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@@ -0,0 +1,887 @@
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+// Copyright 2023 The Go Authors. All rights reserved.
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+// Use of this source code is governed by a BSD-style
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+// license that can be found in the LICENSE file.
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+
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+// Package mlkem768 implements the quantum-resistant key encapsulation method
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+// ML-KEM (formerly known as Kyber).
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+//
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+// Only the recommended ML-KEM-768 parameter set is provided.
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+//
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+// The version currently implemented is the one specified by [NIST FIPS 203 ipd],
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+// with the unintentional transposition of the matrix A reverted to match the
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+// behavior of [Kyber version 3.0]. Future versions of this package might
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+// introduce backwards incompatible changes to implement changes to FIPS 203.
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+//
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+// [Kyber version 3.0]: https://pq-crystals.org/kyber/data/kyber-specification-round3-20210804.pdf
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+// [NIST FIPS 203 ipd]: https://doi.org/10.6028/NIST.FIPS.203.ipd
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+package mlkem768
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+
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+// This package targets security, correctness, simplicity, readability, and
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+// reviewability as its primary goals. All critical operations are performed in
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+// constant time.
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+//
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+// Variable and function names, as well as code layout, are selected to
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+// facilitate reviewing the implementation against the NIST FIPS 203 ipd
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+// document.
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+//
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+// Reviewers unfamiliar with polynomials or linear algebra might find the
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+// background at https://words.filippo.io/kyber-math/ useful.
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+
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+import (
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+ "crypto/rand"
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+ "crypto/subtle"
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+ "errors"
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+
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+ "github.com/Psiphon-Labs/psiphon-tls/byteorder"
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+
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+ "golang.org/x/crypto/sha3"
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+)
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+
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+const (
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+ // ML-KEM global constants.
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+ n = 256
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+ q = 3329
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+
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+ log2q = 12
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+
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+ // ML-KEM-768 parameters. The code makes assumptions based on these values,
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+ // they can't be changed blindly.
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+ k = 3
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+ η = 2
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+ du = 10
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+ dv = 4
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+
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+ // encodingSizeX is the byte size of a ringElement or nttElement encoded
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+ // by ByteEncode_X (FIPS 203 (DRAFT), Algorithm 4).
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+ encodingSize12 = n * log2q / 8
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+ encodingSize10 = n * du / 8
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+ encodingSize4 = n * dv / 8
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+ encodingSize1 = n * 1 / 8
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+
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+ messageSize = encodingSize1
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+ decryptionKeySize = k * encodingSize12
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+ encryptionKeySize = k*encodingSize12 + 32
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+
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+ CiphertextSize = k*encodingSize10 + encodingSize4
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+ EncapsulationKeySize = encryptionKeySize
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+ DecapsulationKeySize = decryptionKeySize + encryptionKeySize + 32 + 32
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+ SharedKeySize = 32
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+ SeedSize = 32 + 32
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+)
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+
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+// A DecapsulationKey is the secret key used to decapsulate a shared key from a
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+// ciphertext. It includes various precomputed values.
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+type DecapsulationKey struct {
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+ dk [DecapsulationKeySize]byte
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+ encryptionKey
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+ decryptionKey
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+}
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+
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+// Bytes returns the extended encoding of the decapsulation key, according to
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+// FIPS 203 (DRAFT).
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+func (dk *DecapsulationKey) Bytes() []byte {
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+ var b [DecapsulationKeySize]byte
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+ copy(b[:], dk.dk[:])
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+ return b[:]
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+}
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+
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+// EncapsulationKey returns the public encapsulation key necessary to produce
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+// ciphertexts.
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+func (dk *DecapsulationKey) EncapsulationKey() []byte {
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+ var b [EncapsulationKeySize]byte
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+ copy(b[:], dk.dk[decryptionKeySize:])
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+ return b[:]
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+}
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+
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+// encryptionKey is the parsed and expanded form of a PKE encryption key.
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+type encryptionKey struct {
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+ t [k]nttElement // ByteDecode₁₂(ek[:384k])
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+ A [k * k]nttElement // A[i*k+j] = sampleNTT(ρ, j, i)
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+}
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+
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+// decryptionKey is the parsed and expanded form of a PKE decryption key.
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+type decryptionKey struct {
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+ s [k]nttElement // ByteDecode₁₂(dk[:decryptionKeySize])
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+}
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+
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+// GenerateKey generates a new decapsulation key, drawing random bytes from
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+// crypto/rand. The decapsulation key must be kept secret.
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+func GenerateKey() (*DecapsulationKey, error) {
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+ // The actual logic is in a separate function to outline this allocation.
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+ dk := &DecapsulationKey{}
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+ return generateKey(dk)
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+}
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+
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+func generateKey(dk *DecapsulationKey) (*DecapsulationKey, error) {
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+ var d [32]byte
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+ if _, err := rand.Read(d[:]); err != nil {
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+ return nil, errors.New("mlkem768: crypto/rand Read failed: " + err.Error())
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+ }
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+ var z [32]byte
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+ if _, err := rand.Read(z[:]); err != nil {
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+ return nil, errors.New("mlkem768: crypto/rand Read failed: " + err.Error())
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+ }
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+ return kemKeyGen(dk, &d, &z), nil
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+}
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+
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+// NewKeyFromSeed deterministically generates a decapsulation key from a 64-byte
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+// seed in the "d || z" form. The seed must be uniformly random.
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+func NewKeyFromSeed(seed []byte) (*DecapsulationKey, error) {
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+ // The actual logic is in a separate function to outline this allocation.
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+ dk := &DecapsulationKey{}
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+ return newKeyFromSeed(dk, seed)
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+}
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+
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+func newKeyFromSeed(dk *DecapsulationKey, seed []byte) (*DecapsulationKey, error) {
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+ if len(seed) != SeedSize {
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+ return nil, errors.New("mlkem768: invalid seed length")
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+ }
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+ d := (*[32]byte)(seed[:32])
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+ z := (*[32]byte)(seed[32:])
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+ return kemKeyGen(dk, d, z), nil
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+}
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+
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+// NewKeyFromExtendedEncoding parses a decapsulation key from its FIPS 203
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+// (DRAFT) extended encoding.
