+					if idx[j] == common.N {
+						continue PolyLoop
+					}
+				}
+			}
+
+			done = false
+		}
+
+		if done {
+			break
+		}
+
+		perm.Permute()
+		stateOffset = 0
+	}
+}
+
+// Samples p uniformly with τ non-zero coefficients in {q-1,1}.
+//
+// The polynomial p will be normalized.
+func PolyDeriveUniformBall(p *common.Poly, seed []byte) {
+	var buf [136]byte // SHAKE-256 rate is 136
+
+	h := sha3.NewShake256()
+	_, _ = h.Write(seed[:])
+	_, _ = h.Read(buf[:])
+
+	// Essentially we generate a sequence of τ ones or minus ones,
+	// prepend 196 zeroes and shuffle the concatenation using the
+	// usual algorithm (Fisher--Yates.)
+	signs := binary.LittleEndian.Uint64(buf[:])
+	bufOff := 8 // offset into buf
+
+	*p = common.Poly{} // zero p
+	for i := uint16(common.N - Tau); i < common.N; i++ {
+		var b uint16
+
+		// Find location of where to move the new coefficient to using
+		// rejection sampling.
+		for {
+			if bufOff >= 136 {
+				_, _ = h.Read(buf[:])
+				bufOff = 0
+			}
+
+			b = uint16(buf[bufOff])
+			bufOff++
+
+			if b <= i {
+				break
+			}
+		}
+
+		p[i] = p[b]
+		p[b] = 1
+		// Takes least significant bit of signs and uses it for the sign.
+		// Note 1 ^ (1 | (Q-1)) = Q-1.
+		p[b] ^= uint32((-(signs & 1)) & (1 | (common.Q - 1)))
+		signs >>= 1
+	}
+}
diff --git a/sign/mldsa/mldsa65/internal/sample_test.go b/sign/mldsa/mldsa65/internal/sample_test.go
new file mode 100644
index 000000000..2059599eb
--- /dev/null
+++ b/sign/mldsa/mldsa65/internal/sample_test.go
@@ -0,0 +1,266 @@
+// Code generated from mode3/internal/sample_test.go by gen.go
+
+package internal
+
+import (
+	"encoding/binary"
+	"testing"
+
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+)
+
+func TestVectorDeriveUniform(t *testing.T) {
+	var p, p2 common.Poly
+	var seed [32]byte
+	if UseAES {
+		p2 = common.Poly{
+			6724291, 310295, 6949524, 4464039, 1482136, 2522903,
+			7025059, 3006320, 7286364, 7516512, 3361305, 1955529,
+			4765954, 1725325, 6933066, 4299100, 6625173, 4272792,
+			583034, 4971409, 2259140, 7715362, 3975394, 2341624,
+			5481174, 8150082, 365246, 5491939, 1083120, 7517301,
+			3104783, 2475292, 184149, 6425226, 4591622, 5964030,
+			4729604, 5471092, 1828227, 1082044, 2516245, 1692580,
+			3274844, 5443294, 7256740, 4989638, 3191250, 7479519,
+			5124211, 5603858, 1230692, 2513454, 2828034, 4254312,
+			1512596, 5245430, 5517392, 2814840, 932545, 6826733,
+			3511094, 4075348, 3233981, 7268882, 2913733, 4870249,
+			4123492, 8124406, 4016949, 5478752, 2750895, 603525,
+			5724798, 3985430, 3483012, 6434230, 3136996, 8297976,
+			4107616, 7307748, 6962904, 7544473, 1193110, 3448595,
+			4814773, 5607932, 8221314, 1054046, 1541208, 1866050,
+			8227412, 2925778, 5293953, 2065416, 4972769, 3616283,
+			7990594, 1105530, 7121836, 1170740, 7417431, 633146,
+			253820, 7235019, 3539504, 6807707, 451390, 5481526,
+			2859902, 1063061, 4579730, 7126652, 7033767, 4294814,
+			1414604, 7620048, 1953268, 8304556, 1156814, 1182881,
+			5311519, 3057534, 5277666, 682843, 2070398, 2874278,
+			4859533, 6376664, 6694074, 1590242, 2620706, 8331066,
+			5643845, 5037538, 2891516, 7004879, 3754327, 5031296,
+			5463118, 2420870, 8116529, 5517696, 7435129, 3873963,
+			710407, 713806, 175647, 4274571, 2655021, 7319503,
+			3027243, 7129679, 4213435, 2429323, 4643873, 4568526,
+			649664, 1720514, 6497260, 2683517, 7672754, 7105190,
+			3148405, 5898369, 5667677, 8050874, 1587139, 7315260,
+			4337416, 2202680, 2338714, 557467, 6752058, 2469794,
+			485071, 1617604, 3590498, 2151466, 2005823, 7727956,
+			7776292, 6783433, 6787146, 1732833, 3596857, 7436284,
+			4483349, 4970142, 4472608, 6478342, 1236215, 5695744,
+			2280717, 2889355, 3233946, 5187812, 978685, 5177364,
+			2922353, 4824807, 5302883, 6739803, 8092453, 5883903,
+			816553, 6041174, 8317591, 1459178, 5332455, 1835058,
+			1368601, 2820950, 3479224, 2589540, 7992934, 3421045,
+			4657128, 8292902, 4153567, 3553988, 7830320, 6722913,
+			2555309, 4149801, 8328975, 1560545, 7757473, 3106458,
+			4310856, 7135453, 3481032, 652626, 1841361, 8126828,
+			6250018, 300536, 7380070, 8174419, 1418793, 6208185,
+			3906256, 6679016, 1605701, 3561489, 5819724, 5746996,
+			8044214, 7087187, 7102330, 4962927, 4253983, 7108567,
+			4119736, 6584065, 441634, 6941656,
+		}
+	} else {
+		p2 = common.Poly{
+			2901364, 562527, 5258502, 3885002, 4190126, 4460268, 6884052,
+			3514511, 5383040, 213206, 2155865, 5179607, 3551954, 2312357,
+			6066350, 8126097, 1179080, 4787182, 6552182, 6713644,
+			1561067, 7626063, 7859743, 5052321, 7032876, 7815031, 157938,
+			1865184, 490802, 5717642, 3451902, 7000218, 3743250, 1677431,
+			1875427, 5596150, 671623, 3819041, 6247594, 1014875, 4933545,
+			7122446, 6682963, 3388398, 3335295, 943002, 1145083, 3113071,
+			105967, 1916675, 7474561, 1107006, 700548, 2147909, 1603855,
+			5049181, 437882, 6118899, 5656914, 6731065, 3066622, 865453,
+			5427634, 981549, 4650873, 861291, 4003872, 5104220, 6171453,
+			3723302, 7426315, 6137283, 4874820, 6052561, 53441, 5032874,
+			5614778, 2248550, 1756499, 8280764, 8263880, 7600081,
+			5118374, 795344, 7543392, 6869925, 1841187, 4181568, 584562,
+			7483939, 4938664, 6863397, 5126354, 5218129, 6236086,
+			4149293, 379169, 4368487, 7490569, 3409215, 1580463, 3081737,
+			1278732, 7109719, 7371700, 2097931, 399836, 1700274, 7188595,
+			6830029, 1548850, 6593138, 6849097, 1518037, 2859442,
+			7772265, 7325153, 3281191, 7856131, 4995056, 4684325,
+			1351194, 8223904, 6817307, 2484146, 131782, 397032, 7436778,
+			7973479, 3171829, 5624626, 3540123, 7150120, 8313283,
+			3604714, 1043574, 117692, 7797783, 7909392, 903315, 7335342,
+			7501562, 5826142, 2709813, 8245473, 2369045, 2782257,
+			5762833, 6474114, 6862031, 424522, 594248, 2626630, 7659983,
+			5642869, 4075194, 1592129, 245547, 5271031, 3205046, 982375,
+			267873, 1286496, 7230481, 3208972, 7485411, 676111, 4944500,
+			2959742, 5934456, 1414847, 6067948, 1709895, 4648315, 126008,
+			8258986, 2183134, 2302072, 4674924, 4306056, 7465311,
+			6500270, 4247428, 4016815, 4973426, 294287, 2456847, 3289700,
+			2732169, 1159447, 5569724, 140001, 3237977, 8007761, 5874533,
+			255652, 3119586, 2102434, 6248250, 8152822, 8006066, 7708625,
+			6997719, 6260212, 6186962, 6636650, 7836834, 7998017,
+			2061516, 1197591, 1706544, 733027, 2392907, 2700000, 8254598,
+			4488002, 160495, 2985325, 2036837, 2703633, 6406550, 3579947,
+			6195178, 5552390, 6804584, 6305468, 5731980, 6095195,
+			3323409, 1322661, 6690942, 3374630, 5615167, 479044, 3136054,
+			4380418, 2833144, 7829577, 1770522, 6056687, 240415, 14780,
+			3740517, 5224226, 3547288, 2083124, 4699398, 3654239,
+			5624978, 585593, 3655369, 2281739, 3338565, 1908093, 7784706,
+			4352830,
+		}
+	}
+	for i := 0; i < 32; i++ {
+		seed[i] = byte(i)
+	}
+	PolyDeriveUniform(&p, &seed, 30000)
+	if p != p2 {
+		t.Fatalf("%v != %v", p, p2)
+	}
+}
+
+func TestDeriveUniform(t *testing.T) {
+	var p common.Poly
+	var seed [32]byte
+	for i := 0; i < 100; i++ {
+		binary.LittleEndian.PutUint64(seed[:], uint64(i))
+		PolyDeriveUniform(&p, &seed, uint16(i))
+		if !PolyNormalized(&p) {
+			t.Fatal()
+		}
+	}
+}
+
+func TestDeriveUniformLeqEta(t *testing.T) {
+	var p common.Poly
+	var seed [64]byte
+	for i := 0; i < 100; i++ {
+		binary.LittleEndian.PutUint64(seed[:], uint64(i))
+		PolyDeriveUniformLeqEta(&p, &seed, uint16(i))
+		for j := 0; j < common.N; j++ {
+			if p[j] < common.Q-Eta || p[j] > common.Q+Eta {
+				t.Fatal()
+			}
+		}
+	}
+}
+
+func TestDeriveUniformLeGamma1(t *testing.T) {
+	var p common.Poly
+	var seed [64]byte
+	for i := 0; i < 100; i++ {
+		binary.LittleEndian.PutUint64(seed[:], uint64(i))
+		PolyDeriveUniformLeGamma1(&p, &seed, uint16(i))
+		for j := 0; j < common.N; j++ {
+			if (p[j] > Gamma1 && p[j] <= common.Q-Gamma1) || p[j] >= common.Q {
+				t.Fatal()
+			}
+		}
+	}
+}
+
+func TestDeriveUniformBall(t *testing.T) {
+	var p common.Poly
+	var seed [32]byte
+	for i := 0; i < 100; i++ {
+		binary.LittleEndian.PutUint64(seed[:], uint64(i))
+		PolyDeriveUniformBall(&p, seed[:])
+		nonzero := 0
+		for j := 0; j < common.N; j++ {
+			if p[j] != 0 {
+				if p[j] != 1 && p[j] != common.Q-1 {
+					t.Fatal()
+				}
+				nonzero++
+			}
+		}
+		if nonzero != Tau {
+			t.Fatal()
+		}
+	}
+}
+
+func TestDeriveUniformX4(t *testing.T) {
+	if !DeriveX4Available {
+		t.SkipNow()
+	}
+	var ps [4]common.Poly
+	var p common.Poly
+	var seed [32]byte
+	nonces := [4]uint16{12345, 54321, 13532, 37377}
+
+	for i := 0; i < len(seed); i++ {
+		seed[i] = byte(i)
+	}
+
+	PolyDeriveUniformX4([4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]}, &seed,
+		nonces)
+	for i := 0; i < 4; i++ {
+		PolyDeriveUniform(&p, &seed, nonces[i])
+		if ps[i] != p {
+			t.Fatal()
+		}
+	}
+}
+
+func TestDeriveUniformBallX4(t *testing.T) {
+	if !DeriveX4Available {
+		t.SkipNow()
+	}
+	var ps [4]common.Poly
+	var p common.Poly
+	var seed [32]byte
+	PolyDeriveUniformBallX4(
+		[4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]},
+		seed[:],
+	)
+	for j := 0; j < 4; j++ {
+		PolyDeriveUniformBall(&p, seed[:])
+		if ps[j] != p {
+			t.Fatalf("%d\n%v\n%v", j, ps[j], p)
+		}
+	}
+}
+
+func BenchmarkPolyDeriveUniformBall(b *testing.B) {
+	var seed [32]byte
+	var p common.Poly
+	var w1 VecK
+	for i := 0; i < b.N; i++ {
+		w1[0][0] = uint32(i)
+		PolyDeriveUniformBall(&p, seed[:])
+	}
+}
+
+func BenchmarkPolyDeriveUniformBallX4(b *testing.B) {
+	var seed [32]byte
+	var p common.Poly
+	var w1 VecK
+	for i := 0; i < b.N; i++ {
+		w1[0][0] = uint32(i)
+		PolyDeriveUniformBallX4(
+			[4]*common.Poly{&p, &p, &p, &p},
+			seed[:],
+		)
+	}
+}
+
+func BenchmarkPolyDeriveUniform(b *testing.B) {
+	var seed [32]byte
+	var p common.Poly
+	for i := 0; i < b.N; i++ {
+		PolyDeriveUniform(&p, &seed, uint16(i))
+	}
+}
+
+func BenchmarkPolyDeriveUniformX4(b *testing.B) {
+	if !DeriveX4Available {
+		b.SkipNow()
+	}
+	var seed [32]byte
+	var p [4]common.Poly
+	for i := 0; i < b.N; i++ {
+		nonce := uint16(4 * i)
+		PolyDeriveUniformX4([4]*common.Poly{&p[0], &p[1], &p[2], &p[3]},
+			&seed, [4]uint16{nonce, nonce + 1, nonce + 2, nonce + 3})
+	}
+}
+
+func BenchmarkPolyDeriveUniformLeGamma1(b *testing.B) {
+	var seed [64]byte
+	var p common.Poly
+	for i := 0; i < b.N; i++ {
+		PolyDeriveUniformLeGamma1(&p, &seed, uint16(i))
+	}
+}
diff --git a/sign/mldsa/mldsa65/internal/vec.go b/sign/mldsa/mldsa65/internal/vec.go
new file mode 100644
index 000000000..d07d3b245
--- /dev/null
+++ b/sign/mldsa/mldsa65/internal/vec.go
@@ -0,0 +1,281 @@
+// Code generated from mode3/internal/vec.go by gen.go
+
+package internal
+
+import (
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+)
+
+// A vector of L polynomials.
