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frodo.go
547 lines (444 loc) · 13.4 KB
/
frodo.go
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// Package frodo640shake implements the variant FrodoKEM-640 with SHAKE.
package frodo640shake
import (
"bytes"
cryptoRand "crypto/rand"
"crypto/subtle"
"io"
"github.com/cloudflare/circl/internal/sha3"
"github.com/cloudflare/circl/kem"
)
const (
paramN = 640
// Denoted by 'mbar' in the FrodoKEM spec.
paramNbar = 8
logQ = 15
logQMask = ((1 << logQ) - 1)
seedASize = 16
pkHashSize = 16
// Denoted by 'B' in the FrodoKEM spec.
extractedBits = 2
messageSize = 16
matrixBpPackedSize = (logQ * (paramN * paramNbar)) / 8
)
const (
// Size of seed for NewKeyFromSeed.
// = len(s) + len(seedSE) + len(z).
KeySeedSize = SharedKeySize + SharedKeySize + 16
// Size of seed for EncapsulateTo.
EncapsulationSeedSize = 16
// Size of the established shared key.
SharedKeySize = 16
// Size of the encapsulated shared key.
CiphertextSize = 9720
// Size of a packed public key.
PublicKeySize = 9616
// Size of a packed private key.
PrivateKeySize = 19888
)
// Multi-dimensional arrays are stored in 1-dimensional arrays in
// row-major order.
type (
nByNU16 [paramN * paramN]uint16
nByNbarU16 [paramN * paramNbar]uint16
nbarByNU16 [paramNbar * paramN]uint16
nbarByNbarU16 [paramNbar * paramNbar]uint16
)
// Type of a FrodoKEM-640-SHAKE public key
type PublicKey struct {
seedA [seedASize]byte
matrixB nByNbarU16
}
// Type of a FrodoKEM-640-SHAKE private key
type PrivateKey struct {
hashInputIfDecapsFail [SharedKeySize]byte
pk *PublicKey
// matrixS stores transpose(S)
matrixS nByNbarU16
// H(packed(pk))
hpk [pkHashSize]byte
}
// NewKeyFromSeed derives a public/private keypair deterministically
// from the given seed.
//
// Panics if seed is not of length KeySeedSize.
func newKeyFromSeed(seed []byte) (*PublicKey, *PrivateKey) {
if len(seed) != KeySeedSize {
panic("seed must be of length KeySeedSize")
}
var sk PrivateKey
var pk PublicKey
var E nByNbarU16
var byteSE [2 * (len(sk.matrixS) + len(E))]byte
var A nByNU16
// Generate the secret value s, and the seed for S, E, and A. Add seedA to the public key
shake128 := sha3.NewShake128()
_, _ = shake128.Write(seed[2*SharedKeySize:])
_, _ = shake128.Read(pk.seedA[:])
shake128.Reset()
_, _ = shake128.Write([]byte{0x5F})
_, _ = shake128.Write(seed[SharedKeySize : 2*SharedKeySize])
_, _ = shake128.Read(byteSE[:])
i := 0
for i < len(sk.matrixS) {
sk.matrixS[i] = uint16(byteSE[i*2]) | (uint16(byteSE[(i*2)+1]) << 8)
i++
}
sample(sk.matrixS[:])
for j := range E {
E[j] = uint16(byteSE[i*2]) | (uint16(byteSE[(i*2)+1]) << 8)
i++
}
sample(E[:])
expandSeedIntoA(&A, &pk.seedA, &shake128)
mulAddASPlusE(&pk.matrixB, &A, &sk.matrixS, &E)
// Populate the private key
copy(sk.hashInputIfDecapsFail[:], seed[0:SharedKeySize])
sk.pk = &pk
// Add H(pk) to the private key
shake128.Reset()
var ppk [PublicKeySize]byte
pk.Pack(ppk[:])
_, _ = shake128.Write(ppk[:])
_, _ = shake128.Read(sk.hpk[:])
return &pk, &sk
}
// GenerateKeyPair generates public and private keys using entropy from rand.
// If rand is nil, crypto/rand.Reader will be used.
func generateKeyPair(rand io.Reader) (*PublicKey, *PrivateKey, error) {
var seed [KeySeedSize]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, err
}
// EncapsulateTo generates a shared key and a ciphertext containing said key
// from the public key and the randomness from seed and writes the shared key
// to ss and ciphertext to ct.
//
// Panics if ss, ct, or seed are not of length SharedKeySize, CiphertextSize
// and EncapsulationSeedSize respectively.
