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indcpa.go
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indcpa.go
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/* SPDX-FileCopyrightText: © 2020-2024 Nadim Kobeissi <[email protected]>
* SPDX-License-Identifier: MIT */
package kyberk2so
import (
"crypto/rand"
"golang.org/x/crypto/sha3"
)
// indcpaPackPublicKey serializes the public key as a concatenation of the
// serialized vector of polynomials of the public key, and the public seed
// used to generate the matrix `A`.
func indcpaPackPublicKey(publicKey polyvec, seed []byte, paramsK int) []byte {
return append(polyvecToBytes(publicKey, paramsK), seed...)
}
// indcpaUnpackPublicKey de-serializes the public key from a byte array
// and represents the approximate inverse of indcpaPackPublicKey.
func indcpaUnpackPublicKey(packedPublicKey []byte, paramsK int) (polyvec, []byte) {
switch paramsK {
case 2:
publicKeyPolyvec := polyvecFromBytes(packedPublicKey[:paramsPolyvecBytesK512], paramsK)
seed := packedPublicKey[paramsPolyvecBytesK512:]
return publicKeyPolyvec, seed
case 3:
publicKeyPolyvec := polyvecFromBytes(packedPublicKey[:paramsPolyvecBytesK768], paramsK)
seed := packedPublicKey[paramsPolyvecBytesK768:]
return publicKeyPolyvec, seed
default:
publicKeyPolyvec := polyvecFromBytes(packedPublicKey[:paramsPolyvecBytesK1024], paramsK)
seed := packedPublicKey[paramsPolyvecBytesK1024:]
return publicKeyPolyvec, seed
}
}
// indcpaPackPrivateKey serializes the private key.
func indcpaPackPrivateKey(privateKey polyvec, paramsK int) []byte {
return polyvecToBytes(privateKey, paramsK)
}
// indcpaUnpackPrivateKey de-serializes the private key and represents
// the inverse of indcpaPackPrivateKey.
func indcpaUnpackPrivateKey(packedPrivateKey []byte, paramsK int) polyvec {
return polyvecFromBytes(packedPrivateKey, paramsK)
}
// indcpaPackCiphertext serializes the ciphertext as a concatenation of
// the compressed and serialized vector of polynomials `b` and the
// compressed and serialized polynomial `v`.
func indcpaPackCiphertext(b polyvec, v poly, paramsK int) []byte {
return append(polyvecCompress(b, paramsK), polyCompress(v, paramsK)...)
}
// indcpaUnpackCiphertext de-serializes and decompresses the ciphertext
// from a byte array, and represents the approximate inverse of
// indcpaPackCiphertext.
func indcpaUnpackCiphertext(c []byte, paramsK int) (polyvec, poly) {
switch paramsK {
case 2:
b := polyvecDecompress(c[:paramsPolyvecCompressedBytesK512], paramsK)
v := polyDecompress(c[paramsPolyvecCompressedBytesK512:], paramsK)
return b, v
case 3:
b := polyvecDecompress(c[:paramsPolyvecCompressedBytesK768], paramsK)
v := polyDecompress(c[paramsPolyvecCompressedBytesK768:], paramsK)
return b, v
default:
b := polyvecDecompress(c[:paramsPolyvecCompressedBytesK1024], paramsK)
v := polyDecompress(c[paramsPolyvecCompressedBytesK1024:], paramsK)
return b, v
}
}
// indcpaRejUniform runs rejection sampling on uniform random bytes
// to generate uniform random integers modulo `Q`.
func indcpaRejUniform(buf []byte, bufl int, l int) (poly, int) {
var r poly
var d1 uint16
var d2 uint16
i := 0
j := 0
for i < l && j+3 <= bufl {
d1 = (uint16((buf[j])>>0) | (uint16(buf[j+1]) << 8)) & 0xFFF
d2 = (uint16((buf[j+1])>>4) | (uint16(buf[j+2]) << 4)) & 0xFFF
j = j + 3
if d1 < uint16(paramsQ) {
r[i] = int16(d1)
i = i + 1
}
if i < l && d2 < uint16(paramsQ) {
r[i] = int16(d2)
i = i + 1
}
}
return r, i
}
// indcpaGenMatrix deterministically generates a matrix `A` (or the transpose of `A`)
// from a seed. Entries of the matrix are polynomials that look uniformly random.
