diff --git a/secretsharing/ss.go b/secretsharing/ss.go
index 9573ddf0..d23da9d1 100644
--- a/secretsharing/ss.go
+++ b/secretsharing/ss.go
@@ -32,49 +32,28 @@ import (
 type Share struct {
 	// ID uniquely identifies a share in a secret sharing instance.
 	ID group.Scalar
-	// Value stores the share generated from a secret sharing instance.
+	// Value stores the share generated by a secret sharing instance.
 	Value group.Scalar
 }
 
+// SecretSharing provides a (t,n) Shamir's secret sharing. It allows splitting
+// a secret into n shares, such that the secret can be only recovered from
+// any subset of t+1 shares.
 type SecretSharing struct {
 	t uint // t is the threshold.
 }
 
-// NewShamirSecretSharing implements a (t,n) Shamir's secret sharing.
-// A (t,n) secret sharing allows to split a secret into n shares, such that the
-// secret can be only recovered from any subset of t+1 shares.
+// NewShamirSecretSharing implements a (t,n) Shamir's secret sharing with
+// threshold t.
 func NewShamirSecretSharing(t uint) SecretSharing { return SecretSharing{t} }
 
-func (s SecretSharing) polyFromSecret(rnd io.Reader, secret group.Scalar) polynomial.Polynomial {
-	c := make([]group.Scalar, s.t+1)
-	g := secret.Group()
-	c[0] = secret.Copy()
-	for i := 1; i < len(c); i++ {
-		c[i] = g.RandomScalar(rnd)
-	}
-	return polynomial.New(c)
-}
-
-// Shard splits the secret into n shares.
+// Shard splits a secret into n shares.
 func (s SecretSharing) Shard(rnd io.Reader, secret group.Scalar, n uint) ([]Share, error) {
-	if n <= s.t {
-		return nil, errThreshold(s.t, n)
-	}
-
-	g := secret.Group()
-	poly := s.polyFromSecret(rnd, secret)
-	shares := make([]Share, n)
-	for i := range shares {
-		id := g.NewScalar().SetUint64(uint64(i + 1))
-		shares[i] = Share{ID: id, Value: poly.Evaluate(id)}
-	}
-
-	return shares, nil
+	return NewSplitter(rnd, s.t, secret).multipleShard(n)
 }
 
 // Recover returns the secret provided more than t shares are given. Returns an
-// error if the number of shares is not above the threshold or goes beyond the
-// maximum number of shares.
+// error if the number of shares is not above the threshold t.
 func (s SecretSharing) Recover(shares []Share) (group.Scalar, error) {
 	if l := len(shares); l <= int(s.t) {
 		return nil, errThreshold(s.t, uint(l))
@@ -95,13 +74,15 @@ func (s SecretSharing) Recover(shares []Share) (group.Scalar, error) {
 
 type SharesCommitment = []group.Element
 
+// VerifiableSecretSharing provides a (t,n) Feldman's verifiable secret sharing.
+// It allows splitting a secret into n shares, such that the secret can be only
+// recovered from any subset of t+1 shares.
+// It's verifiable as it allows checking whether a share is part of a secret
+// committed during sharding.
 type VerifiableSecretSharing struct{ s SecretSharing }
 
 // NewFeldmanSecretSharing implements a (t,n) Feldman's verifiable secret
-// sharing. A (t,n) secret sharing allows to split a secret into n shares, such
-// that the secret can be only recovered from any subset of t+1 shares. It's
-// verifiable as it allows checking whether a share is part of a secret committed
-// during sharding.
+// sharing with threshold t.
 func NewFeldmanSecretSharing(t uint) (v VerifiableSecretSharing) { v.s.t = t; return }
 