//
// seed may be nil, in which case crypto/rand.Reader is used to generate one.
func (pk *PublicKey) EncapsulateTo(ct []byte, ss []byte, seed []byte) {
if seed == nil {
seed = make([]byte, EncapsulationSeedSize)
if _, err := cryptoRand.Read(seed[:]); err != nil {
panic(err)
}
}
if len(seed) != EncapsulationSeedSize {
panic("seed must be of length EncapsulationSeedSize")
}
if len(ct) != CiphertextSize {
panic("ct must be of length CiphertextSize")
}
if len(ss) != SharedKeySize {
panic("ss must be of length SharedKeySize")
}
var G2out [2 * SharedKeySize]byte
var SpEpEpp [(paramN * paramNbar) + (paramN * paramNbar) + (paramNbar * paramNbar)]uint16
var byteSpEpEpp [2 * len(SpEpEpp)]byte
Sp := SpEpEpp[:paramN*paramNbar]
Ep := SpEpEpp[paramN*paramNbar : 2*paramN*paramNbar]
Epp := SpEpEpp[2*paramN*paramNbar:]
var Bp nbarByNU16
var V nbarByNbarU16
var C nbarByNbarU16
var A nByNU16
var hpk [pkHashSize]byte
var mu [messageSize]byte
copy(mu[:], seed[:messageSize])
// compute hpk = G_1(packed(pk))
shake128 := sha3.NewShake128()
var ppk [PublicKeySize]byte
pk.Pack(ppk[:])
_, _ = shake128.Write(ppk[:])
_, _ = shake128.Read(hpk[:])
// compute (seedSE || k) = G_2(hpk || mu)
shake128.Reset()
_, _ = shake128.Write(hpk[:])
_, _ = shake128.Write(mu[:])
_, _ = shake128.Read(G2out[:])
// Generate Sp, Ep, Epp, and A, and compute:
// Bp = Sp*A + Ep
// V = Sp*B + Epp
shake128.Reset()
_, _ = shake128.Write([]byte{0x96})
_, _ = shake128.Write(G2out[:SharedKeySize])
_, _ = shake128.Read(byteSpEpEpp[:])
for i := range SpEpEpp {
SpEpEpp[i] = uint16(byteSpEpEpp[i*2]) | (uint16(byteSpEpEpp[(i*2)+1]) << 8)
}
sample(SpEpEpp[:])
expandSeedIntoA(&A, &pk.seedA, &shake128)
mulAddSAPlusE(&Bp, Sp, &A, Ep)
mulAddSBPlusE(&V, Sp, &pk.matrixB, Epp)
// Encode mu, and compute C = V + enc(mu) (mod q)
encodeMessage(&C, &mu)
add(&C, &V, &C)
// Prepare the ciphertext
pack(ct[:matrixBpPackedSize], Bp[:])
pack(ct[matrixBpPackedSize:], C[:])
// Compute ss = F(ct||k)
shake128.Reset()
_, _ = shake128.Write(ct[:])
_, _ = shake128.Write(G2out[SharedKeySize:])
_, _ = shake128.Read(ss[:])
}
// DecapsulateTo computes the shared key that is encapsulated in ct
// from the private key.
//
// Panics if ct or ss are not of length CiphertextSize and SharedKeySize
// respectively.
func (sk *PrivateKey) DecapsulateTo(ss, ct []byte) {
if len(ct) != CiphertextSize {
panic("ct must be of length CiphertextSize")
}
if len(ss) != SharedKeySize {
panic("ss must be of length SharedKeySize")
}
var Bp nbarByNU16
var C nbarByNbarU16
var W nbarByNbarU16
var CC nbarByNbarU16
var BBp nbarByNU16
var SpEpEpp [(paramN * paramNbar) + (paramN * paramNbar) + (paramNbar * paramNbar)]uint16
var byteSpEpEpp [2 * len(SpEpEpp)]byte
Sp := SpEpEpp[:paramN*paramNbar]
Ep := SpEpEpp[paramN*paramNbar : 2*paramN*paramNbar]
Epp := SpEpEpp[2*paramN*paramNbar:]
var A nByNU16
var muprime [messageSize]byte
var G2out [2 * SharedKeySize]byte
kprime := G2out[SharedKeySize:]
// Compute W = C - Bp*S (mod q), and decode the randomness mu
unpack(Bp[:], ct[0:matrixBpPackedSize])
unpack(C[:], ct[matrixBpPackedSize:])
mulBS(&W, &Bp, &sk.matrixS)
sub(&W, &C, &W)
decodeMessage(&muprime, &W)
// Generate (seedSE' || k') = G_2(hpk || mu')
shake128 := sha3.NewShake128()
_, _ = shake128.Write(sk.hpk[:])
_, _ = shake128.Write(muprime[:])
_, _ = shake128.Read(G2out[:])
// Generate Sp, Ep, Epp, A, and compute BBp = Sp*A + Ep.