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+func NewKeyFromExtendedEncoding(decapsulationKey []byte) (*DecapsulationKey, error) {
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+ // The actual logic is in a separate function to outline this allocation.
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+ dk := &DecapsulationKey{}
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+ return newKeyFromExtendedEncoding(dk, decapsulationKey)
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+}
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+
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+func newKeyFromExtendedEncoding(dk *DecapsulationKey, dkBytes []byte) (*DecapsulationKey, error) {
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+ if len(dkBytes) != DecapsulationKeySize {
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+ return nil, errors.New("mlkem768: invalid decapsulation key length")
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+ }
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+
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+ // Note that we don't check that H(ek) matches ekPKE, as that's not
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+ // specified in FIPS 203 (DRAFT). This is one reason to prefer the seed
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+ // private key format.
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+ dk.dk = [DecapsulationKeySize]byte(dkBytes)
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+
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+ dkPKE := dkBytes[:decryptionKeySize]
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+ if err := parseDK(&dk.decryptionKey, dkPKE); err != nil {
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+ return nil, err
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+ }
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+
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+ ekPKE := dkBytes[decryptionKeySize : decryptionKeySize+encryptionKeySize]
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+ if err := parseEK(&dk.encryptionKey, ekPKE); err != nil {
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+ return nil, err
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+ }
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+
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+ return dk, nil
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+}
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+
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+// kemKeyGen generates a decapsulation key.
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+//
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+// It implements ML-KEM.KeyGen according to FIPS 203 (DRAFT), Algorithm 15, and
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+// K-PKE.KeyGen according to FIPS 203 (DRAFT), Algorithm 12. The two are merged
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+// to save copies and allocations.
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+func kemKeyGen(dk *DecapsulationKey, d, z *[32]byte) *DecapsulationKey {
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+ if dk == nil {
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+ dk = &DecapsulationKey{}
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+ }
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+
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+ G := sha3.Sum512(d[:])
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+ ρ, σ := G[:32], G[32:]
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+
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+ A := &dk.A
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+ for i := byte(0); i < k; i++ {
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+ for j := byte(0); j < k; j++ {
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+ // Note that this is consistent with Kyber round 3, rather than with
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+ // the initial draft of FIPS 203, because NIST signaled that the
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+ // change was involuntary and will be reverted.
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+ A[i*k+j] = sampleNTT(ρ, j, i)
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+ }
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+ }
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+
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+ var N byte
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+ s := &dk.s
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+ for i := range s {
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+ s[i] = ntt(samplePolyCBD(σ, N))
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+ N++
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+ }
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+ e := make([]nttElement, k)
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+ for i := range e {
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+ e[i] = ntt(samplePolyCBD(σ, N))
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+ N++
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+ }
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+
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+ t := &dk.t
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+ for i := range t { // t = A ◦ s + e
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+ t[i] = e[i]
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+ for j := range s {
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+ t[i] = polyAdd(t[i], nttMul(A[i*k+j], s[j]))
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+ }
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+ }
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+
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+ // dkPKE ← ByteEncode₁₂(s)
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+ // ekPKE ← ByteEncode₁₂(t) || ρ
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+ // ek ← ekPKE
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+ // dk ← dkPKE || ek || H(ek) || z
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+ dkB := dk.dk[:0]
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+
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+ for i := range s {
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+ dkB = polyByteEncode(dkB, s[i])
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+ }
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+
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+ for i := range t {
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+ dkB = polyByteEncode(dkB, t[i])
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+ }
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+ dkB = append(dkB, ρ...)
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+
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+ H := sha3.New256()
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+ H.Write(dkB[decryptionKeySize:])
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+ dkB = H.Sum(dkB)
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+
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+ dkB = append(dkB, z[:]...)
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+
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+ if len(dkB) != len(dk.dk) {
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+ panic("mlkem768: internal error: invalid decapsulation key size")
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+ }
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+
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+ return dk
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+}
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+
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+// Encapsulate generates a shared key and an associated ciphertext from an
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+// encapsulation key, drawing random bytes from crypto/rand.
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+// If the encapsulation key is not valid, Encapsulate returns an error.
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+//
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+// The shared key must be kept secret.
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+func Encapsulate(encapsulationKey []byte) (ciphertext, sharedKey []byte, err error) {
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+ // The actual logic is in a separate function to outline this allocation.
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+ var cc [CiphertextSize]byte
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+ return encapsulate(&cc, encapsulationKey)
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+}
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+
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+func encapsulate(cc *[CiphertextSize]byte, encapsulationKey []byte) (ciphertext, sharedKey []byte, err error) {
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+ if len(encapsulationKey) != EncapsulationKeySize {
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+ return nil, nil, errors.New("mlkem768: invalid encapsulation key length")
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+ }
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+ var m [messageSize]byte
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+ if _, err := rand.Read(m[:]); err != nil {
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+ return nil, nil, errors.New("mlkem768: crypto/rand Read failed: " + err.Error())
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+ }
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+ return kemEncaps(cc, encapsulationKey, &m)
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+}
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+
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+// kemEncaps generates a shared key and an associated ciphertext.
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+//
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+// It implements ML-KEM.Encaps according to FIPS 203 (DRAFT), Algorithm 16.
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+func kemEncaps(cc *[CiphertextSize]byte, ek []byte, m *[messageSize]byte) (c, K []byte, err error) {
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+ if cc == nil {
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+ cc = &[CiphertextSize]byte{}
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+ }
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+
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+ H := sha3.Sum256(ek[:])
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+ g := sha3.New512()
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+ g.Write(m[:])
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+ g.Write(H[:])
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+ G := g.Sum(nil)
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+ K, r := G[:SharedKeySize], G[SharedKeySize:]
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+ var ex encryptionKey
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+ if err := parseEK(&ex, ek[:]); err != nil {
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+ return nil, nil, err
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+ }
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+ c = pkeEncrypt(cc, &ex, m, r)
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+ return c, K, nil
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+}
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+
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+// parseEK parses an encryption key from its encoded form.