+type VecL [L]common.Poly
+
+// A vector of K polynomials.
+type VecK [K]common.Poly
+
+// Normalize the polynomials in this vector.
+func (v *VecL) Normalize() {
+	for i := 0; i < L; i++ {
+		v[i].Normalize()
+	}
+}
+
+// Normalize the polynomials in this vector assuming their coefficients
+// are already bounded by 2q.
+func (v *VecL) NormalizeAssumingLe2Q() {
+	for i := 0; i < L; i++ {
+		v[i].NormalizeAssumingLe2Q()
+	}
+}
+
+// Sets v to w + u.  Does not normalize.
+func (v *VecL) Add(w, u *VecL) {
+	for i := 0; i < L; i++ {
+		v[i].Add(&w[i], &u[i])
+	}
+}
+
+// Applies NTT componentwise. See Poly.NTT() for details.
+func (v *VecL) NTT() {
+	for i := 0; i < L; i++ {
+		v[i].NTT()
+	}
+}
+
+// Checks whether any of the coefficients exceeds the given bound in supnorm
+//
+// Requires the vector to be normalized.
+func (v *VecL) Exceeds(bound uint32) bool {
+	for i := 0; i < L; i++ {
+		if v[i].Exceeds(bound) {
+			return true
+		}
+	}
+	return false
+}
+
+// Applies Poly.Power2Round componentwise.
+//
+// Requires the vector to be normalized.
+func (v *VecL) Power2Round(v0PlusQ, v1 *VecL) {
+	for i := 0; i < L; i++ {
+		v[i].Power2Round(&v0PlusQ[i], &v1[i])
+	}
+}
+
+// Applies Poly.Decompose componentwise.
+//
+// Requires the vector to be normalized.
+func (v *VecL) Decompose(v0PlusQ, v1 *VecL) {
+	for i := 0; i < L; i++ {
+		PolyDecompose(&v[i], &v0PlusQ[i], &v1[i])
+	}
+}
+
+// Sequentially packs each polynomial using Poly.PackLeqEta().
+func (v *VecL) PackLeqEta(buf []byte) {
+	offset := 0
+	for i := 0; i < L; i++ {
+		PolyPackLeqEta(&v[i], buf[offset:])
+		offset += PolyLeqEtaSize
+	}
+}
+
+// Sets v to the polynomials packed in buf using VecL.PackLeqEta().
+func (v *VecL) UnpackLeqEta(buf []byte) {
+	offset := 0
+	for i := 0; i < L; i++ {
+		PolyUnpackLeqEta(&v[i], buf[offset:])
+		offset += PolyLeqEtaSize
+	}
+}
+
+// Sequentially packs each polynomial using PolyPackLeGamma1().
+func (v *VecL) PackLeGamma1(buf []byte) {
+	offset := 0
+	for i := 0; i < L; i++ {
+		PolyPackLeGamma1(&v[i], buf[offset:])
+		offset += PolyLeGamma1Size
+	}
+}
+
+// Sets v to the polynomials packed in buf using VecL.PackLeGamma1().
+func (v *VecL) UnpackLeGamma1(buf []byte) {
+	offset := 0
+	for i := 0; i < L; i++ {
+		PolyUnpackLeGamma1(&v[i], buf[offset:])
+		offset += PolyLeGamma1Size
+	}
+}
+
+// Normalize the polynomials in this vector.
+func (v *VecK) Normalize() {
+	for i := 0; i < K; i++ {
+		v[i].Normalize()
+	}
+}
+
+// Normalize the polynomials in this vector assuming their coefficients
+// are already bounded by 2q.
+func (v *VecK) NormalizeAssumingLe2Q() {
+	for i := 0; i < K; i++ {
+		v[i].NormalizeAssumingLe2Q()
+	}
+}
+
+// Sets v to w + u.  Does not normalize.
+func (v *VecK) Add(w, u *VecK) {
+	for i := 0; i < K; i++ {
+		v[i].Add(&w[i], &u[i])
+	}
+}
+
+// Checks whether any of the coefficients exceeds the given bound in supnorm
+//
+// Requires the vector to be normalized.
+func (v *VecK) Exceeds(bound uint32) bool {
+	for i := 0; i < K; i++ {
+		if v[i].Exceeds(bound) {
+			return true
+		}
+	}
+	return false
+}
+
+// Applies Poly.Power2Round componentwise.
+//
+// Requires the vector to be normalized.
+func (v *VecK) Power2Round(v0PlusQ, v1 *VecK) {
+	for i := 0; i < K; i++ {
+		v[i].Power2Round(&v0PlusQ[i], &v1[i])
+	}
+}
+
+// Applies Poly.Decompose componentwise.
+//
+// Requires the vector to be normalized.
+func (v *VecK) Decompose(v0PlusQ, v1 *VecK) {
+	for i := 0; i < K; i++ {
+		PolyDecompose(&v[i], &v0PlusQ[i], &v1[i])
+	}
+}
+
+// Sets v to the hint vector for v0 the modified low bits and v1
+// the unmodified high bits --- see makeHint().
+//
+// Returns the number of ones in the hint vector.
+func (v *VecK) MakeHint(v0, v1 *VecK) (pop uint32) {
+	for i := 0; i < K; i++ {
+		pop += PolyMakeHint(&v[i], &v0[i], &v1[i])
+	}
+	return
+}
+
+// Computes corrections to the high bits of the polynomials in the vector
+// w using the hints in h and sets v to the corrected high bits.  Returns v.
+// See useHint().
+func (v *VecK) UseHint(q, hint *VecK) *VecK {
+	for i := 0; i < K; i++ {
+		PolyUseHint(&v[i], &q[i], &hint[i])
+	}
+	return v
+}
+
+// Sequentially packs each polynomial using Poly.PackT1().
+func (v *VecK) PackT1(buf []byte) {
+	offset := 0
+	for i := 0; i < K; i++ {
+		v[i].PackT1(buf[offset:])
+		offset += common.PolyT1Size
+	}
+}
+
+// Sets v to the vector packed into buf by PackT1().
+func (v *VecK) UnpackT1(buf []byte) {
+	offset := 0
+	for i := 0; i < K; i++ {
+		v[i].UnpackT1(buf[offset:])
+		offset += common.PolyT1Size
+	}
+}
+
+// Sequentially packs each polynomial using Poly.PackT0().
+func (v *VecK) PackT0(buf []byte) {
+	offset := 0
+	for i := 0; i < K; i++ {
+		v[i].PackT0(buf[offset:])
+		offset += common.PolyT0Size
+	}
+}
+
+// Sets v to the vector packed into buf by PackT0().
+func (v *VecK) UnpackT0(buf []byte) {
+	offset := 0
+	for i := 0; i < K; i++ {
+		v[i].UnpackT0(buf[offset:])
+		offset += common.PolyT0Size
+	}
+}
+
+// Sequentially packs each polynomial using Poly.PackLeqEta().
+func (v *VecK) PackLeqEta(buf []byte) {
+	offset := 0
+	for i := 0; i < K; i++ {
+		PolyPackLeqEta(&v[i], buf[offset:])
+		offset += PolyLeqEtaSize
+	}
+}
+
+// Sets v to the polynomials packed in buf using VecK.PackLeqEta().
+func (v *VecK) UnpackLeqEta(buf []byte) {
+	offset := 0
+	for i := 0; i < K; i++ {
+		PolyUnpackLeqEta(&v[i], buf[offset:])
+		offset += PolyLeqEtaSize
+	}
+}
+
+// Applies NTT componentwise. See Poly.NTT() for details.
+func (v *VecK) NTT() {
+	for i := 0; i < K; i++ {
+		v[i].NTT()
+	}
+}
+
+// Sequentially packs each polynomial using PolyPackW1().
+func (v *VecK) PackW1(buf []byte) {
+	offset := 0
+	for i := 0; i < K; i++ {
+		PolyPackW1(&v[i], buf[offset:])
+		offset += PolyW1Size
+	}
+}
+
+// Sets v to a - b.
+//
+// Warning: assumes coefficients of the polynomials of  b are less than 2q.
+func (v *VecK) Sub(a, b *VecK) {
+	for i := 0; i < K; i++ {
+		v[i].Sub(&a[i], &b[i])
+	}
+}
+
+// Sets v to 2ᵈ w without reducing.
+func (v *VecK) MulBy2toD(w *VecK) {
+	for i := 0; i < K; i++ {
+		v[i].MulBy2toD(&w[i])
+	}
+}
+
+// Applies InvNTT componentwise. See Poly.InvNTT() for details.
+func (v *VecK) InvNTT() {
+	for i := 0; i < K; i++ {
+		v[i].InvNTT()
+	}
+}
+
+// Applies Poly.ReduceLe2Q() componentwise.
+func (v *VecK) ReduceLe2Q() {
+	for i := 0; i < K; i++ {
+		v[i].ReduceLe2Q()
+	}
+}
diff --git a/sign/mldsa/mldsa87/dilithium.go b/sign/mldsa/mldsa87/dilithium.go
new file mode 100644
index 000000000..a0aa0cf99
--- /dev/null
+++ b/sign/mldsa/mldsa87/dilithium.go
@@ -0,0 +1,182 @@
+// Code generated from modePkg.templ.go. DO NOT EDIT.
+
+
+// mldsa87 implements NIST signature scheme ML-DSA-87 as defined in FIPS204.
+
+package mldsa87
+
+import (
+	"crypto"
+	"errors"
+	"io"
+
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+
+	"github.com/cloudflare/circl/sign/mldsa/mldsa87/internal"
+
+)
+
+const (
+	// Size of seed for NewKeyFromSeed
+	SeedSize = common.SeedSize
+
+	// Size of a packed PublicKey
+	PublicKeySize = internal.PublicKeySize
+
+	// Size of a packed PrivateKey
+	PrivateKeySize = internal.PrivateKeySize
+
+	// Size of a signature
+	SignatureSize = internal.SignatureSize
+)
+
+// PublicKey is the type of ML-DSA-87 public key
+type PublicKey internal.PublicKey
+
+// PrivateKey is the type of ML-DSA-87 private key
+type PrivateKey internal.PrivateKey
+
+// GenerateKey generates a public/private key pair using entropy from rand.
+// If rand is nil, crypto/rand.Reader will be used.
+func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) {
+	pk, sk, err := internal.GenerateKey(rand)
+	return (*PublicKey)(pk), (*PrivateKey)(sk), err
+}
+
+// NewKeyFromSeed derives a public/private key pair using the given seed.
+func NewKeyFromSeed(seed *[SeedSize]byte) (*PublicKey, *PrivateKey) {
+	pk, sk := internal.NewKeyFromSeed(seed)
+	return (*PublicKey)(pk), (*PrivateKey)(sk)
+}
+
+// SignTo signs the given message and writes the signature into signature.
+// It will panic if signature is not of length at least SignatureSize.
+func SignTo(sk *PrivateKey, msg []byte, signature []byte) {
+	internal.SignTo(
+		(*internal.PrivateKey)(sk),
+		msg,
+		signature,
+	)
+}
+
+// Verify checks whether the given signature by pk on msg is valid.
+func Verify(pk *PublicKey, msg []byte, signature []byte) bool {
+	return internal.Verify(
+		(*internal.PublicKey)(pk),
+		msg,
+		signature,
+	)
+}
+
+// Sets pk to the public key encoded in buf.
+func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) {
+	(*internal.PublicKey)(pk).Unpack(buf)
+}
+
+// Sets sk to the private key encoded in buf.
+func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) {
+	(*internal.PrivateKey)(sk).Unpack(buf)
+}
+
+// Packs the public key into buf.
+func (pk *PublicKey) Pack(buf *[PublicKeySize]byte) {
+	(*internal.PublicKey)(pk).Pack(buf)
+}
+
+// Packs the private key into buf.
+func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) {
+	(*internal.PrivateKey)(sk).Pack(buf)
+}
+
+// Packs the public key.
+func (pk *PublicKey) Bytes() []byte {
+	var buf [PublicKeySize]byte
+	pk.Pack(&buf)
+	return buf[:]
+}
+
+// Packs the private key.
+func (sk *PrivateKey) Bytes() []byte {
+	var buf [PrivateKeySize]byte
+	sk.Pack(&buf)
+	return buf[:]
+}
+
+// Packs the public key.
+func (pk *PublicKey) MarshalBinary() ([]byte, error) {
+	return pk.Bytes(), nil
+}
+
+// Packs the private key.
+func (sk *PrivateKey) MarshalBinary() ([]byte, error) {
+	return sk.Bytes(), nil
+}
+
+// Unpacks the public key from data.
+func (pk *PublicKey) UnmarshalBinary(data []byte) error {
+	if len(data) != PublicKeySize {
+		return errors.New("packed public key must be of mldsa87.PublicKeySize bytes")
+	}
+	var buf [PublicKeySize]byte
+	copy(buf[:], data)
+	pk.Unpack(&buf)
+	return nil
+}
+
+// Unpacks the private key from data.
+func (sk *PrivateKey) UnmarshalBinary(data []byte) error {
+	if len(data) != PrivateKeySize {
+		return errors.New("packed private key must be of mldsa87.PrivateKeySize bytes")
+	}
+	var buf [PrivateKeySize]byte
+	copy(buf[:], data)
+	sk.Unpack(&buf)
+	return nil
+}
+
+// Sign signs the given message.
+//
+// opts.HashFunc() must return zero, which can be achieved by passing
+// crypto.Hash(0) for opts.  rand is ignored.  Will only return an error
+// if opts.HashFunc() is non-zero.
+//
+// This function is used to make PrivateKey implement the crypto.Signer
+// interface.  The package-level SignTo function might be more convenient
+// to use.