// Performs rejection sampling on the output of an extendable-output function (XOF).
func indcpaGenMatrix(seed []byte, transposed bool, paramsK int) ([]polyvec, error) {
r := make([]polyvec, paramsK)
buf := make([]byte, 672)
xof := sha3.NewShake128()
ctr := 0
for i := 0; i < paramsK; i++ {
r[i] = polyvecNew(paramsK)
for j := 0; j < paramsK; j++ {
xof.Reset()
var err error
if transposed {
_, err = xof.Write(append(seed, byte(i), byte(j)))
} else {
_, err = xof.Write(append(seed, byte(j), byte(i)))
}
if err != nil {
return []polyvec{}, err
}
_, err = xof.Read(buf)
if err != nil {
return []polyvec{}, err
}
r[i][j], ctr = indcpaRejUniform(buf[:504], 504, paramsN)
for ctr < paramsN {
missing, ctrn := indcpaRejUniform(buf[504:672], 168, paramsN-ctr)
for k := ctr; k < paramsN; k++ {
r[i][j][k] = missing[k-ctr]
}
ctr = ctr + ctrn
}
}
}
return r, nil
}
// indcpaPrf provides a pseudo-random function (PRF) which returns
// a byte array of length `l`, using the provided key and nonce
// to instantiate the PRF's underlying hash function.
func indcpaPrf(l int, key []byte, nonce byte) []byte {
hash := make([]byte, l)
sha3.ShakeSum256(hash, append(key, nonce))
return hash
}
// indcpaKeypair generates public and private keys for the CPA-secure
// public-key encryption scheme underlying Kyber.
func indcpaKeypair(paramsK int) ([]byte, []byte, error) {
skpv := polyvecNew(paramsK)
pkpv := polyvecNew(paramsK)
e := polyvecNew(paramsK)
buf := make([]byte, 2*paramsSymBytes)
h := sha3.New512()
_, err := rand.Read(buf[:paramsSymBytes])
if err != nil {
return []byte{}, []byte{}, err
}
_, err = h.Write(buf[:paramsSymBytes])
if err != nil {
return []byte{}, []byte{}, err
}
buf = buf[:0]
buf = h.Sum(buf)
publicSeed := make([]byte, paramsSymBytes)
noiseSeed := make([]byte, paramsSymBytes)
copy(publicSeed, buf[:paramsSymBytes])
copy(noiseSeed, buf[paramsSymBytes:])
a, err := indcpaGenMatrix(publicSeed, false, paramsK)
if err != nil {
return []byte{}, []byte{}, err
}
var nonce byte
for i := 0; i < paramsK; i++ {
skpv[i] = polyGetNoise(noiseSeed, nonce, paramsK)
nonce = nonce + 1
}
for i := 0; i < paramsK; i++ {
e[i] = polyGetNoise(noiseSeed, nonce, paramsK)
nonce = nonce + 1
}
polyvecNtt(skpv, paramsK)
polyvecReduce(skpv, paramsK)
polyvecNtt(e, paramsK)
for i := 0; i < paramsK; i++ {
pkpv[i] = polyToMont(polyvecPointWiseAccMontgomery(a[i], skpv, paramsK))
}
polyvecAdd(pkpv, e, paramsK)
polyvecReduce(pkpv, paramsK)
return indcpaPackPrivateKey(skpv, paramsK), indcpaPackPublicKey(pkpv, publicSeed, paramsK), nil
}
// indcpaEncrypt is the encryption function of the CPA-secure
// public-key encryption scheme underlying Kyber.
func indcpaEncrypt(m []byte, publicKey []byte, coins []byte, paramsK int) ([]byte, error) {
sp := polyvecNew(paramsK)
ep := polyvecNew(paramsK)
bp := polyvecNew(paramsK)
publicKeyPolyvec, seed := indcpaUnpackPublicKey(publicKey, paramsK)
k := polyFromMsg(m)
at, err := indcpaGenMatrix(seed[:paramsSymBytes], true, paramsK)
if err != nil {
return []byte{}, err
}
for i := 0; i < paramsK; i++ {
sp[i] = polyGetNoise(coins, byte(i), paramsK)
ep[i] = polyGetNoise(coins, byte(i+paramsK), 3)
}
epp := polyGetNoise(coins, byte(paramsK*2), 3)
polyvecNtt(sp, paramsK)
polyvecReduce(sp, paramsK)
for i := 0; i < paramsK; i++ {
bp[i] = polyvecPointWiseAccMontgomery(at[i], sp, paramsK)
}
v := polyvecPointWiseAccMontgomery(publicKeyPolyvec, sp, paramsK)
polyvecInvNttToMont(bp, paramsK)
v = polyInvNttToMont(v)
polyvecAdd(bp, ep, paramsK)
v = polyAdd(polyAdd(v, epp), k)
polyvecReduce(bp, paramsK)
return indcpaPackCiphertext(bp, polyReduce(v), paramsK), nil
}
// indcpaDecrypt is the decryption function of the CPA-secure
// public-key encryption scheme underlying Kyber.
func indcpaDecrypt(c []byte, privateKey []byte, paramsK int) []byte {
bp, v := indcpaUnpackCiphertext(c, paramsK)
privateKeyPolyvec := indcpaUnpackPrivateKey(privateKey, paramsK)
polyvecNtt(bp, paramsK)
mp := polyvecPointWiseAccMontgomery(privateKeyPolyvec, bp, paramsK)
mp = polyInvNttToMont(mp)
mp = polySub(v, mp)
mp = polyReduce(mp)
return polyToMsg(mp)
}