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+//
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+// It implements the initial stages of K-PKE.Encrypt according to FIPS 203
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+// (DRAFT), Algorithm 13.
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+func parseEK(ex *encryptionKey, ekPKE []byte) error {
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+ if len(ekPKE) != encryptionKeySize {
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+ return errors.New("mlkem768: invalid encryption key length")
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+ }
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+
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+ for i := range ex.t {
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+ var err error
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+ ex.t[i], err = polyByteDecode[nttElement](ekPKE[:encodingSize12])
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+ if err != nil {
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+ return err
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+ }
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+ ekPKE = ekPKE[encodingSize12:]
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+ }
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+ ρ := ekPKE
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+
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+ for i := byte(0); i < k; i++ {
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+ for j := byte(0); j < k; j++ {
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+ // See the note in pkeKeyGen about the order of the indices being
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+ // consistent with Kyber round 3.
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+ ex.A[i*k+j] = sampleNTT(ρ, j, i)
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+ }
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+ }
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+
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+ return nil
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+}
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+
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+// pkeEncrypt encrypt a plaintext message.
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+//
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+// It implements K-PKE.Encrypt according to FIPS 203 (DRAFT), Algorithm 13,
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+// although the computation of t and AT is done in parseEK.
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+func pkeEncrypt(cc *[CiphertextSize]byte, ex *encryptionKey, m *[messageSize]byte, rnd []byte) []byte {
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+ var N byte
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+ r, e1 := make([]nttElement, k), make([]ringElement, k)
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+ for i := range r {
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+ r[i] = ntt(samplePolyCBD(rnd, N))
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+ N++
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+ }
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+ for i := range e1 {
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+ e1[i] = samplePolyCBD(rnd, N)
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+ N++
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+ }
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+ e2 := samplePolyCBD(rnd, N)
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+
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+ u := make([]ringElement, k) // NTT⁻¹(AT ◦ r) + e1
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+ for i := range u {
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+ u[i] = e1[i]
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+ for j := range r {
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+ // Note that i and j are inverted, as we need the transposed of A.
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+ u[i] = polyAdd(u[i], inverseNTT(nttMul(ex.A[j*k+i], r[j])))
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+ }
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+ }
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+
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+ μ := ringDecodeAndDecompress1(m)
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+
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+ var vNTT nttElement // t⊺ ◦ r
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+ for i := range ex.t {
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+ vNTT = polyAdd(vNTT, nttMul(ex.t[i], r[i]))
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+ }
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+ v := polyAdd(polyAdd(inverseNTT(vNTT), e2), μ)
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+
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+ c := cc[:0]
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+ for _, f := range u {
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+ c = ringCompressAndEncode10(c, f)
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+ }
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+ c = ringCompressAndEncode4(c, v)
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+
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+ return c
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+}
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+
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+// Decapsulate generates a shared key from a ciphertext and a decapsulation key.
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+// If the ciphertext is not valid, Decapsulate returns an error.
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+//
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+// The shared key must be kept secret.
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+func Decapsulate(dk *DecapsulationKey, ciphertext []byte) (sharedKey []byte, err error) {
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+ if len(ciphertext) != CiphertextSize {
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+ return nil, errors.New("mlkem768: invalid ciphertext length")
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+ }
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+ c := (*[CiphertextSize]byte)(ciphertext)
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+ return kemDecaps(dk, c), nil
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+}
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+
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+// kemDecaps produces a shared key from a ciphertext.
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+//
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+// It implements ML-KEM.Decaps according to FIPS 203 (DRAFT), Algorithm 17.
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+func kemDecaps(dk *DecapsulationKey, c *[CiphertextSize]byte) (K []byte) {
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+ h := dk.dk[decryptionKeySize+encryptionKeySize : decryptionKeySize+encryptionKeySize+32]
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+ z := dk.dk[decryptionKeySize+encryptionKeySize+32:]
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+
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+ m := pkeDecrypt(&dk.decryptionKey, c)
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+ g := sha3.New512()
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+ g.Write(m[:])
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+ g.Write(h)
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+ G := g.Sum(nil)
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+ Kprime, r := G[:SharedKeySize], G[SharedKeySize:]
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|
|
+ J := sha3.NewShake256()
|
|
|
+ J.Write(z)
|
|
|
+ J.Write(c[:])
|
|
|
+ Kout := make([]byte, SharedKeySize)
|
|
|
+ J.Read(Kout)
|
|
|
+ var cc [CiphertextSize]byte
|
|
|
+ c1 := pkeEncrypt(&cc, &dk.encryptionKey, (*[32]byte)(m), r)
|
|
|
+
|
|
|
+ subtle.ConstantTimeCopy(subtle.ConstantTimeCompare(c[:], c1), Kout, Kprime)
|
|
|
+ return Kout
|
|
|
+}
|
|
|
+
|
|
|
+// parseDK parses a decryption key from its encoded form.
|
|
|
+//
|
|
|
+// It implements the computation of s from K-PKE.Decrypt according to FIPS 203
|
|
|
+// (DRAFT), Algorithm 14.
|
|
|
+func parseDK(dx *decryptionKey, dkPKE []byte) error {
|
|
|
+ if len(dkPKE) != decryptionKeySize {
|
|
|
+ return errors.New("mlkem768: invalid decryption key length")
|
|
|
+ }
|
|
|
+
|
|
|
+ for i := range dx.s {
|
|
|
+ f, err := polyByteDecode[nttElement](dkPKE[:encodingSize12])
|
|
|
+ if err != nil {
|
|
|
+ return err
|
|
|
+ }
|
|
|
+ dx.s[i] = f
|
|
|
+ dkPKE = dkPKE[encodingSize12:]
|
|
|
+ }
|
|
|
+
|
|
|
+ return nil
|
|
|
+}
|
|
|
+
|
|
|
+// pkeDecrypt decrypts a ciphertext.