+func (sk *PrivateKey) Sign(rand io.Reader, msg []byte, opts crypto.SignerOpts) (
+	signature []byte, err error) {
+	var sig [SignatureSize]byte
+
+	if opts.HashFunc() != crypto.Hash(0) {
+		return nil, errors.New("dilithium: cannot sign hashed message")
+	}
+
+	SignTo(sk, msg, sig[:])
+	return sig[:], nil
+}
+
+// Computes the public key corresponding to this private key.
+//
+// Returns a *PublicKey.  The type crypto.PublicKey is used to make
+// PrivateKey implement the crypto.Signer interface.
+func (sk *PrivateKey) Public() crypto.PublicKey {
+	return (*PublicKey)((*internal.PrivateKey)(sk).Public())
+}
+
+// Equal returns whether the two private keys equal.
+func (sk *PrivateKey) Equal(other crypto.PrivateKey) bool {
+	castOther, ok := other.(*PrivateKey)
+	if !ok {
+		return false
+	}
+	return (*internal.PrivateKey)(sk).Equal((*internal.PrivateKey)(castOther))
+}
+
+// Equal returns whether the two public keys equal.
+func (pk *PublicKey) Equal(other crypto.PublicKey) bool {
+	castOther, ok := other.(*PublicKey)
+	if !ok {
+		return false
+	}
+	return (*internal.PublicKey)(pk).Equal((*internal.PublicKey)(castOther))
+}
diff --git a/sign/mldsa/mldsa87/internal/dilithium.go b/sign/mldsa/mldsa87/internal/dilithium.go
new file mode 100644
index 000000000..7869d0475
--- /dev/null
+++ b/sign/mldsa/mldsa87/internal/dilithium.go
@@ -0,0 +1,482 @@
+// Code generated from mode3/internal/dilithium.go by gen.go
+
+package internal
+
+import (
+	cryptoRand "crypto/rand"
+	"crypto/subtle"
+	"io"
+
+	"github.com/cloudflare/circl/internal/sha3"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+)
+
+const (
+	// Size of a packed polynomial of norm ≤η.
+	// (Note that the  formula is not valid in general.)
+	PolyLeqEtaSize = (common.N * DoubleEtaBits) / 8
+
+	// β = τη, the maximum size of c s₂.
+	Beta = Tau * Eta
+
+	// γ₁ range of y
+	Gamma1 = 1 << Gamma1Bits
+
+	// Size of packed polynomial of norm <γ₁ such as z
+	PolyLeGamma1Size = (Gamma1Bits + 1) * common.N / 8
+
+	// α = 2γ₂ parameter for decompose
+	Alpha = 2 * Gamma2
+
+	// Size of a packed private key
+	PrivateKeySize = 32 + 32 + TRSize + PolyLeqEtaSize*(L+K) + common.PolyT0Size*K
+
+	// Size of a packed public key
+	PublicKeySize = 32 + common.PolyT1Size*K
+
+	// Size of a packed signature
+	SignatureSize = L*PolyLeGamma1Size + Omega + K + CTildeSize
+
+	// Size of packed w₁
+	PolyW1Size = (common.N * (common.QBits - Gamma1Bits)) / 8
+)
+
+// PublicKey is the type of Dilithium public keys.
+type PublicKey struct {
+	rho [32]byte
+	t1  VecK
+
+	// Cached values
+	t1p [common.PolyT1Size * K]byte
+	A   *Mat
+	tr  *[TRSize]byte
+}
+
+// PrivateKey is the type of Dilithium private keys.
+type PrivateKey struct {
+	rho [32]byte
+	key [32]byte
+	s1  VecL
+	s2  VecK
+	t0  VecK
+	tr  [TRSize]byte
+
+	// Cached values
+	A   Mat  // ExpandA(ρ)
+	s1h VecL // NTT(s₁)
+	s2h VecK // NTT(s₂)
+	t0h VecK // NTT(t₀)
+}
+
+type unpackedSignature struct {
+	z    VecL
+	hint VecK
+	c    [CTildeSize]byte
+}
+
+// Packs the signature into buf.
+func (sig *unpackedSignature) Pack(buf []byte) {
+	copy(buf[:], sig.c[:])
+	sig.z.PackLeGamma1(buf[CTildeSize:])
+	sig.hint.PackHint(buf[CTildeSize+L*PolyLeGamma1Size:])
+}
+
+// Sets sig to the signature encoded in the buffer.
+//
+// Returns whether buf contains a properly packed signature.
+func (sig *unpackedSignature) Unpack(buf []byte) bool {
+	if len(buf) < SignatureSize {
+		return false
+	}
+	copy(sig.c[:], buf[:])
+	sig.z.UnpackLeGamma1(buf[CTildeSize:])
+	if sig.z.Exceeds(Gamma1 - Beta) {
+		return false
+	}
+	if !sig.hint.UnpackHint(buf[CTildeSize+L*PolyLeGamma1Size:]) {
+		return false
+	}
+	return true
+}
+
+// Packs the public key into buf.
+func (pk *PublicKey) Pack(buf *[PublicKeySize]byte) {
+	copy(buf[:32], pk.rho[:])
+	copy(buf[32:], pk.t1p[:])
+}
+
+// Sets pk to the public key encoded in buf.
+func (pk *PublicKey) Unpack(buf *[PublicKeySize]byte) {
+	copy(pk.rho[:], buf[:32])
+	copy(pk.t1p[:], buf[32:])
+
+	pk.t1.UnpackT1(pk.t1p[:])
+	pk.A = new(Mat)
+	pk.A.Derive(&pk.rho)
+
+	// tr = CRH(ρ ‖ t1) = CRH(pk)
+	pk.tr = new([TRSize]byte)
+	h := sha3.NewShake256()
+	_, _ = h.Write(buf[:])
+	_, _ = h.Read(pk.tr[:])
+}
+
+// Packs the private key into buf.
+func (sk *PrivateKey) Pack(buf *[PrivateKeySize]byte) {
+	copy(buf[:32], sk.rho[:])
+	copy(buf[32:64], sk.key[:])
+	copy(buf[64:64+TRSize], sk.tr[:])
+	offset := 64 + TRSize
+	sk.s1.PackLeqEta(buf[offset:])
+	offset += PolyLeqEtaSize * L
+	sk.s2.PackLeqEta(buf[offset:])
+	offset += PolyLeqEtaSize * K
+	sk.t0.PackT0(buf[offset:])
+}
+
+// Sets sk to the private key encoded in buf.
+func (sk *PrivateKey) Unpack(buf *[PrivateKeySize]byte) {
+	copy(sk.rho[:], buf[:32])
+	copy(sk.key[:], buf[32:64])
+	copy(sk.tr[:], buf[64:64+TRSize])
+	offset := 64 + TRSize
+	sk.s1.UnpackLeqEta(buf[offset:])
+	offset += PolyLeqEtaSize * L
+	sk.s2.UnpackLeqEta(buf[offset:])
+	offset += PolyLeqEtaSize * K
+	sk.t0.UnpackT0(buf[offset:])
+
+	// Cached values
+	sk.A.Derive(&sk.rho)
+	sk.t0h = sk.t0
+	sk.t0h.NTT()
+	sk.s1h = sk.s1
+	sk.s1h.NTT()
+	sk.s2h = sk.s2
+	sk.s2h.NTT()
+}
+
+// GenerateKey generates a public/private key pair using entropy from rand.
+// If rand is nil, crypto/rand.Reader will be used.
+func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) {
+	var seed [32]byte
+	if rand == nil {
+		rand = cryptoRand.Reader
+	}
+	_, err := io.ReadFull(rand, seed[:])
+	if err != nil {
+		return nil, nil, err
+	}
+	pk, sk := NewKeyFromSeed(&seed)
+	return pk, sk, nil
+}
+
+// NewKeyFromSeed derives a public/private key pair using the given seed.
+func NewKeyFromSeed(seed *[common.SeedSize]byte) (*PublicKey, *PrivateKey) {
+	var eSeed [128]byte // expanded seed
+	var pk PublicKey
+	var sk PrivateKey
+	var sSeed [64]byte
+
+	h := sha3.NewShake256()
+	_, _ = h.Write(seed[:])
+	_, _ = h.Read(eSeed[:])
+
+	copy(pk.rho[:], eSeed[:32])
+	copy(sSeed[:], eSeed[32:96])
+	copy(sk.key[:], eSeed[96:])
+	copy(sk.rho[:], pk.rho[:])
+
+	sk.A.Derive(&pk.rho)
+
+	for i := uint16(0); i < L; i++ {
+		PolyDeriveUniformLeqEta(&sk.s1[i], &sSeed, i)
+	}
+
+	for i := uint16(0); i < K; i++ {
+		PolyDeriveUniformLeqEta(&sk.s2[i], &sSeed, i+L)
+	}
+
+	sk.s1h = sk.s1
+	sk.s1h.NTT()
+	sk.s2h = sk.s2
+	sk.s2h.NTT()
+
+	sk.computeT0andT1(&sk.t0, &pk.t1)
+
+	sk.t0h = sk.t0
+	sk.t0h.NTT()
+
+	// Complete public key far enough to be packed
+	pk.t1.PackT1(pk.t1p[:])
+	pk.A = &sk.A
+
+	// Finish private key
+	var packedPk [PublicKeySize]byte
+	pk.Pack(&packedPk)
+
+	// tr = CRH(ρ ‖ t1) = CRH(pk)
+	h.Reset()
+	_, _ = h.Write(packedPk[:])
+	_, _ = h.Read(sk.tr[:])
+
+	// Finish cache of public key
+	pk.tr = &sk.tr
+
+	return &pk, &sk
+}
+
+// Computes t0 and t1 from sk.s1h, sk.s2 and sk.A.
+func (sk *PrivateKey) computeT0andT1(t0, t1 *VecK) {
+	var t VecK
+
+	// Set t to A s₁ + s₂
+	for i := 0; i < K; i++ {
+		PolyDotHat(&t[i], &sk.A[i], &sk.s1h)
+		t[i].ReduceLe2Q()
+		t[i].InvNTT()
+	}
+	t.Add(&t, &sk.s2)
+	t.Normalize()
+
+	// Compute t₀, t₁ = Power2Round(t)
+	t.Power2Round(t0, t1)
+}
+
+// Verify checks whether the given signature by pk on msg is valid.
+func Verify(pk *PublicKey, msg []byte, signature []byte) bool {
+	var sig unpackedSignature
+	var mu [64]byte
+	var zh VecL
+	var Az, Az2dct1, w1 VecK
+	var ch common.Poly
+	var cp [CTildeSize]byte
+	var w1Packed [PolyW1Size * K]byte
+
+	// Note that Unpack() checked whether ‖z‖_∞ < γ₁ - β
+	// and ensured that there at most ω ones in pk.hint.
+	if !sig.Unpack(signature) {
+		return false
+	}
+
+	// μ = CRH(tr ‖ msg)
+	h := sha3.NewShake256()
+	_, _ = h.Write(pk.tr[:])
+	_, _ = h.Write(msg)
+	_, _ = h.Read(mu[:])
+
+	// Compute Az
+	zh = sig.z
+	zh.NTT()
+
+	for i := 0; i < K; i++ {
+		PolyDotHat(&Az[i], &pk.A[i], &zh)
+	}
+
+	// Next, we compute Az - 2ᵈ·c·t₁.
+	// Note that the coefficients of t₁ are bounded by 256 = 2⁹,
+	// so the coefficients of Az2dct1 will bounded by 2⁹⁺ᵈ = 2²³ < 2q,
+	// which is small enough for NTT().
+	Az2dct1.MulBy2toD(&pk.t1)
+	Az2dct1.NTT()
+	PolyDeriveUniformBall(&ch, sig.c[:32])
+	ch.NTT()
+	for i := 0; i < K; i++ {
+		Az2dct1[i].MulHat(&Az2dct1[i], &ch)
+	}
+	Az2dct1.Sub(&Az, &Az2dct1)
+	Az2dct1.ReduceLe2Q()
+	Az2dct1.InvNTT()
+	Az2dct1.NormalizeAssumingLe2Q()
+
+	// UseHint(pk.hint, Az - 2ᵈ·c·t₁)
+	//    = UseHint(pk.hint, w - c·s₂ + c·t₀)
+	//    = UseHint(pk.hint, r + c·t₀)
+	//    = r₁ = w₁.
+	w1.UseHint(&Az2dct1, &sig.hint)
+	w1.PackW1(w1Packed[:])
+
+	// c' = H(μ, w₁)
+	h.Reset()
+	_, _ = h.Write(mu[:])
+	_, _ = h.Write(w1Packed[:])
+	_, _ = h.Read(cp[:])
+
+	return sig.c == cp
+}
+
+// SignTo signs the given message and writes the signature into signature.
+//
+//nolint:funlen
+func SignTo(sk *PrivateKey, msg []byte, signature []byte) {
+	var mu, rhop [64]byte
+	var w1Packed [PolyW1Size * K]byte
+	var y, yh VecL
+	var w, w0, w1, w0mcs2, ct0, w0mcs2pct0 VecK
+	var ch common.Poly
+	var yNonce uint16
+	var sig unpackedSignature
+
+	if len(signature) < SignatureSize {
+		panic("Signature does not fit in that byteslice")
+	}
+
+	//  μ = CRH(tr ‖ msg)
+	h := sha3.NewShake256()
+	_, _ = h.Write(sk.tr[:])
+	_, _ = h.Write(msg)
+	_, _ = h.Read(mu[:])
+
+	// ρ' = CRH(key ‖ μ)
+	h.Reset()
+	_, _ = h.Write(sk.key[:])
+	if NIST {
+		// We implement the deterministic variant  where rnd is all zeroes.
+		// TODO expose randomized variant?
+		_, _ = h.Write(make([]byte, 32))
+	}
+	_, _ = h.Write(mu[:])
+	_, _ = h.Read(rhop[:])
+
+	// Main rejection loop
+	attempt := 0
+	for {
+		attempt++
+		if attempt >= 576 {
+			// Depending on the mode, one try has a chance between 1/7 and 1/4
+			// of succeeding.  Thus it is safe to say that 576 iterations
+			// are enough as (6/7)⁵⁷⁶ < 2⁻¹²⁸.
