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// Copyright 2013 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package cipher
import (
subtleoverlap "crypto/internal/subtle"
// AEAD is a cipher mode providing authenticated encryption with associated
// data. For a description of the methodology, see
type AEAD interface {
// NonceSize returns the size of the nonce that must be passed to Seal
// and Open.
NonceSize() int
// Overhead returns the maximum difference between the lengths of a
// plaintext and its ciphertext.
Overhead() int
// Seal encrypts and authenticates plaintext, authenticates the
// additional data and appends the result to dst, returning the updated
// slice. The nonce must be NonceSize() bytes long and unique for all
// time, for a given key.
// To reuse plaintext's storage for the encrypted output, use plaintext[:0]
// as dst. Otherwise, the remaining capacity of dst must not overlap plaintext.
Seal(dst, nonce, plaintext, additionalData []byte) []byte
// Open decrypts and authenticates ciphertext, authenticates the
// additional data and, if successful, appends the resulting plaintext
// to dst, returning the updated slice. The nonce must be NonceSize()
// bytes long and both it and the additional data must match the
// value passed to Seal.
// To reuse ciphertext's storage for the decrypted output, use ciphertext[:0]
// as dst. Otherwise, the remaining capacity of dst must not overlap plaintext.
// Even if the function fails, the contents of dst, up to its capacity,
// may be overwritten.
Open(dst, nonce, ciphertext, additionalData []byte) ([]byte, error)
// gcmAble is an interface implemented by ciphers that have a specific optimized
// implementation of GCM, like crypto/aes. NewGCM will check for this interface
// and return the specific AEAD if found.
type gcmAble interface {
NewGCM(nonceSize, tagSize int) (AEAD, error)
// gcmFieldElement represents a value in GF(2¹²⁸). In order to reflect the GCM
// standard and make binary.BigEndian suitable for marshaling these values, the
// bits are stored in big endian order. For example:
// the coefficient of x⁰ can be obtained by v.low >> 63.
// the coefficient of x⁶³ can be obtained by v.low & 1.
// the coefficient of x⁶⁴ can be obtained by v.high >> 63.
// the coefficient of x¹²⁷ can be obtained by v.high & 1.
type gcmFieldElement struct {
low, high uint64
// gcm represents a Galois Counter Mode with a specific key. See
type gcm struct {
cipher Block
nonceSize int
tagSize int
// productTable contains the first sixteen powers of the key, H.
// However, they are in bit reversed order. See NewGCMWithNonceSize.
productTable [16]gcmFieldElement
// NewGCM returns the given 128-bit, block cipher wrapped in Galois Counter Mode
// with the standard nonce length.
// In general, the GHASH operation performed by this implementation of GCM is not constant-time.
// An exception is when the underlying Block was created by aes.NewCipher
// on systems with hardware support for AES. See the crypto/aes package documentation for details.
func NewGCM(cipher Block) (AEAD, error) {
return newGCMWithNonceAndTagSize(cipher, gcmStandardNonceSize, gcmTagSize)
// NewGCMWithNonceSize returns the given 128-bit, block cipher wrapped in Galois
// Counter Mode, which accepts nonces of the given length. The length must not
// be zero.
// Only use this function if you require compatibility with an existing
// cryptosystem that uses non-standard nonce lengths. All other users should use
// NewGCM, which is faster and more resistant to misuse.
func NewGCMWithNonceSize(cipher Block, size int) (AEAD, error) {
return newGCMWithNonceAndTagSize(cipher, size, gcmTagSize)
// NewGCMWithTagSize returns the given 128-bit, block cipher wrapped in Galois
// Counter Mode, which generates tags with the given length.
// Tag sizes between 12 and 16 bytes are allowed.
// Only use this function if you require compatibility with an existing
// cryptosystem that uses non-standard tag lengths. All other users should use
// NewGCM, which is more resistant to misuse.
func NewGCMWithTagSize(cipher Block, tagSize int) (AEAD, error) {
return newGCMWithNonceAndTagSize(cipher, gcmStandardNonceSize, tagSize)
func newGCMWithNonceAndTagSize(cipher Block, nonceSize, tagSize int) (AEAD, error) {
if tagSize < gcmMinimumTagSize || tagSize > gcmBlockSize {
return nil, errors.New("cipher: incorrect tag size given to GCM")
if nonceSize <= 0 {
return nil, errors.New("cipher: the nonce can't have zero length, or the security of the key will be immediately compromised")
if cipher, ok := cipher.(gcmAble); ok {
return cipher.NewGCM(nonceSize, tagSize)
if cipher.BlockSize() != gcmBlockSize {
return nil, errors.New("cipher: NewGCM requires 128-bit block cipher")
var key [gcmBlockSize]byte
cipher.Encrypt(key[:], key[:])
g := &gcm{cipher: cipher, nonceSize: nonceSize, tagSize: tagSize}
// We precompute 16 multiples of |key|. However, when we do lookups
// into this table we'll be using bits from a field element and
// therefore the bits will be in the reverse order. So normally one
// would expect, say, 4*key to be in index 4 of the table but due to
// this bit ordering it will actually be in index 0010 (base 2) = 2.