|
|
|
+//
|
|
|
+// It implements K-PKE.Decrypt according to FIPS 203 (DRAFT), Algorithm 14,
|
|
|
+// although the computation of s is done in parseDK.
|
|
|
+func pkeDecrypt(dx *decryptionKey, c *[CiphertextSize]byte) []byte {
|
|
|
+ u := make([]ringElement, k)
|
|
|
+ for i := range u {
|
|
|
+ b := (*[encodingSize10]byte)(c[encodingSize10*i : encodingSize10*(i+1)])
|
|
|
+ u[i] = ringDecodeAndDecompress10(b)
|
|
|
+ }
|
|
|
+
|
|
|
+ b := (*[encodingSize4]byte)(c[encodingSize10*k:])
|
|
|
+ v := ringDecodeAndDecompress4(b)
|
|
|
+
|
|
|
+ var mask nttElement // s⊺ ◦ NTT(u)
|
|
|
+ for i := range dx.s {
|
|
|
+ mask = polyAdd(mask, nttMul(dx.s[i], ntt(u[i])))
|
|
|
+ }
|
|
|
+ w := polySub(v, inverseNTT(mask))
|
|
|
+
|
|
|
+ return ringCompressAndEncode1(nil, w)
|
|
|
+}
|
|
|
+
|
|
|
+// fieldElement is an integer modulo q, an element of ℤ_q. It is always reduced.
|
|
|
+type fieldElement uint16
|
|
|
+
|
|
|
+// fieldCheckReduced checks that a value a is < q.
|
|
|
+func fieldCheckReduced(a uint16) (fieldElement, error) {
|
|
|
+ if a >= q {
|
|
|
+ return 0, errors.New("unreduced field element")
|
|
|
+ }
|
|
|
+ return fieldElement(a), nil
|
|
|
+}
|
|
|
+
|
|
|
+// fieldReduceOnce reduces a value a < 2q.
|
|
|
+func fieldReduceOnce(a uint16) fieldElement {
|
|
|
+ x := a - q
|
|
|
+ // If x underflowed, then x >= 2¹⁶ - q > 2¹⁵, so the top bit is set.
|
|
|
+ x += (x >> 15) * q
|
|
|
+ return fieldElement(x)
|
|
|
+}
|
|
|
+
|
|
|
+func fieldAdd(a, b fieldElement) fieldElement {
|
|
|
+ x := uint16(a + b)
|
|
|
+ return fieldReduceOnce(x)
|
|
|
+}
|
|
|
+
|
|
|
+func fieldSub(a, b fieldElement) fieldElement {
|
|
|
+ x := uint16(a - b + q)
|
|
|
+ return fieldReduceOnce(x)
|
|
|
+}
|
|
|
+
|
|
|
+const (
|
|
|
+ barrettMultiplier = 5039 // 2¹² * 2¹² / q
|
|
|
+ barrettShift = 24 // log₂(2¹² * 2¹²)
|
|
|
+)
|
|
|
+
|
|
|
+// fieldReduce reduces a value a < 2q² using Barrett reduction, to avoid
|
|
|
+// potentially variable-time division.
|
|
|
+func fieldReduce(a uint32) fieldElement {
|
|
|
+ quotient := uint32((uint64(a) * barrettMultiplier) >> barrettShift)
|
|
|
+ return fieldReduceOnce(uint16(a - quotient*q))
|
|
|
+}
|
|
|
+
|
|
|
+func fieldMul(a, b fieldElement) fieldElement {
|
|
|
+ x := uint32(a) * uint32(b)
|
|
|
+ return fieldReduce(x)
|
|
|
+}
|
|
|
+
|
|
|
+// fieldMulSub returns a * (b - c). This operation is fused to save a
|
|
|
+// fieldReduceOnce after the subtraction.
|
|
|
+func fieldMulSub(a, b, c fieldElement) fieldElement {
|
|
|
+ x := uint32(a) * uint32(b-c+q)
|
|
|
+ return fieldReduce(x)
|
|
|
+}
|
|
|
+
|
|
|
+// fieldAddMul returns a * b + c * d. This operation is fused to save a
|
|
|
+// fieldReduceOnce and a fieldReduce.
|
|
|
+func fieldAddMul(a, b, c, d fieldElement) fieldElement {
|
|
|
+ x := uint32(a) * uint32(b)
|
|
|
+ x += uint32(c) * uint32(d)
|
|
|
+ return fieldReduce(x)
|
|
|
+}
|
|
|
+
|
|
|
+// compress maps a field element uniformly to the range 0 to 2ᵈ-1, according to
|
|
|
+// FIPS 203 (DRAFT), Definition 4.5.
|
|
|
+func compress(x fieldElement, d uint8) uint16 {
|
|
|
+ // We want to compute (x * 2ᵈ) / q, rounded to nearest integer, with 1/2
|
|
|
+ // rounding up (see FIPS 203 (DRAFT), Section 2.3).
|
|
|
+
|
|
|
+ // Barrett reduction produces a quotient and a remainder in the range [0, 2q),
|
|
|
+ // such that dividend = quotient * q + remainder.
|
|
|
+ dividend := uint32(x) << d // x * 2ᵈ
|
|
|
+ quotient := uint32(uint64(dividend) * barrettMultiplier >> barrettShift)
|
|
|
+ remainder := dividend - quotient*q
|
|
|
+
|
|
|
+ // Since the remainder is in the range [0, 2q), not [0, q), we need to
|
|
|
+ // portion it into three spans for rounding.