+			panic("This should only happen 1 in  2^{128}: something is wrong.")
+		}
+
+		// y = ExpandMask(ρ', key)
+		VecLDeriveUniformLeGamma1(&y, &rhop, yNonce)
+		yNonce += uint16(L)
+
+		// Set w to A y
+		yh = y
+		yh.NTT()
+		for i := 0; i < K; i++ {
+			PolyDotHat(&w[i], &sk.A[i], &yh)
+			w[i].ReduceLe2Q()
+			w[i].InvNTT()
+		}
+
+		// Decompose w into w₀ and w₁
+		w.NormalizeAssumingLe2Q()
+		w.Decompose(&w0, &w1)
+
+		// c~ = H(μ ‖ w₁)
+		w1.PackW1(w1Packed[:])
+		h.Reset()
+		_, _ = h.Write(mu[:])
+		_, _ = h.Write(w1Packed[:])
+		_, _ = h.Read(sig.c[:])
+
+		PolyDeriveUniformBall(&ch, sig.c[:32])
+		ch.NTT()
+
+		// Ensure ‖ w₀ - c·s2 ‖_∞ < γ₂ - β.
+		//
+		// By Lemma 3 of the specification this is equivalent to checking that
+		// both ‖ r₀ ‖_∞ < γ₂ - β and r₁ = w₁, for the decomposition
+		// w - c·s₂	 = r₁ α + r₀ as computed by decompose().
+		// See also §4.1 of the specification.
+		for i := 0; i < K; i++ {
+			w0mcs2[i].MulHat(&ch, &sk.s2h[i])
+			w0mcs2[i].InvNTT()
+		}
+		w0mcs2.Sub(&w0, &w0mcs2)
+		w0mcs2.Normalize()
+
+		if w0mcs2.Exceeds(Gamma2 - Beta) {
+			continue
+		}
+
+		// z = y + c·s₁
+		for i := 0; i < L; i++ {
+			sig.z[i].MulHat(&ch, &sk.s1h[i])
+			sig.z[i].InvNTT()
+		}
+		sig.z.Add(&sig.z, &y)
+		sig.z.Normalize()
+
+		// Ensure  ‖z‖_∞ < γ₁ - β
+		if sig.z.Exceeds(Gamma1 - Beta) {
+			continue
+		}
+
+		// Compute c·t₀
+		for i := 0; i < K; i++ {
+			ct0[i].MulHat(&ch, &sk.t0h[i])
+			ct0[i].InvNTT()
+		}
+		ct0.NormalizeAssumingLe2Q()
+
+		// Ensure ‖c·t₀‖_∞ < γ₂.
+		if ct0.Exceeds(Gamma2) {
+			continue
+		}
+
+		// Create the hint to be able to reconstruct w₁ from w - c·s₂ + c·t0.
+		// Note that we're not using makeHint() in the obvious way as we
+		// do not know whether ‖ sc·s₂ - c·t₀ ‖_∞ < γ₂.  Instead we note
+		// that our makeHint() is actually the same as a makeHint for a
+		// different decomposition:
+		//
+		// Earlier we ensured indirectly with a check that r₁ = w₁ where
+		// r = w - c·s₂.  Hence r₀ = r - r₁ α = w - c·s₂ - w₁ α = w₀ - c·s₂.
+		// Thus  MakeHint(w₀ - c·s₂ + c·t₀, w₁) = MakeHint(r0 + c·t₀, r₁)
+		// and UseHint(w - c·s₂ + c·t₀, w₁) = UseHint(r + c·t₀, r₁).
+		// As we just ensured that ‖ c·t₀ ‖_∞ < γ₂ our usage is correct.
+		w0mcs2pct0.Add(&w0mcs2, &ct0)
+		w0mcs2pct0.NormalizeAssumingLe2Q()
+		hintPop := sig.hint.MakeHint(&w0mcs2pct0, &w1)
+		if hintPop > Omega {
+			continue
+		}
+
+		break
+	}
+
+	sig.Pack(signature[:])
+}
+
+// Computes the public key corresponding to this private key.
+func (sk *PrivateKey) Public() *PublicKey {
+	var t0 VecK
+	pk := &PublicKey{
+		rho: sk.rho,
+		A:   &sk.A,
+		tr:  &sk.tr,
+	}
+	sk.computeT0andT1(&t0, &pk.t1)
+	pk.t1.PackT1(pk.t1p[:])
+	return pk
+}
+
+// Equal returns whether the two public keys are equal
+func (pk *PublicKey) Equal(other *PublicKey) bool {
+	return pk.rho == other.rho && pk.t1 == other.t1
+}
+
+// Equal returns whether the two private keys are equal
+func (sk *PrivateKey) Equal(other *PrivateKey) bool {
+	ret := (subtle.ConstantTimeCompare(sk.rho[:], other.rho[:]) &
+		subtle.ConstantTimeCompare(sk.key[:], other.key[:]) &
+		subtle.ConstantTimeCompare(sk.tr[:], other.tr[:]))
+
+	acc := uint32(0)
+	for i := 0; i < L; i++ {
+		for j := 0; j < common.N; j++ {
+			acc |= sk.s1[i][j] ^ other.s1[i][j]
+		}
+	}
+	for i := 0; i < K; i++ {
+		for j := 0; j < common.N; j++ {
+			acc |= sk.s2[i][j] ^ other.s2[i][j]
+			acc |= sk.t0[i][j] ^ other.t0[i][j]
+		}
+	}
+	return (ret & subtle.ConstantTimeEq(int32(acc), 0)) == 1
+}
diff --git a/sign/mldsa/mldsa87/internal/dilithium_test.go b/sign/mldsa/mldsa87/internal/dilithium_test.go
new file mode 100644
index 000000000..825e7da08
--- /dev/null
+++ b/sign/mldsa/mldsa87/internal/dilithium_test.go
@@ -0,0 +1,144 @@
+// Code generated from mode3/internal/dilithium_test.go by gen.go
+
+package internal
+
+import (
+	"encoding/binary"
+	"testing"
+
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+)
+
+// Checks whether p is normalized.  Only used in tests.
+func PolyNormalized(p *common.Poly) bool {
+	p2 := *p
+	p2.Normalize()
+	return p2 == *p
+}
+
+func BenchmarkSkUnpack(b *testing.B) {
+	var buf [PrivateKeySize]byte
+	var sk PrivateKey
+	for i := 0; i < b.N; i++ {
+		sk.Unpack(&buf)
+	}
+}
+
+func BenchmarkPkUnpack(b *testing.B) {
+	var buf [PublicKeySize]byte
+	var pk PublicKey
+	for i := 0; i < b.N; i++ {
+		pk.Unpack(&buf)
+	}
+}
+
+func BenchmarkVerify(b *testing.B) {
+	// Note that the expansion of the matrix A is done at Unpacking/Keygen
+	// instead of at the moment of verification (as in the reference
+	// implementation.)
+	var seed [32]byte
+	var msg [8]byte
+	var sig [SignatureSize]byte
+	pk, sk := NewKeyFromSeed(&seed)
+	SignTo(sk, msg[:], sig[:])
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		// We should generate a new signature for every verify attempt,
+		// as this influences the time a little bit.  This difference, however,
+		// is small and generating a new signature in between creates a lot
+		// pressure on the allocator which makes an accurate measurement hard.
+		Verify(pk, msg[:], sig[:])
+	}
+}
+
+func BenchmarkSign(b *testing.B) {
+	// Note that the expansion of the matrix A is done at Unpacking/Keygen
+	// instead of at the moment of signing (as in the reference implementation.)
+	var seed [32]byte
+	var msg [8]byte
+	var sig [SignatureSize]byte
+	_, sk := NewKeyFromSeed(&seed)
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		binary.LittleEndian.PutUint64(msg[:], uint64(i))
+		SignTo(sk, msg[:], sig[:])
+	}
+}
+
+func BenchmarkGenerateKey(b *testing.B) {
+	var seed [32]byte
+	for i := 0; i < b.N; i++ {
+		binary.LittleEndian.PutUint64(seed[:], uint64(i))
+		NewKeyFromSeed(&seed)
+	}
+}
+
+func BenchmarkPublicFromPrivate(b *testing.B) {
+	var seed [32]byte
+	for i := 0; i < b.N; i++ {
+		b.StopTimer()
+		binary.LittleEndian.PutUint64(seed[:], uint64(i))
+		_, sk := NewKeyFromSeed(&seed)
+		b.StartTimer()
+		sk.Public()
+	}
+}
+
+func TestSignThenVerifyAndPkSkPacking(t *testing.T) {
+	var seed [common.SeedSize]byte
+	var sig [SignatureSize]byte
+	var msg [8]byte
+	var pkb [PublicKeySize]byte
+	var skb [PrivateKeySize]byte
+	var pk2 PublicKey
+	var sk2 PrivateKey
+	for i := uint64(0); i < 100; i++ {
+		binary.LittleEndian.PutUint64(seed[:], i)
+		pk, sk := NewKeyFromSeed(&seed)
+		if !sk.Equal(sk) {
+			t.Fatal()
+		}
+		for j := uint64(0); j < 10; j++ {
+			binary.LittleEndian.PutUint64(msg[:], j)
+			SignTo(sk, msg[:], sig[:])
+			if !Verify(pk, msg[:], sig[:]) {
+				t.Fatal()
+			}
+		}
+		pk.Pack(&pkb)
+		pk2.Unpack(&pkb)
+		if !pk.Equal(&pk2) {
+			t.Fatal()
+		}
+		sk.Pack(&skb)
+		sk2.Unpack(&skb)
+		if !sk.Equal(&sk2) {
+			t.Fatal()
+		}
+	}
+}
+
+func TestPublicFromPrivate(t *testing.T) {
+	var seed [common.SeedSize]byte
+	for i := uint64(0); i < 100; i++ {
+		binary.LittleEndian.PutUint64(seed[:], i)
+		pk, sk := NewKeyFromSeed(&seed)
+		pk2 := sk.Public()
+		if !pk.Equal(pk2) {
+			t.Fatal()
+		}
+	}
+}
+
+func TestGamma1Size(t *testing.T) {
+	var expected int
+	switch Gamma1Bits {
+	case 17:
+		expected = 576
+	case 19:
+		expected = 640
+	}
+	if expected != PolyLeGamma1Size {
+		t.Fatal()
+	}
+}
diff --git a/sign/mldsa/mldsa87/internal/mat.go b/sign/mldsa/mldsa87/internal/mat.go
new file mode 100644
index 000000000..ceaf634fa
--- /dev/null
+++ b/sign/mldsa/mldsa87/internal/mat.go
@@ -0,0 +1,59 @@
+// Code generated from mode3/internal/mat.go by gen.go
+
+package internal
+
+import (
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+)
+
+// A k by l matrix of polynomials.
+type Mat [K]VecL
+
+// Expands the given seed to a complete matrix.
+//
+// This function is called ExpandA in the specification.
+func (m *Mat) Derive(seed *[32]byte) {
+	if !DeriveX4Available {
+		for i := uint16(0); i < K; i++ {
+			for j := uint16(0); j < L; j++ {
+				PolyDeriveUniform(&m[i][j], seed, (i<<8)+j)
+			}
+		}
+		return
+	}
+
+	idx := 0
+	var nonces [4]uint16
+	var ps [4]*common.Poly
+	for i := uint16(0); i < K; i++ {
+		for j := uint16(0); j < L; j++ {
+			nonces[idx] = (i << 8) + j
+			ps[idx] = &m[i][j]
+			idx++
+			if idx == 4 {
+				idx = 0
+				PolyDeriveUniformX4(ps, seed, nonces)
+			}
+		}
+	}
+	if idx != 0 {
+		for i := idx; i < 4; i++ {
+			ps[i] = nil
+		}
+		PolyDeriveUniformX4(ps, seed, nonces)
+	}
+}
+
+// Set p to the inner product of a and b using pointwise multiplication.
+//
+// Assumes a and b are in Montgomery form and their coefficients are
+// pairwise sufficiently small to multiply, see Poly.MulHat().  Resulting
+// coefficients are bounded by 2Lq.
+func PolyDotHat(p *common.Poly, a, b *VecL) {
+	var t common.Poly
+	*p = common.Poly{} // zero p
+	for i := 0; i < L; i++ {
+		t.MulHat(&a[i], &b[i])
+		p.Add(&t, p)
+	}
+}
diff --git a/sign/mldsa/mldsa87/internal/pack.go b/sign/mldsa/mldsa87/internal/pack.go
new file mode 100644
index 000000000..1854b4197
--- /dev/null
+++ b/sign/mldsa/mldsa87/internal/pack.go
@@ -0,0 +1,270 @@
+// Code generated from mode3/internal/pack.go by gen.go
+
+package internal
+
+import (
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+)
+
+// Writes p with norm less than or equal η into buf, which must be of
+// size PolyLeqEtaSize.
+//
+// Assumes coefficients of p are not normalized, but in [q-η,q+η].
+func PolyPackLeqEta(p *common.Poly, buf []byte) {
+	if DoubleEtaBits == 4 { // compiler eliminates branch
+		j := 0
+		for i := 0; i < PolyLeqEtaSize; i++ {
+			buf[i] = (byte(common.Q+Eta-p[j]) |
+				byte(common.Q+Eta-p[j+1])<<4)
+			j += 2
+		}
+	} else if DoubleEtaBits == 3 {
+		j := 0
+		for i := 0; i < PolyLeqEtaSize; i += 3 {
+			buf[i] = (byte(common.Q+Eta-p[j]) |
+				(byte(common.Q+Eta-p[j+1]) << 3) |
+				(byte(common.Q+Eta-p[j+2]) << 6))
+			buf[i+1] = ((byte(common.Q+Eta-p[j+2]) >> 2) |
+				(byte(common.Q+Eta-p[j+3]) << 1) |
+				(byte(common.Q+Eta-p[j+4]) << 4) |
+				(byte(common.Q+Eta-p[j+5]) << 7))
+			buf[i+2] = ((byte(common.Q+Eta-p[j+5]) >> 1) |
+				(byte(common.Q+Eta-p[j+6]) << 2) |
+				(byte(common.Q+Eta-p[j+7]) << 5))
+			j += 8
+		}
+	} else {
+		panic("eta not supported")
+	}
+}
+
+// Sets p to the polynomial of norm less than or equal η encoded in the
+// given buffer of size PolyLeqEtaSize.