shake128.Reset()
_, _ = shake128.Write([]byte{0x96})
_, _ = shake128.Write(G2out[:SharedKeySize])
_, _ = shake128.Read(byteSpEpEpp[:])
for i := range SpEpEpp {
SpEpEpp[i] = uint16(byteSpEpEpp[i*2]) | (uint16(byteSpEpEpp[(i*2)+1]) << 8)
}
sample(SpEpEpp[:])
expandSeedIntoA(&A, &sk.pk.seedA, &shake128)
mulAddSAPlusE(&BBp, Sp[:], &A, Ep[:])
// Reduce BBp modulo q
for i := range BBp {
BBp[i] = BBp[i] & logQMask
}
// compute W = Sp*B + Epp
mulAddSBPlusE(&W, Sp, &sk.pk.matrixB, Epp)
// Encode mu, and compute CC = W + enc(mu') (mod q)
encodeMessage(&CC, &muprime)
add(&CC, &W, &CC)
// Prepare input to F
// If (Bp == BBp & C == CC) then ss = F(ct || k'), else ss = F(ct || s)
// Needs to avoid branching on secret data as per:
// Qian Guo, Thomas Johansson, Alexander Nilsson. A key-recovery timing attack on post-quantum
// primitives using the Fujisaki-Okamoto transformation and its application on FrodoKEM. In CRYPTO 2020.
selector := ctCompareU16(Bp[:], BBp[:]) | ctCompareU16(C[:], CC[:])
// If (selector == 0) then load k' to do ss = F(ct || k'), else if (selector == 1) load s to do ss = F(ct || s)
subtle.ConstantTimeCopy(selector, kprime[:], sk.hashInputIfDecapsFail[:])
shake128.Reset()
_, _ = shake128.Write(ct[:])
_, _ = shake128.Write(kprime[:])
_, _ = shake128.Read(ss[:])
}
// Packs sk to buf.
//
// Panics if buf is not of size PrivateKeySize.
func (sk *PrivateKey) Pack(buf []byte) {
if len(buf) != PrivateKeySize {
panic("buf must be of length PrivateKeySize")
}
copy(buf[:SharedKeySize], sk.hashInputIfDecapsFail[:])
buf = buf[SharedKeySize:]
sk.pk.Pack(buf[:PublicKeySize])
buf = buf[PublicKeySize:]
j := 0
for i := range sk.matrixS {
buf[j] = byte(sk.matrixS[i])
buf[j+1] = byte(sk.matrixS[i] >> 8)
j += 2
}
buf = buf[j:]
copy(buf[:], sk.hpk[:])
}
// Unpacks sk from buf.
//
// Panics if buf is not of size PrivateKeySize.
func (sk *PrivateKey) Unpack(buf []byte) {
if len(buf) != PrivateKeySize {
panic("buf must be of length PrivateKeySize")
}
copy(sk.hashInputIfDecapsFail[:], buf[:SharedKeySize])
buf = buf[SharedKeySize:]
sk.pk = new(PublicKey)
sk.pk.Unpack(buf[:PublicKeySize])
buf = buf[PublicKeySize:]
for i := range sk.matrixS {
sk.matrixS[i] = uint16(buf[i*2]) | (uint16(buf[(i*2)+1]) << 8)
}
buf = buf[len(sk.matrixS)*2:]
copy(sk.hpk[:], buf[:])
}
// Packs pk to buf.
//
// Panics if buf is not of size PublicKeySize.
func (pk *PublicKey) Pack(buf []byte) {
if len(buf) != PublicKeySize {
panic("buf must be of length PublicKeySize")
}
copy(buf[:seedASize], pk.seedA[:])
pack(buf[seedASize:], pk.matrixB[:])
}
// TODO: Unpacks pk from buf.