|
|
|
+ //
|
|
|
+ // [ 0, q/2 ) -> round to 0
|
|
|
+ // [ q/2, q + q/2 ) -> round to 1
|
|
|
+ // [ q + q/2, 2q ) -> round to 2
|
|
|
+ //
|
|
|
+ // We can convert that to the following logic: add 1 if remainder > q/2,
|
|
|
+ // then add 1 again if remainder > q + q/2.
|
|
|
+ //
|
|
|
+ // Note that if remainder > x, then ⌊x⌋ - remainder underflows, and the top
|
|
|
+ // bit of the difference will be set.
|
|
|
+ quotient += (q/2 - remainder) >> 31 & 1
|
|
|
+ quotient += (q + q/2 - remainder) >> 31 & 1
|
|
|
+
|
|
|
+ // quotient might have overflowed at this point, so reduce it by masking.
|
|
|
+ var mask uint32 = (1 << d) - 1
|
|
|
+ return uint16(quotient & mask)
|
|
|
+}
|
|
|
+
|
|
|
+// decompress maps a number x between 0 and 2ᵈ-1 uniformly to the full range of
|
|
|
+// field elements, according to FIPS 203 (DRAFT), Definition 4.6.
|
|
|
+func decompress(y uint16, d uint8) fieldElement {
|
|
|
+ // We want to compute (y * q) / 2ᵈ, rounded to nearest integer, with 1/2
|
|
|
+ // rounding up (see FIPS 203 (DRAFT), Section 2.3).
|
|
|
+
|
|
|
+ dividend := uint32(y) * q
|
|
|
+ quotient := dividend >> d // (y * q) / 2ᵈ
|
|
|
+
|
|
|
+ // The d'th least-significant bit of the dividend (the most significant bit
|
|
|
+ // of the remainder) is 1 for the top half of the values that divide to the
|
|
|
+ // same quotient, which are the ones that round up.
|
|
|
+ quotient += dividend >> (d - 1) & 1
|
|
|
+
|
|
|
+ // quotient is at most (2¹¹-1) * q / 2¹¹ + 1 = 3328, so it didn't overflow.
|
|
|
+ return fieldElement(quotient)
|
|
|
+}
|
|
|
+
|
|
|
+// ringElement is a polynomial, an element of R_q, represented as an array
|
|
|
+// according to FIPS 203 (DRAFT), Section 2.4.
|
|
|
+type ringElement [n]fieldElement
|
|
|
+
|
|
|
+// polyAdd adds two ringElements or nttElements.
|
|
|
+func polyAdd[T ~[n]fieldElement](a, b T) (s T) {
|
|
|
+ for i := range s {
|
|
|
+ s[i] = fieldAdd(a[i], b[i])
|
|
|
+ }
|
|
|
+ return s
|
|
|
+}
|
|
|
+
|
|
|
+// polySub subtracts two ringElements or nttElements.
|
|
|
+func polySub[T ~[n]fieldElement](a, b T) (s T) {
|
|
|
+ for i := range s {
|
|
|
+ s[i] = fieldSub(a[i], b[i])
|
|
|
+ }
|
|
|
+ return s
|
|
|
+}
|
|
|
+
|
|
|
+// polyByteEncode appends the 384-byte encoding of f to b.
|
|
|
+//
|
|
|
+// It implements ByteEncode₁₂, according to FIPS 203 (DRAFT), Algorithm 4.
|
|
|
+func polyByteEncode[T ~[n]fieldElement](b []byte, f T) []byte {
|
|
|
+ out, B := sliceForAppend(b, encodingSize12)
|
|
|
+ for i := 0; i < n; i += 2 {
|
|
|
+ x := uint32(f[i]) | uint32(f[i+1])<<12
|
|
|
+ B[0] = uint8(x)
|
|
|
+ B[1] = uint8(x >> 8)
|
|
|
+ B[2] = uint8(x >> 16)
|
|
|
+ B = B[3:]
|
|
|
+ }
|
|
|
+ return out
|
|
|
+}
|
|
|
+
|
|
|
+// polyByteDecode decodes the 384-byte encoding of a polynomial, checking that
|
|
|
+// all the coefficients are properly reduced. This achieves the "Modulus check"
|
|
|
+// step of ML-KEM Encapsulation Input Validation.
|
|
|
+//
|
|
|
+// polyByteDecode is also used in ML-KEM Decapsulation, where the input
|
|
|
+// validation is not required, but implicitly allowed by the specification.
|
|
|
+//
|
|
|
+// It implements ByteDecode₁₂, according to FIPS 203 (DRAFT), Algorithm 5.
|
|
|
+func polyByteDecode[T ~[n]fieldElement](b []byte) (T, error) {
|
|
|
+ if len(b) != encodingSize12 {
|
|
|
+ return T{}, errors.New("mlkem768: invalid encoding length")
|
|
|
+ }
|
|
|
+ var f T
|
|
|
+ for i := 0; i < n; i += 2 {
|
|
|
+ d := uint32(b[0]) | uint32(b[1])<<8 | uint32(b[2])<<16
|
|
|
+ const mask12 = 0b1111_1111_1111
|
|
|
+ var err error
|
|
|
+ if f[i], err = fieldCheckReduced(uint16(d & mask12)); err != nil {
|
|
|
+ return T{}, errors.New("mlkem768: invalid polynomial encoding")
|
|
|
+ }
|
|
|
+ if f[i+1], err = fieldCheckReduced(uint16(d >> 12)); err != nil {
|
|
|
+ return T{}, errors.New("mlkem768: invalid polynomial encoding")
|
|
|
+ }
|
|
|
+ b = b[3:]
|
|
|
+ }
|
|
|
+ return f, nil
|
|
|
+}
|
|
|
+
|
|
|
+// sliceForAppend takes a slice and a requested number of bytes. It returns a
|
|
|
+// slice with the contents of the given slice followed by that many bytes and a
|
|
|
+// second slice that aliases into it and contains only the extra bytes. If the
|
|
|
+// original slice has sufficient capacity then no allocation is performed.