+//
+// Output coefficients of p are not normalized, but in [q-η,q+η] provided
+// buf was created using PackLeqEta.
+//
+// Beware, for arbitrary buf the coefficients of p might end up in
+// the interval [q-2^b,q+2^b] where b is the least b with η≤2^b.
+func PolyUnpackLeqEta(p *common.Poly, buf []byte) {
+	if DoubleEtaBits == 4 { // compiler eliminates branch
+		j := 0
+		for i := 0; i < PolyLeqEtaSize; i++ {
+			p[j] = common.Q + Eta - uint32(buf[i]&15)
+			p[j+1] = common.Q + Eta - uint32(buf[i]>>4)
+			j += 2
+		}
+	} else if DoubleEtaBits == 3 {
+		j := 0
+		for i := 0; i < PolyLeqEtaSize; i += 3 {
+			p[j] = common.Q + Eta - uint32(buf[i]&7)
+			p[j+1] = common.Q + Eta - uint32((buf[i]>>3)&7)
+			p[j+2] = common.Q + Eta - uint32((buf[i]>>6)|((buf[i+1]<<2)&7))
+			p[j+3] = common.Q + Eta - uint32((buf[i+1]>>1)&7)
+			p[j+4] = common.Q + Eta - uint32((buf[i+1]>>4)&7)
+			p[j+5] = common.Q + Eta - uint32((buf[i+1]>>7)|((buf[i+2]<<1)&7))
+			p[j+6] = common.Q + Eta - uint32((buf[i+2]>>2)&7)
+			p[j+7] = common.Q + Eta - uint32((buf[i+2]>>5)&7)
+			j += 8
+		}
+	} else {
+		panic("eta not supported")
+	}
+}
+
+// Writes v with coefficients in {0, 1} of which at most ω non-zero
+// to buf, which must have length ω+k.
+func (v *VecK) PackHint(buf []byte) {
+	// The packed hint starts with the indices of the non-zero coefficients
+	// For instance:
+	//
+	//    (x⁵⁶ + x¹⁰⁰, x²⁵⁵, 0, x² + x²³, x¹)
+	//
+	// Yields
+	//
+	//  56, 100, 255, 2, 23, 1
+	//
+	// Then we pad with zeroes until we have a list of ω items:
+	// //  56, 100, 255, 2, 23, 1, 0, 0, ..., 0
+	//
+	// Then we finish with a list of the switch-over-indices in this
+	// list between polynomials, so:
+	//
+	//  56, 100, 255, 2, 23, 1, 0, 0, ..., 0, 2, 3, 3, 5, 6
+
+	off := uint8(0)
+	for i := 0; i < K; i++ {
+		for j := uint16(0); j < common.N; j++ {
+			if v[i][j] != 0 {
+				buf[off] = uint8(j)
+				off++
+			}
+		}
+		buf[Omega+i] = off
+	}
+	for ; off < Omega; off++ {
+		buf[off] = 0
+	}
+}
+
+// Sets v to the vector encoded using VecK.PackHint()
+//
+// Returns whether unpacking was successful.
+func (v *VecK) UnpackHint(buf []byte) bool {
+	// A priori, there would be several reasonable ways to encode the same
+	// hint vector.  We take care to only allow only one encoding, to ensure
+	// "strong unforgeability".
+	//
+	// See PackHint() source for description of the encoding.
+	*v = VecK{}         // zero v
+	prevSOP := uint8(0) // previous switch-over-point
+	for i := 0; i < K; i++ {
+		SOP := buf[Omega+i]
+		if SOP < prevSOP || SOP > Omega {
+			return false // ensures switch-over-points are increasing
+		}
+		for j := prevSOP; j < SOP; j++ {
+			if j > prevSOP && buf[j] <= buf[j-1] {
+				return false // ensures indices are increasing (within a poly)
+			}
+			v[i][buf[j]] = 1
+		}
+		prevSOP = SOP
+	}
+	for j := prevSOP; j < Omega; j++ {
+		if buf[j] != 0 {
+			return false // ensures padding indices are zero
+		}
+	}
+
+	return true
+}
+
+// Sets p to the polynomial packed into buf by PolyPackLeGamma1.
+//
+// p will be normalized.
+func PolyUnpackLeGamma1(p *common.Poly, buf []byte) {
+	if Gamma1Bits == 17 {
+		j := 0
+		for i := 0; i < PolyLeGamma1Size; i += 9 {
+			p0 := uint32(buf[i]) | (uint32(buf[i+1]) << 8) |
+				(uint32(buf[i+2]&0x3) << 16)
+			p1 := uint32(buf[i+2]>>2) | (uint32(buf[i+3]) << 6) |
+				(uint32(buf[i+4]&0xf) << 14)
+			p2 := uint32(buf[i+4]>>4) | (uint32(buf[i+5]) << 4) |
+				(uint32(buf[i+6]&0x3f) << 12)
+			p3 := uint32(buf[i+6]>>6) | (uint32(buf[i+7]) << 2) |
+				(uint32(buf[i+8]) << 10)
+
+			// coefficients in [0,…,2γ₁)
+			p0 = Gamma1 - p0 // (-γ₁,…,γ₁]
+			p1 = Gamma1 - p1
+			p2 = Gamma1 - p2
+			p3 = Gamma1 - p3
+
+			p0 += uint32(int32(p0)>>31) & common.Q // normalize
+			p1 += uint32(int32(p1)>>31) & common.Q
+			p2 += uint32(int32(p2)>>31) & common.Q
+			p3 += uint32(int32(p3)>>31) & common.Q
+
+			p[j] = p0
+			p[j+1] = p1
+			p[j+2] = p2
+			p[j+3] = p3
+
+			j += 4
+		}
+	} else if Gamma1Bits == 19 {
+		j := 0
+		for i := 0; i < PolyLeGamma1Size; i += 5 {
+			p0 := uint32(buf[i]) | (uint32(buf[i+1]) << 8) |
+				(uint32(buf[i+2]&0xf) << 16)
+			p1 := uint32(buf[i+2]>>4) | (uint32(buf[i+3]) << 4) |
+				(uint32(buf[i+4]) << 12)
+
+			p0 = Gamma1 - p0
+			p1 = Gamma1 - p1
+
+			p0 += uint32(int32(p0)>>31) & common.Q
+			p1 += uint32(int32(p1)>>31) & common.Q
+
+			p[j] = p0
+			p[j+1] = p1
+
+			j += 2
+		}
+	} else {
+		panic("γ₁ not supported")
+	}
+}
+
+// Writes p whose coefficients are in (-γ₁,γ₁] into buf
+// which has to be of length PolyLeGamma1Size.
+//
+// Assumes p is normalized.
+func PolyPackLeGamma1(p *common.Poly, buf []byte) {
+	if Gamma1Bits == 17 {
+		j := 0
+		// coefficients in [0,…,γ₁] ∪ (q-γ₁,…,q)
+		for i := 0; i < PolyLeGamma1Size; i += 9 {
+			p0 := Gamma1 - p[j]                    // [0,…,γ₁] ∪ (γ₁-q,…,2γ₁-q)
+			p0 += uint32(int32(p0)>>31) & common.Q // [0,…,2γ₁)
+			p1 := Gamma1 - p[j+1]
+			p1 += uint32(int32(p1)>>31) & common.Q
+			p2 := Gamma1 - p[j+2]
+			p2 += uint32(int32(p2)>>31) & common.Q
+			p3 := Gamma1 - p[j+3]
+			p3 += uint32(int32(p3)>>31) & common.Q
+
+			buf[i+0] = byte(p0)
+			buf[i+1] = byte(p0 >> 8)
+			buf[i+2] = byte(p0>>16) | byte(p1<<2)
+			buf[i+3] = byte(p1 >> 6)
+			buf[i+4] = byte(p1>>14) | byte(p2<<4)
+			buf[i+5] = byte(p2 >> 4)
+			buf[i+6] = byte(p2>>12) | byte(p3<<6)
+			buf[i+7] = byte(p3 >> 2)
+			buf[i+8] = byte(p3 >> 10)
+
+			j += 4
+		}
+	} else if Gamma1Bits == 19 {
+		j := 0
+		for i := 0; i < PolyLeGamma1Size; i += 5 {
+			// Coefficients are in [0, γ₁] ∪ (Q-γ₁, Q)
+			p0 := Gamma1 - p[j]
+			p0 += uint32(int32(p0)>>31) & common.Q
+			p1 := Gamma1 - p[j+1]
+			p1 += uint32(int32(p1)>>31) & common.Q
+
+			buf[i+0] = byte(p0)
+			buf[i+1] = byte(p0 >> 8)
+			buf[i+2] = byte(p0>>16) | byte(p1<<4)
+			buf[i+3] = byte(p1 >> 4)
+			buf[i+4] = byte(p1 >> 12)
+
+			j += 2
+		}
+	} else {
+		panic("γ₁ not supported")
+	}
+}
+
+// Pack w₁ into buf, which must be of length PolyW1Size.
+//
+// Assumes w₁ is normalized.
+func PolyPackW1(p *common.Poly, buf []byte) {
+	if Gamma1Bits == 19 {
+		p.PackLe16(buf)
+	} else if Gamma1Bits == 17 {
+		j := 0
+		for i := 0; i < PolyW1Size; i += 3 {
+			buf[i] = byte(p[j]) | byte(p[j+1]<<6)
+			buf[i+1] = byte(p[j+1]>>2) | byte(p[j+2]<<4)
+			buf[i+2] = byte(p[j+2]>>4) | byte(p[j+3]<<2)
+			j += 4
+		}
+	} else {
+		panic("unsupported γ₁")
+	}
+}
diff --git a/sign/mldsa/mldsa87/internal/pack_test.go b/sign/mldsa/mldsa87/internal/pack_test.go
new file mode 100644
index 000000000..f952c6a09
--- /dev/null
+++ b/sign/mldsa/mldsa87/internal/pack_test.go
@@ -0,0 +1,93 @@
+// Code generated from mode3/internal/pack_test.go by gen.go
+
+package internal
+
+import (
+	"testing"
+
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+)
+
+func TestPolyPackLeqEta(t *testing.T) {
+	var p1, p2 common.Poly
+	var seed [64]byte
+	var buf [PolyLeqEtaSize]byte
+
+	for i := uint16(0); i < 100; i++ {
+		// Note that DeriveUniformLeqEta sets p to the right kind of
+		// unnormalized vector.
+		PolyDeriveUniformLeqEta(&p1, &seed, i)
+		for j := 0; j < PolyLeqEtaSize; j++ {
+			if p1[j] < common.Q-Eta || p1[j] > common.Q+Eta {
+				t.Fatalf("DerveUniformLeqEta out of bounds")
+			}
+		}
+		PolyPackLeqEta(&p1, buf[:])
+		PolyUnpackLeqEta(&p2, buf[:])
+		if p1 != p2 {
+			t.Fatalf("%v != %v", p1, p2)
+		}
+	}
+}
+
+func TestPolyPackT1(t *testing.T) {
+	var p1, p2 common.Poly
+	var seed [32]byte
+	var buf [common.PolyT1Size]byte
+
+	for i := uint16(0); i < 100; i++ {
+		PolyDeriveUniform(&p1, &seed, i)
+		p1.Normalize()
+		for j := 0; j < common.N; j++ {
+			p1[j] &= 0x1ff
+		}
+		p1.PackT1(buf[:])
+		p2.UnpackT1(buf[:])
+		if p1 != p2 {
+			t.Fatalf("%v != %v", p1, p2)
+		}
+	}
+}
+
+func TestPolyPackT0(t *testing.T) {
+	var p, p0, p1, p2 common.Poly
+	var seed [32]byte
+	var buf [common.PolyT0Size]byte
+
+	for i := uint16(0); i < 100; i++ {
+		PolyDeriveUniform(&p, &seed, i)
+		p.Normalize()
+		p.Power2Round(&p0, &p1)
+
+		p0.PackT0(buf[:])
+		p2.UnpackT0(buf[:])
+		if p0 != p2 {
+			t.Fatalf("%v !=\n%v", p0, p2)
+		}
+	}
+}
+
+func BenchmarkUnpackLeGamma1(b *testing.B) {
+	var p common.Poly
+	var buf [PolyLeGamma1Size]byte
+	for i := 0; i < b.N; i++ {
+		PolyUnpackLeGamma1(&p, buf[:])
+	}
+}
+
+func TestPolyPackLeGamma1(t *testing.T) {
+	var p0, p1 common.Poly
+	var seed [64]byte
+	var buf [PolyLeGamma1Size]byte
+
+	for i := uint16(0); i < 100; i++ {
+		PolyDeriveUniformLeGamma1(&p0, &seed, i)
+		p0.Normalize()
+
+		PolyPackLeGamma1(&p0, buf[:])
+		PolyUnpackLeGamma1(&p1, buf[:])
+		if p0 != p1 {
+			t.Fatalf("%v != %v", p0, p1)
+		}
+	}
+}
diff --git a/sign/mldsa/mldsa87/internal/params.go b/sign/mldsa/mldsa87/internal/params.go
new file mode 100644
index 000000000..e60c4d35f
--- /dev/null
+++ b/sign/mldsa/mldsa87/internal/params.go
@@ -0,0 +1,19 @@
+// Code generated from params.templ.go. DO NOT EDIT.
+
+package internal
+
+const (
+	Name          = "ML-DSA-87"
+	UseAES        = false
+	K             = 8
+	L             = 7
+	Eta           = 2
+	DoubleEtaBits = 3
+	Omega         = 75
+	Tau           = 60
+	Gamma1Bits    = 19
+	Gamma2        = 261888
+	NIST          = true
+	TRSize        = 64
+	CTildeSize    = 64
+)
diff --git a/sign/mldsa/mldsa87/internal/rounding.go b/sign/mldsa/mldsa87/internal/rounding.go
new file mode 100644
index 000000000..58123c090
--- /dev/null
+++ b/sign/mldsa/mldsa87/internal/rounding.go
@@ -0,0 +1,142 @@
+// Code generated from mode3/internal/rounding.go by gen.go
+
+package internal
+
+import (
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+)
+
+// Splits 0 ≤ a < q into a₀ and a₁ with a = a₁*α + a₀ with -α/2 < a₀ ≤ α/2,
+// except for when we would have a₁ = (q-1)/α in which case a₁=0 is taken
+// and -α/2 ≤ a₀ < 0.  Returns a₀ + q.  Note 0 ≤ a₁ < (q-1)/α.