//
// Panics if buf is not of size PublicKeySize.
func (pk *PublicKey) Unpack(buf []byte) {
if len(buf) != PublicKeySize {
panic("buf must be of length PublicKeySize")
}
copy(pk.seedA[:], buf[:seedASize])
unpack(pk.matrixB[:], buf[seedASize:])
}
// Boilerplate down below for the KEM scheme API.
type scheme struct{}
var sch kem.Scheme = &scheme{}
// Scheme returns a KEM interface.
func Scheme() kem.Scheme { return sch }
func (scheme) Name() string { return "FrodoKEM-640-SHAKE" }
func (*scheme) PublicKeySize() int { return PublicKeySize }
func (*scheme) PrivateKeySize() int { return PrivateKeySize }
func (*scheme) SeedSize() int { return KeySeedSize }
func (*scheme) SharedKeySize() int { return SharedKeySize }
func (*scheme) CiphertextSize() int { return CiphertextSize }
func (*scheme) EncapsulationSeedSize() int { return EncapsulationSeedSize }
func (sk *PrivateKey) Scheme() kem.Scheme { return sch }
func (pk *PublicKey) Scheme() kem.Scheme { return sch }
func (sk *PrivateKey) MarshalBinary() ([]byte, error) {
var ret [PrivateKeySize]byte
sk.Pack(ret[:])
return ret[:], nil
}
func (sk *PrivateKey) Equal(other kem.PrivateKey) bool {
oth, ok := other.(*PrivateKey)
if !ok {
return false
}
if sk.pk == nil && oth.pk == nil {
return true
}
if sk.pk == nil || oth.pk == nil {
return false
}
return ctCompareU16(sk.matrixS[:], oth.matrixS[:]) == 0 &&
subtle.ConstantTimeCompare(sk.hashInputIfDecapsFail[:], oth.hashInputIfDecapsFail[:]) == 1 &&
sk.pk.Equal(oth.pk) &&
bytes.Equal(sk.hpk[:], oth.hpk[:])
}
func (pk *PublicKey) Equal(other kem.PublicKey) bool {
oth, ok := other.(*PublicKey)
if !ok {
return false
}
if pk == nil && oth == nil {
return true
}
if pk == nil || oth == nil {
return false
}
for i := range pk.matrixB {
if (pk.matrixB[i] & logQMask) != (oth.matrixB[i] & logQMask) {
return false
}
}
return bytes.Equal(pk.seedA[:], oth.seedA[:])
}
func (sk *PrivateKey) Public() kem.PublicKey {
return sk.pk
}
func (pk *PublicKey) MarshalBinary() ([]byte, error) {
var ret [PublicKeySize]byte
pk.Pack(ret[:])
return ret[:], nil
}
func (*scheme) GenerateKeyPair() (kem.PublicKey, kem.PrivateKey, error) {
return generateKeyPair(cryptoRand.Reader)
}
func (*scheme) DeriveKeyPair(seed []byte) (kem.PublicKey, kem.PrivateKey) {
if len(seed) != KeySeedSize {
panic(kem.ErrSeedSize)
}
return newKeyFromSeed(seed[:])
}
func (*scheme) Encapsulate(pk kem.PublicKey) (ct, ss []byte, err error) {
ct = make([]byte, CiphertextSize)
ss = make([]byte, SharedKeySize)
pub, ok := pk.(*PublicKey)
if !ok {
return nil, nil, kem.ErrTypeMismatch
}
pub.EncapsulateTo(ct, ss, nil)
return
}
func (*scheme) EncapsulateDeterministically(
pk kem.PublicKey, seed []byte,
) (ct, ss []byte, err error) {
if len(seed) != EncapsulationSeedSize {
return nil, nil, kem.ErrSeedSize
}
ct = make([]byte, CiphertextSize)
ss = make([]byte, SharedKeySize)
pub, ok := pk.(*PublicKey)
if !ok {
return nil, nil, kem.ErrTypeMismatch
}
pub.EncapsulateTo(ct, ss, seed)
return
}
func (*scheme) Decapsulate(sk kem.PrivateKey, ct []byte) ([]byte, error) {
if len(ct) != CiphertextSize {
return nil, kem.ErrCiphertextSize
}
priv, ok := sk.(*PrivateKey)
if !ok {
return nil, kem.ErrTypeMismatch
}
ss := make([]byte, SharedKeySize)
priv.DecapsulateTo(ss, ct)
return ss, nil
}
func (*scheme) UnmarshalBinaryPublicKey(buf []byte) (kem.PublicKey, error) {
if len(buf) != PublicKeySize {
return nil, kem.ErrPubKeySize
}
var ret PublicKey
ret.Unpack(buf)
return &ret, nil
}
func (*scheme) UnmarshalBinaryPrivateKey(buf []byte) (kem.PrivateKey, error) {
if len(buf) != PrivateKeySize {
return nil, kem.ErrPrivKeySize
}
var ret PrivateKey
ret.Unpack(buf)
return &ret, nil
}