|
|
|
+func sliceForAppend(in []byte, n int) (head, tail []byte) {
|
|
|
+ if total := len(in) + n; cap(in) >= total {
|
|
|
+ head = in[:total]
|
|
|
+ } else {
|
|
|
+ head = make([]byte, total)
|
|
|
+ copy(head, in)
|
|
|
+ }
|
|
|
+ tail = head[len(in):]
|
|
|
+ return
|
|
|
+}
|
|
|
+
|
|
|
+// ringCompressAndEncode1 appends a 32-byte encoding of a ring element to s,
|
|
|
+// compressing one coefficients per bit.
|
|
|
+//
|
|
|
+// It implements Compress₁, according to FIPS 203 (DRAFT), Definition 4.5,
|
|
|
+// followed by ByteEncode₁, according to FIPS 203 (DRAFT), Algorithm 4.
|
|
|
+func ringCompressAndEncode1(s []byte, f ringElement) []byte {
|
|
|
+ s, b := sliceForAppend(s, encodingSize1)
|
|
|
+ for i := range b {
|
|
|
+ b[i] = 0
|
|
|
+ }
|
|
|
+ for i := range f {
|
|
|
+ b[i/8] |= uint8(compress(f[i], 1) << (i % 8))
|
|
|
+ }
|
|
|
+ return s
|
|
|
+}
|
|
|
+
|
|
|
+// ringDecodeAndDecompress1 decodes a 32-byte slice to a ring element where each
|
|
|
+// bit is mapped to 0 or ⌈q/2⌋.
|
|
|
+//
|
|
|
+// It implements ByteDecode₁, according to FIPS 203 (DRAFT), Algorithm 5,
|
|
|
+// followed by Decompress₁, according to FIPS 203 (DRAFT), Definition 4.6.
|
|
|
+func ringDecodeAndDecompress1(b *[encodingSize1]byte) ringElement {
|
|
|
+ var f ringElement
|
|
|
+ for i := range f {
|
|
|
+ b_i := b[i/8] >> (i % 8) & 1
|
|
|
+ const halfQ = (q + 1) / 2 // ⌈q/2⌋, rounded up per FIPS 203 (DRAFT), Section 2.3
|
|
|
+ f[i] = fieldElement(b_i) * halfQ // 0 decompresses to 0, and 1 to ⌈q/2⌋
|
|
|
+ }
|
|
|
+ return f
|
|
|
+}
|
|
|
+
|
|
|
+// ringCompressAndEncode4 appends a 128-byte encoding of a ring element to s,
|
|
|
+// compressing two coefficients per byte.
|
|
|
+//
|
|
|
+// It implements Compress₄, according to FIPS 203 (DRAFT), Definition 4.5,
|
|
|
+// followed by ByteEncode₄, according to FIPS 203 (DRAFT), Algorithm 4.
|
|
|
+func ringCompressAndEncode4(s []byte, f ringElement) []byte {
|
|
|
+ s, b := sliceForAppend(s, encodingSize4)
|
|
|
+ for i := 0; i < n; i += 2 {
|
|
|
+ b[i/2] = uint8(compress(f[i], 4) | compress(f[i+1], 4)<<4)
|
|
|
+ }
|
|
|
+ return s
|
|
|
+}
|
|
|
+
|
|
|
+// ringDecodeAndDecompress4 decodes a 128-byte encoding of a ring element where
|
|
|
+// each four bits are mapped to an equidistant distribution.
|
|
|
+//
|
|
|
+// It implements ByteDecode₄, according to FIPS 203 (DRAFT), Algorithm 5,
|
|
|
+// followed by Decompress₄, according to FIPS 203 (DRAFT), Definition 4.6.
|
|
|
+func ringDecodeAndDecompress4(b *[encodingSize4]byte) ringElement {
|
|
|
+ var f ringElement
|
|
|
+ for i := 0; i < n; i += 2 {
|
|
|
+ f[i] = fieldElement(decompress(uint16(b[i/2]&0b1111), 4))
|
|
|
+ f[i+1] = fieldElement(decompress(uint16(b[i/2]>>4), 4))
|
|
|
+ }
|
|
|
+ return f
|
|
|
+}
|
|
|
+
|
|
|
+// ringCompressAndEncode10 appends a 320-byte encoding of a ring element to s,
|
|
|
+// compressing four coefficients per five bytes.
|
|
|
+//
|
|
|
+// It implements Compress₁₀, according to FIPS 203 (DRAFT), Definition 4.5,
|
|
|
+// followed by ByteEncode₁₀, according to FIPS 203 (DRAFT), Algorithm 4.
|
|
|
+func ringCompressAndEncode10(s []byte, f ringElement) []byte {
|
|
|
+ s, b := sliceForAppend(s, encodingSize10)
|
|
|
+ for i := 0; i < n; i += 4 {
|
|
|
+ var x uint64
|
|
|
+ x |= uint64(compress(f[i+0], 10))
|
|
|
+ x |= uint64(compress(f[i+1], 10)) << 10
|
|
|
+ x |= uint64(compress(f[i+2], 10)) << 20
|
|
|
+ x |= uint64(compress(f[i+3], 10)) << 30
|
|
|
+ b[0] = uint8(x)
|
|
|
+ b[1] = uint8(x >> 8)
|
|
|
+ b[2] = uint8(x >> 16)
|
|
|
+ b[3] = uint8(x >> 24)
|
|
|
+ b[4] = uint8(x >> 32)
|
|
|
+ b = b[5:]
|
|
|
+ }
|
|
|
+ return s
|
|
|
+}
|
|
|
+
|
|
|
+// ringDecodeAndDecompress10 decodes a 320-byte encoding of a ring element where
|
|
|
+// each ten bits are mapped to an equidistant distribution.
|
|
|
+//
|
|
|
+// It implements ByteDecode₁₀, according to FIPS 203 (DRAFT), Algorithm 5,
|
|
|
+// followed by Decompress₁₀, according to FIPS 203 (DRAFT), Definition 4.6.