+// Recall α = 2γ₂.
+func decompose(a uint32) (a0plusQ, a1 uint32) {
+	// a₁ = ⌈a / 128⌉
+	a1 = (a + 127) >> 7
+
+	if Alpha == 523776 {
+		// 1025/2²² is close enough to 1/4092 so that a₁
+		// becomes a/α rounded down.
+		a1 = ((a1*1025 + (1 << 21)) >> 22)
+
+		// For the corner-case a₁ = (q-1)/α = 16, we have to set a₁=0.
+		a1 &= 15
+	} else if Alpha == 190464 {
+		// 1488/2²⁴ is close enough to 1/1488 so that a₁
+		// becomes a/α rounded down.
+		a1 = ((a1 * 11275) + (1 << 23)) >> 24
+
+		// For the corner-case a₁ = (q-1)/α = 44, we have to set a₁=0.
+		a1 ^= uint32(int32(43-a1)>>31) & a1
+	} else {
+		panic("unsupported α")
+	}
+
+	a0plusQ = a - a1*Alpha
+
+	// In the corner-case, when we set a₁=0, we will incorrectly
+	// have a₀ > (q-1)/2 and we'll need to subtract q.  As we
+	// return a₀ + q, that comes down to adding q if a₀ < (q-1)/2.
+	a0plusQ += uint32(int32(a0plusQ-(common.Q-1)/2)>>31) & common.Q
+
+	return
+}
+
+// Assume 0 ≤ r, f < Q with ‖f‖_∞ ≤ α/2.  Decompose r as r = r1*α + r0 as
+// computed by decompose().  Write r' := r - f (mod Q).  Now, decompose
+// r'=r-f again as  r' = r'1*α + r'0 using decompose().  As f is small, we
+// have r'1 = r1 + h, where h ∈ {-1, 0, 1}.  makeHint() computes |h|
+// given z0 := r0 - f (mod Q) and r1.  With |h|, which is called the hint,
+// we can reconstruct r1 using only r' = r - f, which is done by useHint().
+// To wit:
+//
+//	useHint( r - f, makeHint( r0 - f, r1 ) ) = r1.
+//
+// Assumes 0 ≤ z0 < Q.
+func makeHint(z0, r1 uint32) uint32 {
+	// If -α/2 < r0 - f ≤ α/2, then r1*α + r0 - f is a valid decomposition of r'
+	// with the restrictions of decompose() and so r'1 = r1.  So the hint
+	// should be 0. This is covered by the first two inequalities.
+	// There is one other case: if r0 - f = -α/2, then r1*α + r0 - f is also
+	// a valid decomposition if r1 = 0.  In the other cases a one is carried
+	// and the hint should be 1.
+	if z0 <= Gamma2 || z0 > common.Q-Gamma2 || (z0 == common.Q-Gamma2 && r1 == 0) {
+		return 0
+	}
+	return 1
+}
+
+// Uses the hint created by makeHint() to reconstruct r1 from r'=r-f; see
+// documentation of makeHint() for context.
+// Assumes 0 ≤ r' < Q.
+func useHint(rp uint32, hint uint32) uint32 {
+	rp0plusQ, rp1 := decompose(rp)
+	if hint == 0 {
+		return rp1
+	}
+	if rp0plusQ > common.Q {
+		return (rp1 + 1) & 15
+	}
+	return (rp1 - 1) & 15
+}
+
+// Sets p to the hint polynomial for p0 the modified low bits and p1
+// the unmodified high bits --- see makeHint().
+//
+// Returns the number of ones in the hint polynomial.
+func PolyMakeHint(p, p0, p1 *common.Poly) (pop uint32) {
+	for i := 0; i < common.N; i++ {
+		h := makeHint(p0[i], p1[i])
+		pop += h
+		p[i] = h
+	}
+	return
+}
+
+// Computes corrections to the high bits of the polynomial q according
+// to the hints in h and sets p to the corrected high bits.  Returns p.
+func PolyUseHint(p, q, hint *common.Poly) {
+	var q0PlusQ common.Poly
+
+	// See useHint() and makeHint() for an explanation.  We reimplement it
+	// here so that we can call Poly.Decompose(), which might be way faster
+	// than calling decompose() in a loop (for instance when having AVX2.)
+
+	PolyDecompose(q, &q0PlusQ, p)
+
+	for i := 0; i < common.N; i++ {
+		if hint[i] == 0 {
+			continue
+		}
+		if Gamma2 == 261888 {
+			if q0PlusQ[i] > common.Q {
+				p[i] = (p[i] + 1) & 15
+			} else {
+				p[i] = (p[i] - 1) & 15
+			}
+		} else if Gamma2 == 95232 {
+			if q0PlusQ[i] > common.Q {
+				if p[i] == 43 {
+					p[i] = 0
+				} else {
+					p[i]++
+				}
+			} else {
+				if p[i] == 0 {
+					p[i] = 43
+				} else {
+					p[i]--
+				}
+			}
+		} else {
+			panic("unsupported γ₂")
+		}
+	}
+}
+
+// Splits each of the coefficients of p using decompose.
+func PolyDecompose(p, p0PlusQ, p1 *common.Poly) {
+	for i := 0; i < common.N; i++ {
+		p0PlusQ[i], p1[i] = decompose(p[i])
+	}
+}
diff --git a/sign/mldsa/mldsa87/internal/rounding_test.go b/sign/mldsa/mldsa87/internal/rounding_test.go
new file mode 100644
index 000000000..ad653ca3f
--- /dev/null
+++ b/sign/mldsa/mldsa87/internal/rounding_test.go
@@ -0,0 +1,81 @@
+// Code generated from mode3/internal/rounding_test.go by gen.go
+
+package internal
+
+import (
+	"flag"
+	"testing"
+
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+)
+
+var runVeryLongTest = flag.Bool("very-long", false, "runs very long tests")
+
+func TestDecompose(t *testing.T) {
+	for a := uint32(0); a < common.Q; a++ {
+		a0PlusQ, a1 := decompose(a)
+		a0 := int32(a0PlusQ) - int32(common.Q)
+		recombined := a0 + int32(Alpha*a1)
+		if a1 == 0 && recombined < 0 {
+			recombined += common.Q
+			if -(Alpha/2) > a0 || a0 >= 0 {
+				t.Fatalf("decompose(%v): a0 out of bounds", a)
+			}
+		} else {
+			if (-(Alpha / 2) >= a0) || (a0 > Alpha/2) {
+				t.Fatalf("decompose(%v): a0 out of bounds", a)
+			}
+		}
+		if int32(a) != recombined {
+			t.Fatalf("decompose(%v) doesn't recombine %v %v", a, a0, a1)
+		}
+	}
+}
+
+func TestMakeHint(t *testing.T) {
+	if !*runVeryLongTest {
+		t.SkipNow()
+	}
+	for w := uint32(0); w < common.Q; w++ {
+		w0, w1 := decompose(w)
+		for fn := uint32(0); fn <= Gamma2; fn++ {
+			fsign := false
+			for {
+				var f uint32
+				if fsign {
+					if fn == 0 {
+						break
+					}
+					f = common.Q - fn
+				} else {
+					f = fn
+				}
+
+				hint := makeHint(common.ReduceLe2Q(w0+common.Q-f), w1)
+				w1p := useHint(common.ReduceLe2Q(w+common.Q-f), hint)
+				if w1p != w1 {
+					t.Fatal()
+				}
+
+				if fsign {
+					break
+				}
+				fsign = true
+			}
+		}
+	}
+}
+
+func BenchmarkDecompose(b *testing.B) {
+	var p, p0, p1 common.Poly
+	for i := 0; i < b.N; i++ {
+		PolyDecompose(&p, &p0, &p1)
+	}
+}
+
+func BenchmarkMakeHint(b *testing.B) {
+	var p, p0, p1 common.Poly
+	for i := 0; i < b.N; i++ {
+		PolyMakeHint(&p, &p0, &p1)
+	}
+}
diff --git a/sign/mldsa/mldsa87/internal/sample.go b/sign/mldsa/mldsa87/internal/sample.go
new file mode 100644
index 000000000..62c261332
--- /dev/null
+++ b/sign/mldsa/mldsa87/internal/sample.go
@@ -0,0 +1,370 @@
+// Code generated from mode3/internal/sample.go by gen.go
+
+package internal
+
+import (
+	"encoding/binary"
+
+	"github.com/cloudflare/circl/internal/sha3"
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+	"github.com/cloudflare/circl/simd/keccakf1600"
+)
+
+// DeriveX4Available indicates whether the system supports the quick fourway
+// sampling variants like PolyDeriveUniformX4.
+var DeriveX4Available = keccakf1600.IsEnabledX4() && !UseAES
+
+// For each i, sample ps[i] uniformly from the given seed and nonces[i].
+// ps[i] may be nil and is ignored in that case.
+//
+// Can only be called when DeriveX4Available is true.
+func PolyDeriveUniformX4(ps [4]*common.Poly, seed *[32]byte, nonces [4]uint16) {
+	var perm keccakf1600.StateX4
+	state := perm.Initialize(false)
+
+	// Absorb the seed in the four states
+	for i := 0; i < 4; i++ {
+		v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)])
+		for j := 0; j < 4; j++ {
+			state[i*4+j] = v
+		}
+	}
+
+	// Absorb the nonces, the SHAKE128 domain separator (0b1111), the
+	// start of the padding (0b...001) and the end of the padding 0b100...
+	// Recall that the rate of SHAKE128 is 168 --- i.e. 21 uint64s.
+	for j := 0; j < 4; j++ {
+		state[4*4+j] = uint64(nonces[j]) | (0x1f << 16)
+		state[20*4+j] = 0x80 << 56
+	}
+
+	var idx [4]int // indices into ps
+	for j := 0; j < 4; j++ {
+		if ps[j] == nil {
+			idx[j] = common.N // mark nil polynomial as completed
+		}
+	}
+
+	done := false
+	for !done {
+		// Applies KeccaK-f[1600] to state to get the next 21 uint64s of each
+		// of the four SHAKE128 streams.
+		perm.Permute()
+
+		done = true
+
+	PolyLoop:
+		for j := 0; j < 4; j++ {
+			if idx[j] == common.N {
+				continue
+			}
+			for i := 0; i < 7; i++ {
+				var t [8]uint32
+				t[0] = uint32(state[i*3*4+j] & 0x7fffff)
+				t[1] = uint32((state[i*3*4+j] >> 24) & 0x7fffff)
+				t[2] = uint32((state[i*3*4+j] >> 48) |
+					((state[(i*3+1)*4+j] & 0x7f) << 16))
+				t[3] = uint32((state[(i*3+1)*4+j] >> 8) & 0x7fffff)
+				t[4] = uint32((state[(i*3+1)*4+j] >> 32) & 0x7fffff)
+				t[5] = uint32((state[(i*3+1)*4+j] >> 56) |
+					((state[(i*3+2)*4+j] & 0x7fff) << 8))
+				t[6] = uint32((state[(i*3+2)*4+j] >> 16) & 0x7fffff)
+				t[7] = uint32((state[(i*3+2)*4+j] >> 40) & 0x7fffff)
+
+				for k := 0; k < 8; k++ {
+					if t[k] < common.Q {
+						ps[j][idx[j]] = t[k]
+						idx[j]++
+						if idx[j] == common.N {
+							continue PolyLoop
+						}
+					}
+				}
+			}
+			done = false
+		}
+	}
+}
+
+// Sample p uniformly from the given seed and nonce.
+//
+// p will be normalized.
+func PolyDeriveUniform(p *common.Poly, seed *[32]byte, nonce uint16) {
+	var i, length int
+	var buf [12 * 16]byte // fits 168B SHAKE-128 rate and 12 16B AES blocks
+
+	if UseAES {
+		length = 12 * 16
+	} else {
+		length = 168
+	}
+
+	sample := func() {
+		// Note that 3 divides into 168 and 12*16, so we use up buf completely.
+		for j := 0; j < length && i < common.N; j += 3 {
+			t := (uint32(buf[j]) | (uint32(buf[j+1]) << 8) |
+				(uint32(buf[j+2]) << 16)) & 0x7fffff
+
+			// We use rejection sampling
+			if t < common.Q {
+				p[i] = t
+				i++
+			}
+		}
+	}
+
+	if UseAES {
+		h := common.NewAesStream128(seed, nonce)
+
+		for i < common.N {
+			h.SqueezeInto(buf[:length])
+			sample()
+		}
+	} else {
+		var iv [32 + 2]byte // 32 byte seed + uint16 nonce
+		h := sha3.NewShake128()
+		copy(iv[:32], seed[:])
+		iv[32] = uint8(nonce)
+		iv[33] = uint8(nonce >> 8)
+		_, _ = h.Write(iv[:])
+
+		for i < common.N {
+			_, _ = h.Read(buf[:168])
+			sample()
+		}
+	}
+}
+
+// Sample p uniformly with coefficients of norm less than or equal η,
+// using the given seed and nonce.
+//
+// p will not be normalized, but will have coefficients in [q-η,q+η].
+func PolyDeriveUniformLeqEta(p *common.Poly, seed *[64]byte, nonce uint16) {
+	// Assumes 2 < η < 8.