 // Shard splits the secret into n shares, and also returns a commitment to both
@@ -109,28 +90,23 @@ func NewFeldmanSecretSharing(t uint) (v VerifiableSecretSharing) { v.s.t = t; re
 // so each party can verify its share is correct. Sharding a secret more
 // than once produces ShareCommitments with the same first entry.
 func (v VerifiableSecretSharing) Shard(rnd io.Reader, secret group.Scalar, n uint) ([]Share, SharesCommitment, error) {
-	if n <= v.s.t {
-		return nil, nil, errThreshold(v.s.t, n)
+	splitter := NewSplitter(rnd, v.s.t, secret)
+	shares, err := splitter.multipleShard(n)
+	if err != nil {
+		return nil, nil, err
 	}
 
 	g := secret.Group()
-	poly := v.s.polyFromSecret(rnd, secret)
-	shares := make([]Share, n)
-	for i := range shares {
-		id := g.NewScalar().SetUint64(uint64(i + 1))
-		shares[i] = Share{ID: id, Value: poly.Evaluate(id)}
-	}
-	shareComs := make(SharesCommitment, poly.Degree()+1)
+	shareComs := make(SharesCommitment, splitter.poly.Degree()+1)
 	for i := range shareComs {
-		shareComs[i] = g.NewElement().MulGen(poly.Coefficient(uint(i)))
+		shareComs[i] = g.NewElement().MulGen(splitter.poly.Coefficient(uint(i)))
 	}
 
 	return shares, shareComs, nil
 }
 
-// Verify returns true if a share was produced by sharding a secret. It uses
-// the share commitments generated by the Shard function to verify this
-// property.
+// Verify returns true if a share was produced by sharding a secret. It uses the
+// share commitments generated by the Shard function.
 func (v VerifiableSecretSharing) Verify(s Share, c SharesCommitment) bool {
 	if len(c) != int(v.s.t+1) {
 		return false
@@ -148,12 +124,60 @@ func (v VerifiableSecretSharing) Verify(s Share, c SharesCommitment) bool {
 }
 
 // Recover returns the secret provided more than t shares are given. Returns an
-// error if the number of shares is not above the threshold (t) or is larger
-// than the maximum number of shares (n).
+// error if the number of shares is not above the threshold t.
 func (v VerifiableSecretSharing) Recover(shares []Share) (group.Scalar, error) {
 	return v.s.Recover(shares)
 }
 
-var errThreshold = func(t, n uint) error {
+type Splitter struct {
+	g    group.Group
+	t    uint
+	poly polynomial.Polynomial
+}
+
+// NewSplitter returns a Splitter that can shard a secret with threshold t.
+func NewSplitter(rnd io.Reader, t uint, secret group.Scalar) (sp Splitter) {
+	sp.g = secret.Group()
+	sp.t = t
+
+	c := make([]group.Scalar, sp.t+1)
+	c[0] = secret.Copy()
+	for i := 1; i < len(c); i++ {
+		c[i] = sp.g.RandomScalar(rnd)
+	}
+	sp.poly = polynomial.New(c)
+
+	return
+}
+
+func (sp Splitter) multipleShard(n uint) ([]Share, error) {
+	if n <= sp.t {
+		return nil, errThreshold(sp.t, n)
+	}
+
+	shares := make([]Share, n)
+	id := sp.g.NewScalar()
+	for i := range shares {
+		shares[i] = sp.ShardWithID(id.SetUint64(uint64(i + 1)))
+	}
+
+	return shares, nil
+}
+
+func (sp Splitter) Shard(rnd io.Reader) (s Share) {
+	return sp.ShardWithID(sp.g.RandomNonZeroScalar(rnd))
+}
+
+func (sp Splitter) ShardWithID(id group.Scalar) (s Share) {
+	if id.IsZero() {
+		panic("secretsharing: id cannot be zero")
+	}
+
+	s.ID = id.Copy()
+	s.Value = sp.poly.Evaluate(s.ID)
+	return
+}
+
+func errThreshold(t, n uint) error {
 	return fmt.Errorf("secretsharing: number of shares (n=%v) must be above the threshold (t=%v)", n, t)
 }