|
|
|
+func ringDecodeAndDecompress10(bb *[encodingSize10]byte) ringElement {
|
|
|
+ b := bb[:]
|
|
|
+ var f ringElement
|
|
|
+ for i := 0; i < n; i += 4 {
|
|
|
+ x := uint64(b[0]) | uint64(b[1])<<8 | uint64(b[2])<<16 | uint64(b[3])<<24 | uint64(b[4])<<32
|
|
|
+ b = b[5:]
|
|
|
+ f[i] = fieldElement(decompress(uint16(x>>0&0b11_1111_1111), 10))
|
|
|
+ f[i+1] = fieldElement(decompress(uint16(x>>10&0b11_1111_1111), 10))
|
|
|
+ f[i+2] = fieldElement(decompress(uint16(x>>20&0b11_1111_1111), 10))
|
|
|
+ f[i+3] = fieldElement(decompress(uint16(x>>30&0b11_1111_1111), 10))
|
|
|
+ }
|
|
|
+ return f
|
|
|
+}
|
|
|
+
|
|
|
+// samplePolyCBD draws a ringElement from the special Dη distribution given a
|
|
|
+// stream of random bytes generated by the PRF function, according to FIPS 203
|
|
|
+// (DRAFT), Algorithm 7 and Definition 4.1.
|
|
|
+func samplePolyCBD(s []byte, b byte) ringElement {
|
|
|
+ prf := sha3.NewShake256()
|
|
|
+ prf.Write(s)
|
|
|
+ prf.Write([]byte{b})
|
|
|
+ B := make([]byte, 128)
|
|
|
+ prf.Read(B)
|
|
|
+
|
|
|
+ // SamplePolyCBD simply draws four (2η) bits for each coefficient, and adds
|
|
|
+ // the first two and subtracts the last two.
|
|
|
+
|
|
|
+ var f ringElement
|
|
|
+ for i := 0; i < n; i += 2 {
|
|
|
+ b := B[i/2]
|
|
|
+ b_7, b_6, b_5, b_4 := b>>7, b>>6&1, b>>5&1, b>>4&1
|
|
|
+ b_3, b_2, b_1, b_0 := b>>3&1, b>>2&1, b>>1&1, b&1
|
|
|
+ f[i] = fieldSub(fieldElement(b_0+b_1), fieldElement(b_2+b_3))
|
|
|
+ f[i+1] = fieldSub(fieldElement(b_4+b_5), fieldElement(b_6+b_7))
|
|
|
+ }
|
|
|
+ return f
|
|
|
+}
|
|
|
+
|
|
|
+// nttElement is an NTT representation, an element of T_q, represented as an
|
|
|
+// array according to FIPS 203 (DRAFT), Section 2.4.
|
|
|
+type nttElement [n]fieldElement
|
|
|
+
|
|
|
+// gammas are the values ζ^2BitRev7(i)+1 mod q for each index i.
|
|
|
+var gammas = [128]fieldElement{17, 3312, 2761, 568, 583, 2746, 2649, 680, 1637, 1692, 723, 2606, 2288, 1041, 1100, 2229, 1409, 1920, 2662, 667, 3281, 48, 233, 3096, 756, 2573, 2156, 1173, 3015, 314, 3050, 279, 1703, 1626, 1651, 1678, 2789, 540, 1789, 1540, 1847, 1482, 952, 2377, 1461, 1868, 2687, 642, 939, 2390, 2308, 1021, 2437, 892, 2388, 941, 733, 2596, 2337, 992, 268, 3061, 641, 2688, 1584, 1745, 2298, 1031, 2037, 1292, 3220, 109, 375, 2954, 2549, 780, 2090, 1239, 1645, 1684, 1063, 2266, 319, 3010, 2773, 556, 757, 2572, 2099, 1230, 561, 2768, 2466, 863, 2594, 735, 2804, 525, 1092, 2237, 403, 2926, 1026, 2303, 1143, 2186, 2150, 1179, 2775, 554, 886, 2443, 1722, 1607, 1212, 2117, 1874, 1455, 1029, 2300, 2110, 1219, 2935, 394, 885, 2444, 2154, 1175}
|
|
|
+
|
|
|
+// nttMul multiplies two nttElements.
|
|
|
+//
|
|
|
+// It implements MultiplyNTTs, according to FIPS 203 (DRAFT), Algorithm 10.
|
|
|
+func nttMul(f, g nttElement) nttElement {
|
|
|
+ var h nttElement
|
|
|
+ // We use i += 2 for bounds check elimination. See https://go.dev/issue/66826.
|
|
|
+ for i := 0; i < 256; i += 2 {
|
|
|
+ a0, a1 := f[i], f[i+1]
|
|
|
+ b0, b1 := g[i], g[i+1]
|
|
|
+ h[i] = fieldAddMul(a0, b0, fieldMul(a1, b1), gammas[i/2])
|
|
|
+ h[i+1] = fieldAddMul(a0, b1, a1, b0)
|
|
|
+ }
|
|
|
+ return h
|
|
|
+}
|
|
|
+
|
|
|
+// zetas are the values ζ^BitRev7(k) mod q for each index k.
|
|
|
+var zetas = [128]fieldElement{1, 1729, 2580, 3289, 2642, 630, 1897, 848, 1062, 1919, 193, 797, 2786, 3260, 569, 1746, 296, 2447, 1339, 1476, 3046, 56, 2240, 1333, 1426, 2094, 535, 2882, 2393, 2879, 1974, 821, 289, 331, 3253, 1756, 1197, 2304, 2277, 2055, 650, 1977, 2513, 632, 2865, 33, 1320, 1915, 2319, 1435, 807, 452, 1438, 2868, 1534, 2402, 2647, 2617, 1481, 648, 2474, 3110, 1227, 910, 17, 2761, 583, 2649, 1637, 723, 2288, 1100, 1409, 2662, 3281, 233, 756, 2156, 3015, 3050, 1703, 1651, 2789, 1789, 1847, 952, 1461, 2687, 939, 2308, 2437, 2388, 733, 2337, 268, 641, 1584, 2298, 2037, 3220, 375, 2549, 2090, 1645, 1063, 319, 2773, 757, 2099, 561, 2466, 2594, 2804, 1092, 403, 1026, 1143, 2150, 2775, 886, 1722, 1212, 1874, 1029, 2110, 2935, 885, 2154}
|
|
|
+
|
|
|
+// ntt maps a ringElement to its nttElement representation.