+	var i, length int
+	var buf [9 * 16]byte // fits 136B SHAKE-256 rate and 9 16B AES blocks
+
+	if UseAES {
+		length = 9 * 16
+	} else {
+		length = 136
+	}
+
+	sample := func() {
+		// We use rejection sampling
+		for j := 0; j < length && i < common.N; j++ {
+			t1 := uint32(buf[j]) & 15
+			t2 := uint32(buf[j]) >> 4
+			if Eta == 2 { // branch is eliminated by compiler
+				if t1 <= 14 {
+					t1 -= ((205 * t1) >> 10) * 5 // reduce mod  5
+					p[i] = common.Q + Eta - t1
+					i++
+				}
+				if t2 <= 14 && i < common.N {
+					t2 -= ((205 * t2) >> 10) * 5 // reduce mod 5
+					p[i] = common.Q + Eta - t2
+					i++
+				}
+			} else if Eta == 4 {
+				if t1 <= 2*Eta {
+					p[i] = common.Q + Eta - t1
+					i++
+				}
+				if t2 <= 2*Eta && i < common.N {
+					p[i] = common.Q + Eta - t2
+					i++
+				}
+			} else {
+				panic("unsupported η")
+			}
+		}
+	}
+
+	if UseAES {
+		h := common.NewAesStream256(seed, nonce)
+
+		for i < common.N {
+			h.SqueezeInto(buf[:length])
+			sample()
+		}
+	} else {
+		var iv [64 + 2]byte // 64 byte seed + uint16 nonce
+
+		h := sha3.NewShake256()
+		copy(iv[:64], seed[:])
+		iv[64] = uint8(nonce)
+		iv[65] = uint8(nonce >> 8)
+
+		// 136 is SHAKE-256 rate
+		_, _ = h.Write(iv[:])
+
+		for i < common.N {
+			_, _ = h.Read(buf[:136])
+			sample()
+		}
+	}
+}
+
+// Sample v[i] uniformly with coefficients in (-γ₁,…,γ₁]  using the
+// given seed and nonce+i
+//
+// p will be normalized.
+func VecLDeriveUniformLeGamma1(v *VecL, seed *[64]byte, nonce uint16) {
+	for i := 0; i < L; i++ {
+		PolyDeriveUniformLeGamma1(&v[i], seed, nonce+uint16(i))
+	}
+}
+
+// Sample p uniformly with coefficients in (-γ₁,…,γK1s] using the
+// given seed and nonce.
+//
+// p will be normalized.
+func PolyDeriveUniformLeGamma1(p *common.Poly, seed *[64]byte, nonce uint16) {
+	var buf [PolyLeGamma1Size]byte
+
+	if UseAES {
+		h := common.NewAesStream256(seed, nonce)
+		h.SqueezeInto(buf[:])
+	} else {
+		var iv [66]byte
+		h := sha3.NewShake256()
+		copy(iv[:64], seed[:])
+		iv[64] = uint8(nonce)
+		iv[65] = uint8(nonce >> 8)
+		_, _ = h.Write(iv[:])
+		_, _ = h.Read(buf[:])
+	}
+
+	PolyUnpackLeGamma1(p, buf[:])
+}
+
+// For each i, sample ps[i] uniformly with τ non-zero coefficients in {q-1,1}
+// using the given seed and w1[i].  ps[i] may be nil and is ignored
+// in that case.  ps[i] will be normalized.
+//
+// Can only be called when DeriveX4Available is true.
+//
+// This function is currently not used (yet).
+func PolyDeriveUniformBallX4(ps [4]*common.Poly, seed []byte) {
+	var perm keccakf1600.StateX4
+	state := perm.Initialize(false)
+
+	// Absorb the seed in the four states
+	for i := 0; i < 32/8; i++ {
+		v := binary.LittleEndian.Uint64(seed[8*i : 8*(i+1)])
+		for j := 0; j < 4; j++ {
+			state[i*4+j] = v
+		}
+	}
+
+	// SHAKE256 domain separator and padding
+	for j := 0; j < 4; j++ {
+		state[(32/8)*4+j] ^= 0x1f
+		state[16*4+j] ^= 0x80 << 56
+	}
+	perm.Permute()
+
+	var signs [4]uint64
+	var idx [4]uint16 // indices into ps
+
+	for j := 0; j < 4; j++ {
+		if ps[j] != nil {
+			signs[j] = state[j]
+			*ps[j] = common.Poly{} // zero ps[j]
+			idx[j] = common.N - Tau
+		} else {
+			idx[j] = common.N // mark as completed
+		}
+	}
+
+	stateOffset := 1
+	for {
+		done := true
+
+	PolyLoop:
+		for j := 0; j < 4; j++ {
+			if idx[j] == common.N {
+				continue
+			}
+
+			for i := stateOffset; i < 17; i++ {
+				var bs [8]byte
+				binary.LittleEndian.PutUint64(bs[:], state[4*i+j])
+				for k := 0; k < 8; k++ {
+					b := uint16(bs[k])
+
+					if b > idx[j] {
+						continue
+					}
+
+					ps[j][idx[j]] = ps[j][b]
+					ps[j][b] = 1
+					// Takes least significant bit of signs and uses it for the sign.
+					// Note 1 ^ (1 | (Q-1)) = Q-1.
+					ps[j][b] ^= uint32((-(signs[j] & 1)) & (1 | (common.Q - 1)))
+					signs[j] >>= 1
+
+					idx[j]++
+					if idx[j] == common.N {
+						continue PolyLoop
+					}
+				}
+			}
+
+			done = false
+		}
+
+		if done {
+			break
+		}
+
+		perm.Permute()
+		stateOffset = 0
+	}
+}
+
+// Samples p uniformly with τ non-zero coefficients in {q-1,1}.
+//
+// The polynomial p will be normalized.
+func PolyDeriveUniformBall(p *common.Poly, seed []byte) {
+	var buf [136]byte // SHAKE-256 rate is 136
+
+	h := sha3.NewShake256()
+	_, _ = h.Write(seed[:])
+	_, _ = h.Read(buf[:])
+
+	// Essentially we generate a sequence of τ ones or minus ones,
+	// prepend 196 zeroes and shuffle the concatenation using the
+	// usual algorithm (Fisher--Yates.)
+	signs := binary.LittleEndian.Uint64(buf[:])
+	bufOff := 8 // offset into buf
+
+	*p = common.Poly{} // zero p
+	for i := uint16(common.N - Tau); i < common.N; i++ {
+		var b uint16
+
+		// Find location of where to move the new coefficient to using
+		// rejection sampling.
+		for {
+			if bufOff >= 136 {
+				_, _ = h.Read(buf[:])
+				bufOff = 0
+			}
+
+			b = uint16(buf[bufOff])
+			bufOff++
+
+			if b <= i {
+				break
+			}
+		}
+
+		p[i] = p[b]
+		p[b] = 1
+		// Takes least significant bit of signs and uses it for the sign.
+		// Note 1 ^ (1 | (Q-1)) = Q-1.
+		p[b] ^= uint32((-(signs & 1)) & (1 | (common.Q - 1)))
+		signs >>= 1
+	}
+}
diff --git a/sign/mldsa/mldsa87/internal/sample_test.go b/sign/mldsa/mldsa87/internal/sample_test.go
new file mode 100644
index 000000000..2059599eb
--- /dev/null
+++ b/sign/mldsa/mldsa87/internal/sample_test.go
@@ -0,0 +1,266 @@
+// Code generated from mode3/internal/sample_test.go by gen.go
+
+package internal
+
+import (
+	"encoding/binary"
+	"testing"
+
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+)
+
+func TestVectorDeriveUniform(t *testing.T) {
+	var p, p2 common.Poly
+	var seed [32]byte
+	if UseAES {
+		p2 = common.Poly{
+			6724291, 310295, 6949524, 4464039, 1482136, 2522903,
+			7025059, 3006320, 7286364, 7516512, 3361305, 1955529,
+			4765954, 1725325, 6933066, 4299100, 6625173, 4272792,
+			583034, 4971409, 2259140, 7715362, 3975394, 2341624,
+			5481174, 8150082, 365246, 5491939, 1083120, 7517301,
+			3104783, 2475292, 184149, 6425226, 4591622, 5964030,
+			4729604, 5471092, 1828227, 1082044, 2516245, 1692580,
+			3274844, 5443294, 7256740, 4989638, 3191250, 7479519,
+			5124211, 5603858, 1230692, 2513454, 2828034, 4254312,
+			1512596, 5245430, 5517392, 2814840, 932545, 6826733,
+			3511094, 4075348, 3233981, 7268882, 2913733, 4870249,
+			4123492, 8124406, 4016949, 5478752, 2750895, 603525,
+			5724798, 3985430, 3483012, 6434230, 3136996, 8297976,
+			4107616, 7307748, 6962904, 7544473, 1193110, 3448595,
+			4814773, 5607932, 8221314, 1054046, 1541208, 1866050,
+			8227412, 2925778, 5293953, 2065416, 4972769, 3616283,
+			7990594, 1105530, 7121836, 1170740, 7417431, 633146,
+			253820, 7235019, 3539504, 6807707, 451390, 5481526,
+			2859902, 1063061, 4579730, 7126652, 7033767, 4294814,
+			1414604, 7620048, 1953268, 8304556, 1156814, 1182881,
+			5311519, 3057534, 5277666, 682843, 2070398, 2874278,
+			4859533, 6376664, 6694074, 1590242, 2620706, 8331066,
+			5643845, 5037538, 2891516, 7004879, 3754327, 5031296,
+			5463118, 2420870, 8116529, 5517696, 7435129, 3873963,
+			710407, 713806, 175647, 4274571, 2655021, 7319503,
+			3027243, 7129679, 4213435, 2429323, 4643873, 4568526,
+			649664, 1720514, 6497260, 2683517, 7672754, 7105190,
+			3148405, 5898369, 5667677, 8050874, 1587139, 7315260,
+			4337416, 2202680, 2338714, 557467, 6752058, 2469794,
+			485071, 1617604, 3590498, 2151466, 2005823, 7727956,
+			7776292, 6783433, 6787146, 1732833, 3596857, 7436284,
+			4483349, 4970142, 4472608, 6478342, 1236215, 5695744,
+			2280717, 2889355, 3233946, 5187812, 978685, 5177364,
+			2922353, 4824807, 5302883, 6739803, 8092453, 5883903,
+			816553, 6041174, 8317591, 1459178, 5332455, 1835058,
+			1368601, 2820950, 3479224, 2589540, 7992934, 3421045,
+			4657128, 8292902, 4153567, 3553988, 7830320, 6722913,
+			2555309, 4149801, 8328975, 1560545, 7757473, 3106458,
+			4310856, 7135453, 3481032, 652626, 1841361, 8126828,
+			6250018, 300536, 7380070, 8174419, 1418793, 6208185,
+			3906256, 6679016, 1605701, 3561489, 5819724, 5746996,
+			8044214, 7087187, 7102330, 4962927, 4253983, 7108567,
+			4119736, 6584065, 441634, 6941656,
+		}
+	} else {
+		p2 = common.Poly{
+			2901364, 562527, 5258502, 3885002, 4190126, 4460268, 6884052,
+			3514511, 5383040, 213206, 2155865, 5179607, 3551954, 2312357,
+			6066350, 8126097, 1179080, 4787182, 6552182, 6713644,
+			1561067, 7626063, 7859743, 5052321, 7032876, 7815031, 157938,
+			1865184, 490802, 5717642, 3451902, 7000218, 3743250, 1677431,
+			1875427, 5596150, 671623, 3819041, 6247594, 1014875, 4933545,
+			7122446, 6682963, 3388398, 3335295, 943002, 1145083, 3113071,
+			105967, 1916675, 7474561, 1107006, 700548, 2147909, 1603855,
+			5049181, 437882, 6118899, 5656914, 6731065, 3066622, 865453,
+			5427634, 981549, 4650873, 861291, 4003872, 5104220, 6171453,
+			3723302, 7426315, 6137283, 4874820, 6052561, 53441, 5032874,
+			5614778, 2248550, 1756499, 8280764, 8263880, 7600081,
+			5118374, 795344, 7543392, 6869925, 1841187, 4181568, 584562,
+			7483939, 4938664, 6863397, 5126354, 5218129, 6236086,
+			4149293, 379169, 4368487, 7490569, 3409215, 1580463, 3081737,
+			1278732, 7109719, 7371700, 2097931, 399836, 1700274, 7188595,
+			6830029, 1548850, 6593138, 6849097, 1518037, 2859442,
+			7772265, 7325153, 3281191, 7856131, 4995056, 4684325,
+			1351194, 8223904, 6817307, 2484146, 131782, 397032, 7436778,
+			7973479, 3171829, 5624626, 3540123, 7150120, 8313283,
+			3604714, 1043574, 117692, 7797783, 7909392, 903315, 7335342,
+			7501562, 5826142, 2709813, 8245473, 2369045, 2782257,
+			5762833, 6474114, 6862031, 424522, 594248, 2626630, 7659983,
+			5642869, 4075194, 1592129, 245547, 5271031, 3205046, 982375,
+			267873, 1286496, 7230481, 3208972, 7485411, 676111, 4944500,
+			2959742, 5934456, 1414847, 6067948, 1709895, 4648315, 126008,
+			8258986, 2183134, 2302072, 4674924, 4306056, 7465311,
+			6500270, 4247428, 4016815, 4973426, 294287, 2456847, 3289700,
+			2732169, 1159447, 5569724, 140001, 3237977, 8007761, 5874533,
+			255652, 3119586, 2102434, 6248250, 8152822, 8006066, 7708625,
+			6997719, 6260212, 6186962, 6636650, 7836834, 7998017,
+			2061516, 1197591, 1706544, 733027, 2392907, 2700000, 8254598,
+			4488002, 160495, 2985325, 2036837, 2703633, 6406550, 3579947,
+			6195178, 5552390, 6804584, 6305468, 5731980, 6095195,
+			3323409, 1322661, 6690942, 3374630, 5615167, 479044, 3136054,
+			4380418, 2833144, 7829577, 1770522, 6056687, 240415, 14780,
