/
dilithium.go
477 lines (401 loc) · 11 KB
/
dilithium.go
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// 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"
"github.com/cloudflare/circl/sign/dilithium/internal/common"
)
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 + 32 + 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
// 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 *[32]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 [32]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 [32]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:])
}
// 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[32:])
if sig.z.Exceeds(Gamma1 - Beta) {
return false
}
if !sig.hint.UnpackHint(buf[32+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([32]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[64:96], sk.tr[:])
offset := 96
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[64:96])
offset := 96
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 [32]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)
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[:])
_, _ = 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)
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
}