|
|
|
+//
|
|
|
+// It implements NTT, according to FIPS 203 (DRAFT), Algorithm 8.
|
|
|
+func ntt(f ringElement) nttElement {
|
|
|
+ k := 1
|
|
|
+ for len := 128; len >= 2; len /= 2 {
|
|
|
+ for start := 0; start < 256; start += 2 * len {
|
|
|
+ zeta := zetas[k]
|
|
|
+ k++
|
|
|
+ // Bounds check elimination hint.
|
|
|
+ f, flen := f[start:start+len], f[start+len:start+len+len]
|
|
|
+ for j := 0; j < len; j++ {
|
|
|
+ t := fieldMul(zeta, flen[j])
|
|
|
+ flen[j] = fieldSub(f[j], t)
|
|
|
+ f[j] = fieldAdd(f[j], t)
|
|
|
+ }
|
|
|
+ }
|
|
|
+ }
|
|
|
+ return nttElement(f)
|
|
|
+}
|
|
|
+
|
|
|
+// inverseNTT maps a nttElement back to the ringElement it represents.
|
|
|
+//
|
|
|
+// It implements NTT⁻¹, according to FIPS 203 (DRAFT), Algorithm 9.
|
|
|
+func inverseNTT(f nttElement) ringElement {
|
|
|
+ k := 127
|
|
|
+ for len := 2; len <= 128; len *= 2 {
|
|
|
+ for start := 0; start < 256; start += 2 * len {
|
|
|
+ zeta := zetas[k]
|
|
|
+ k--
|
|
|
+ // Bounds check elimination hint.
|
|
|
+ f, flen := f[start:start+len], f[start+len:start+len+len]
|
|
|
+ for j := 0; j < len; j++ {
|
|
|
+ t := f[j]
|
|
|
+ f[j] = fieldAdd(t, flen[j])
|
|
|
+ flen[j] = fieldMulSub(zeta, flen[j], t)
|
|
|
+ }
|
|
|
+ }
|
|
|
+ }
|
|
|
+ for i := range f {
|
|
|
+ f[i] = fieldMul(f[i], 3303) // 3303 = 128⁻¹ mod q
|
|
|
+ }
|
|
|
+ return ringElement(f)
|
|
|
+}
|
|
|
+
|
|
|
+// sampleNTT draws a uniformly random nttElement from a stream of uniformly
|
|
|
+// random bytes generated by the XOF function, according to FIPS 203 (DRAFT),
|
|
|
+// Algorithm 6 and Definition 4.2.
|
|
|
+func sampleNTT(rho []byte, ii, jj byte) nttElement {
|
|
|
+ B := sha3.NewShake128()
|
|
|
+ B.Write(rho)
|
|
|
+ B.Write([]byte{ii, jj})
|
|
|
+
|
|
|
+ // SampleNTT essentially draws 12 bits at a time from r, interprets them in
|
|
|
+ // little-endian, and rejects values higher than q, until it drew 256
|
|
|
+ // values. (The rejection rate is approximately 19%.)
|
|
|
+ //
|
|
|
+ // To do this from a bytes stream, it draws three bytes at a time, and
|
|
|
+ // splits them into two uint16 appropriately masked.
|
|
|
+ //
|
|
|
+ // r₀ r₁ r₂
|
|
|
+ // |- - - - - - - -|- - - - - - - -|- - - - - - - -|
|
|
|
+ //
|
|
|
+ // Uint16(r₀ || r₁)
|
|
|
+ // |- - - - - - - - - - - - - - - -|
|
|
|
+ // |- - - - - - - - - - - -|
|
|
|
+ // d₁
|
|
|
+ //
|
|
|
+ // Uint16(r₁ || r₂)
|
|
|
+ // |- - - - - - - - - - - - - - - -|
|
|
|
+ // |- - - - - - - - - - - -|
|
|
|
+ // d₂
|
|
|
+ //
|
|
|
+ // Note that in little-endian, the rightmost bits are the most significant
|
|
|
+ // bits (dropped with a mask) and the leftmost bits are the least
|
|
|
+ // significant bits (dropped with a right shift).
|
|
|
+
|
|
|
+ var a nttElement
|
|
|
+ var j int // index into a
|
|
|
+ var buf [24]byte // buffered reads from B
|
|
|
+ off := len(buf) // index into buf, starts in a "buffer fully consumed" state
|
|
|
+ for {
|
|
|
+ if off >= len(buf) {
|
|
|
+ B.Read(buf[:])
|
|
|
+ off = 0
|
|
|
+ }
|
|
|
+ d1 := byteorder.LeUint16(buf[off:]) & 0b1111_1111_1111
|
|
|
+ d2 := byteorder.LeUint16(buf[off+1:]) >> 4
|
|
|
+ off += 3
|
|
|
+ if d1 < q {
|
|
|
+ a[j] = fieldElement(d1)
|
|
|
+ j++
|
|
|
+ }
|
|
|
+ if j >= len(a) {
|
|
|
+ break
|
|
|
+ }
|
|
|
+ if d2 < q {
|
|
|
+ a[j] = fieldElement(d2)
|
|
|
+ j++
|
|
|
+ }
|
|
|
+ if j >= len(a) {
|
|
|
+ break
|
|
|
+ }
|
|
|
+ }
|
|
|
+ return a
|
|
|
+}
|