+			3740517, 5224226, 3547288, 2083124, 4699398, 3654239,
+			5624978, 585593, 3655369, 2281739, 3338565, 1908093, 7784706,
+			4352830,
+		}
+	}
+	for i := 0; i < 32; i++ {
+		seed[i] = byte(i)
+	}
+	PolyDeriveUniform(&p, &seed, 30000)
+	if p != p2 {
+		t.Fatalf("%v != %v", p, p2)
+	}
+}
+
+func TestDeriveUniform(t *testing.T) {
+	var p common.Poly
+	var seed [32]byte
+	for i := 0; i < 100; i++ {
+		binary.LittleEndian.PutUint64(seed[:], uint64(i))
+		PolyDeriveUniform(&p, &seed, uint16(i))
+		if !PolyNormalized(&p) {
+			t.Fatal()
+		}
+	}
+}
+
+func TestDeriveUniformLeqEta(t *testing.T) {
+	var p common.Poly
+	var seed [64]byte
+	for i := 0; i < 100; i++ {
+		binary.LittleEndian.PutUint64(seed[:], uint64(i))
+		PolyDeriveUniformLeqEta(&p, &seed, uint16(i))
+		for j := 0; j < common.N; j++ {
+			if p[j] < common.Q-Eta || p[j] > common.Q+Eta {
+				t.Fatal()
+			}
+		}
+	}
+}
+
+func TestDeriveUniformLeGamma1(t *testing.T) {
+	var p common.Poly
+	var seed [64]byte
+	for i := 0; i < 100; i++ {
+		binary.LittleEndian.PutUint64(seed[:], uint64(i))
+		PolyDeriveUniformLeGamma1(&p, &seed, uint16(i))
+		for j := 0; j < common.N; j++ {
+			if (p[j] > Gamma1 && p[j] <= common.Q-Gamma1) || p[j] >= common.Q {
+				t.Fatal()
+			}
+		}
+	}
+}
+
+func TestDeriveUniformBall(t *testing.T) {
+	var p common.Poly
+	var seed [32]byte
+	for i := 0; i < 100; i++ {
+		binary.LittleEndian.PutUint64(seed[:], uint64(i))
+		PolyDeriveUniformBall(&p, seed[:])
+		nonzero := 0
+		for j := 0; j < common.N; j++ {
+			if p[j] != 0 {
+				if p[j] != 1 && p[j] != common.Q-1 {
+					t.Fatal()
+				}
+				nonzero++
+			}
+		}
+		if nonzero != Tau {
+			t.Fatal()
+		}
+	}
+}
+
+func TestDeriveUniformX4(t *testing.T) {
+	if !DeriveX4Available {
+		t.SkipNow()
+	}
+	var ps [4]common.Poly
+	var p common.Poly
+	var seed [32]byte
+	nonces := [4]uint16{12345, 54321, 13532, 37377}
+
+	for i := 0; i < len(seed); i++ {
+		seed[i] = byte(i)
+	}
+
+	PolyDeriveUniformX4([4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]}, &seed,
+		nonces)
+	for i := 0; i < 4; i++ {
+		PolyDeriveUniform(&p, &seed, nonces[i])
+		if ps[i] != p {
+			t.Fatal()
+		}
+	}
+}
+
+func TestDeriveUniformBallX4(t *testing.T) {
+	if !DeriveX4Available {
+		t.SkipNow()
+	}
+	var ps [4]common.Poly
+	var p common.Poly
+	var seed [32]byte
+	PolyDeriveUniformBallX4(
+		[4]*common.Poly{&ps[0], &ps[1], &ps[2], &ps[3]},
+		seed[:],
+	)
+	for j := 0; j < 4; j++ {
+		PolyDeriveUniformBall(&p, seed[:])
+		if ps[j] != p {
+			t.Fatalf("%d\n%v\n%v", j, ps[j], p)
+		}
+	}
+}
+
+func BenchmarkPolyDeriveUniformBall(b *testing.B) {
+	var seed [32]byte
+	var p common.Poly
+	var w1 VecK
+	for i := 0; i < b.N; i++ {
+		w1[0][0] = uint32(i)
+		PolyDeriveUniformBall(&p, seed[:])
+	}
+}
+
+func BenchmarkPolyDeriveUniformBallX4(b *testing.B) {
+	var seed [32]byte
+	var p common.Poly
+	var w1 VecK
+	for i := 0; i < b.N; i++ {
+		w1[0][0] = uint32(i)
+		PolyDeriveUniformBallX4(
+			[4]*common.Poly{&p, &p, &p, &p},
+			seed[:],
+		)
+	}
+}
+
+func BenchmarkPolyDeriveUniform(b *testing.B) {
+	var seed [32]byte
+	var p common.Poly
+	for i := 0; i < b.N; i++ {
+		PolyDeriveUniform(&p, &seed, uint16(i))
+	}
+}
+
+func BenchmarkPolyDeriveUniformX4(b *testing.B) {
+	if !DeriveX4Available {
+		b.SkipNow()
+	}
+	var seed [32]byte
+	var p [4]common.Poly
+	for i := 0; i < b.N; i++ {
+		nonce := uint16(4 * i)
+		PolyDeriveUniformX4([4]*common.Poly{&p[0], &p[1], &p[2], &p[3]},
+			&seed, [4]uint16{nonce, nonce + 1, nonce + 2, nonce + 3})
+	}
+}
+
+func BenchmarkPolyDeriveUniformLeGamma1(b *testing.B) {
+	var seed [64]byte
+	var p common.Poly
+	for i := 0; i < b.N; i++ {
+		PolyDeriveUniformLeGamma1(&p, &seed, uint16(i))
+	}
+}
diff --git a/sign/mldsa/mldsa87/internal/vec.go b/sign/mldsa/mldsa87/internal/vec.go
new file mode 100644
index 000000000..d07d3b245
--- /dev/null
+++ b/sign/mldsa/mldsa87/internal/vec.go
@@ -0,0 +1,281 @@
+// Code generated from mode3/internal/vec.go by gen.go
+
+package internal
+
+import (
+	common "github.com/cloudflare/circl/sign/internal/dilithium"
+)
+
+// A vector of L polynomials.
+type VecL [L]common.Poly
+
+// A vector of K polynomials.
+type VecK [K]common.Poly
+
+// Normalize the polynomials in this vector.
+func (v *VecL) Normalize() {
+	for i := 0; i < L; i++ {
+		v[i].Normalize()
+	}
+}
+
+// Normalize the polynomials in this vector assuming their coefficients
+// are already bounded by 2q.
+func (v *VecL) NormalizeAssumingLe2Q() {
+	for i := 0; i < L; i++ {
+		v[i].NormalizeAssumingLe2Q()
+	}
+}
+
+// Sets v to w + u.  Does not normalize.
+func (v *VecL) Add(w, u *VecL) {
+	for i := 0; i < L; i++ {
+		v[i].Add(&w[i], &u[i])
+	}
+}
+
+// Applies NTT componentwise. See Poly.NTT() for details.
+func (v *VecL) NTT() {
+	for i := 0; i < L; i++ {
+		v[i].NTT()
+	}
+}
+
+// Checks whether any of the coefficients exceeds the given bound in supnorm
+//
+// Requires the vector to be normalized.
+func (v *VecL) Exceeds(bound uint32) bool {
+	for i := 0; i < L; i++ {
+		if v[i].Exceeds(bound) {
+			return true
+		}
+	}
+	return false
+}
+
+// Applies Poly.Power2Round componentwise.
+//
+// Requires the vector to be normalized.
+func (v *VecL) Power2Round(v0PlusQ, v1 *VecL) {
+	for i := 0; i < L; i++ {
+		v[i].Power2Round(&v0PlusQ[i], &v1[i])
+	}
+}
+
+// Applies Poly.Decompose componentwise.
+//
+// Requires the vector to be normalized.
+func (v *VecL) Decompose(v0PlusQ, v1 *VecL) {
+	for i := 0; i < L; i++ {
+		PolyDecompose(&v[i], &v0PlusQ[i], &v1[i])
+	}
+}
+
+// Sequentially packs each polynomial using Poly.PackLeqEta().
+func (v *VecL) PackLeqEta(buf []byte) {
+	offset := 0
+	for i := 0; i < L; i++ {
+		PolyPackLeqEta(&v[i], buf[offset:])
+		offset += PolyLeqEtaSize
+	}
+}
+
+// Sets v to the polynomials packed in buf using VecL.PackLeqEta().
+func (v *VecL) UnpackLeqEta(buf []byte) {
+	offset := 0
+	for i := 0; i < L; i++ {
+		PolyUnpackLeqEta(&v[i], buf[offset:])
+		offset += PolyLeqEtaSize
+	}
+}
+
+// Sequentially packs each polynomial using PolyPackLeGamma1().
+func (v *VecL) PackLeGamma1(buf []byte) {
+	offset := 0
+	for i := 0; i < L; i++ {
+		PolyPackLeGamma1(&v[i], buf[offset:])
+		offset += PolyLeGamma1Size
+	}
+}
+
+// Sets v to the polynomials packed in buf using VecL.PackLeGamma1().
+func (v *VecL) UnpackLeGamma1(buf []byte) {
+	offset := 0
+	for i := 0; i < L; i++ {
+		PolyUnpackLeGamma1(&v[i], buf[offset:])
+		offset += PolyLeGamma1Size
+	}
+}
+
+// Normalize the polynomials in this vector.
+func (v *VecK) Normalize() {
+	for i := 0; i < K; i++ {
+		v[i].Normalize()
+	}
+}
+
+// Normalize the polynomials in this vector assuming their coefficients
+// are already bounded by 2q.
+func (v *VecK) NormalizeAssumingLe2Q() {
+	for i := 0; i < K; i++ {
+		v[i].NormalizeAssumingLe2Q()
+	}
+}
+
+// Sets v to w + u.  Does not normalize.
+func (v *VecK) Add(w, u *VecK) {
+	for i := 0; i < K; i++ {
+		v[i].Add(&w[i], &u[i])
+	}
+}
+
+// Checks whether any of the coefficients exceeds the given bound in supnorm
+//
+// Requires the vector to be normalized.
+func (v *VecK) Exceeds(bound uint32) bool {
+	for i := 0; i < K; i++ {
+		if v[i].Exceeds(bound) {
+			return true
+		}
+	}
+	return false
+}
+
+// Applies Poly.Power2Round componentwise.
+//
+// Requires the vector to be normalized.
+func (v *VecK) Power2Round(v0PlusQ, v1 *VecK) {
+	for i := 0; i < K; i++ {
+		v[i].Power2Round(&v0PlusQ[i], &v1[i])
+	}
+}
+
+// Applies Poly.Decompose componentwise.
+//
+// Requires the vector to be normalized.
+func (v *VecK) Decompose(v0PlusQ, v1 *VecK) {
+	for i := 0; i < K; i++ {
+		PolyDecompose(&v[i], &v0PlusQ[i], &v1[i])
+	}
+}
+
+// Sets v to the hint vector for v0 the modified low bits and v1
+// the unmodified high bits --- see makeHint().
+//
+// Returns the number of ones in the hint vector.
+func (v *VecK) MakeHint(v0, v1 *VecK) (pop uint32) {
+	for i := 0; i < K; i++ {
+		pop += PolyMakeHint(&v[i], &v0[i], &v1[i])
+	}
+	return
+}
+
+// Computes corrections to the high bits of the polynomials in the vector
+// w using the hints in h and sets v to the corrected high bits.  Returns v.
+// See useHint().
+func (v *VecK) UseHint(q, hint *VecK) *VecK {
+	for i := 0; i < K; i++ {
+		PolyUseHint(&v[i], &q[i], &hint[i])
+	}
+	return v
+}
+
+// Sequentially packs each polynomial using Poly.PackT1().
+func (v *VecK) PackT1(buf []byte) {
+	offset := 0
+	for i := 0; i < K; i++ {
+		v[i].PackT1(buf[offset:])
+		offset += common.PolyT1Size
+	}
+}
+
+// Sets v to the vector packed into buf by PackT1().
+func (v *VecK) UnpackT1(buf []byte) {
+	offset := 0
+	for i := 0; i < K; i++ {
+		v[i].UnpackT1(buf[offset:])
+		offset += common.PolyT1Size
+	}
+}
+
+// Sequentially packs each polynomial using Poly.PackT0().
+func (v *VecK) PackT0(buf []byte) {
+	offset := 0
+	for i := 0; i < K; i++ {
+		v[i].PackT0(buf[offset:])
+		offset += common.PolyT0Size
+	}
+}
+
+// Sets v to the vector packed into buf by PackT0().
+func (v *VecK) UnpackT0(buf []byte) {
+	offset := 0
+	for i := 0; i < K; i++ {
+		v[i].UnpackT0(buf[offset:])
+		offset += common.PolyT0Size
+	}
+}
+
+// Sequentially packs each polynomial using Poly.PackLeqEta().
+func (v *VecK) PackLeqEta(buf []byte) {
+	offset := 0
+	for i := 0; i < K; i++ {
+		PolyPackLeqEta(&v[i], buf[offset:])
+		offset += PolyLeqEtaSize
+	}
+}
+
+// Sets v to the polynomials packed in buf using VecK.PackLeqEta().
+func (v *VecK) UnpackLeqEta(buf []byte) {
+	offset := 0
+	for i := 0; i < K; i++ {
+		PolyUnpackLeqEta(&v[i], buf[offset:])
+		offset += PolyLeqEtaSize
+	}
+}
+
+// Applies NTT componentwise. See Poly.NTT() for details.
+func (v *VecK) NTT() {
+	for i := 0; i < K; i++ {
+		v[i].NTT()
+	}
+}
+
+// Sequentially packs each polynomial using PolyPackW1().
+func (v *VecK) PackW1(buf []byte) {
+	offset := 0
+	for i := 0; i < K; i++ {
+		PolyPackW1(&v[i], buf[offset:])
+		offset += PolyW1Size
+	}
+}
+
+// Sets v to a - b.
+//
+// Warning: assumes coefficients of the polynomials of  b are less than 2q.
+func (v *VecK) Sub(a, b *VecK) {
+	for i := 0; i < K; i++ {
+		v[i].Sub(&a[i], &b[i])
+	}
+}
+
+// Sets v to 2ᵈ w without reducing.
+func (v *VecK) MulBy2toD(w *VecK) {
+	for i := 0; i < K; i++ {
+		v[i].MulBy2toD(&w[i])
+	}
+}
+
+// Applies InvNTT componentwise. See Poly.InvNTT() for details.
+func (v *VecK) InvNTT() {
+	for i := 0; i < K; i++ {
+		v[i].InvNTT()
+	}
+}
+
+// Applies Poly.ReduceLe2Q() componentwise.
+func (v *VecK) ReduceLe2Q() {
+	for i := 0; i < K; i++ {
+		v[i].ReduceLe2Q()
+	}
+}