x := gcmFieldElement{
g.productTable[reverseBits(1)] = x
for i := 2; i < 16; i += 2 {
g.productTable[reverseBits(i)] = gcmDouble(&g.productTable[reverseBits(i/2)])
g.productTable[reverseBits(i+1)] = gcmAdd(&g.productTable[reverseBits(i)], &x)
return g, nil
const (
gcmBlockSize = 16
gcmTagSize = 16
gcmMinimumTagSize = 12 // NIST SP 800-38D recommends tags with 12 or more bytes.
gcmStandardNonceSize = 12
func (g *gcm) NonceSize() int {
return g.nonceSize
func (g *gcm) Overhead() int {
return g.tagSize
func (g *gcm) Seal(dst, nonce, plaintext, data []byte) []byte {
if len(nonce) != g.nonceSize {
panic("crypto/cipher: incorrect nonce length given to GCM")
if uint64(len(plaintext)) > ((1<<32)-2)*uint64(g.cipher.BlockSize()) {
panic("crypto/cipher: message too large for GCM")
ret, out := sliceForAppend(dst, len(plaintext)+g.tagSize)
if subtleoverlap.InexactOverlap(out, plaintext) {
panic("crypto/cipher: invalid buffer overlap")
var counter, tagMask [gcmBlockSize]byte
g.deriveCounter(&counter, nonce)
g.cipher.Encrypt(tagMask[:], counter[:])
g.counterCrypt(out, plaintext, &counter)
var tag [gcmTagSize]byte
g.auth(tag[:], out[:len(plaintext)], data, &tagMask)
copy(out[len(plaintext):], tag[:])
return ret
var errOpen = errors.New("cipher: message authentication failed")
func (g *gcm) Open(dst, nonce, ciphertext, data []byte) ([]byte, error) {
if len(nonce) != g.nonceSize {
panic("crypto/cipher: incorrect nonce length given to GCM")
// Sanity check to prevent the authentication from always succeeding if an implementation
// leaves tagSize uninitialized, for example.
if g.tagSize < gcmMinimumTagSize {
panic("crypto/cipher: incorrect GCM tag size")
if len(ciphertext) < g.tagSize {
return nil, errOpen
if uint64(len(ciphertext)) > ((1<<32)-2)*uint64(g.cipher.BlockSize())+uint64(g.tagSize) {
return nil, errOpen
tag := ciphertext[len(ciphertext)-g.tagSize:]
ciphertext = ciphertext[:len(ciphertext)-g.tagSize]
var counter, tagMask [gcmBlockSize]byte
g.deriveCounter(&counter, nonce)
g.cipher.Encrypt(tagMask[:], counter[:])
var expectedTag [gcmTagSize]byte
g.auth(expectedTag[:], ciphertext, data, &tagMask)
ret, out := sliceForAppend(dst, len(ciphertext))
if subtleoverlap.InexactOverlap(out, ciphertext) {
panic("crypto/cipher: invalid buffer overlap")
if subtle.ConstantTimeCompare(expectedTag[:g.tagSize], tag) != 1 {
// The AESNI code decrypts and authenticates concurrently, and
// so overwrites dst in the event of a tag mismatch. That
// behavior is mimicked here in order to be consistent across
// platforms.
for i := range out {
out[i] = 0
return nil, errOpen
g.counterCrypt(out, ciphertext, &counter)
return ret, nil
// reverseBits reverses the order of the bits of 4-bit number in i.
func reverseBits(i int) int {
i = ((i << 2) & 0xc) | ((i >> 2) & 0x3)
i = ((i << 1) & 0xa) | ((i >> 1) & 0x5)
return i
// gcmAdd adds two elements of GF(2¹²⁸) and returns the sum.
func gcmAdd(x, y *gcmFieldElement) gcmFieldElement {
// Addition in a characteristic 2 field is just XOR.
return gcmFieldElement{x.low ^ y.low, x.high ^ y.high}
// gcmDouble returns the result of doubling an element of GF(2¹²⁸).
func gcmDouble(x *gcmFieldElement) (double gcmFieldElement) {
msbSet := x.high&1 == 1
// Because of the bit-ordering, doubling is actually a right shift.
double.high = x.high >> 1
double.high |= x.low << 63
double.low = x.low >> 1
// If the most-significant bit was set before shifting then it,
// conceptually, becomes a term of x^128. This is greater than the
// irreducible polynomial so the result has to be reduced. The
// irreducible polynomial is 1+x+x^2+x^7+x^128. We can subtract that to
// eliminate the term at x^128 which also means subtracting the other
// four terms. In characteristic 2 fields, subtraction == addition ==
// XOR.
if msbSet {
double.low ^= 0xe100000000000000
var gcmReductionTable = []uint16{
0x0000, 0x1c20, 0x3840, 0x2460, 0x7080, 0x6ca0, 0x48c0, 0x54e0,
0xe100, 0xfd20, 0xd940, 0xc560, 0x9180, 0x8da0, 0xa9c0, 0xb5e0,
// mul sets y to y*H, where H is the GCM key, fixed during NewGCMWithNonceSize.
func (g *gcm) mul(y *gcmFieldElement) {
var z gcmFieldElement
for i := 0; i < 2; i++ {
word := y.high
if i == 1 {
word = y.low
// Multiplication works by multiplying z by 16 and adding in
// one of the precomputed multiples of H.
for j := 0; j < 64; j += 4 {
msw := z.high & 0xf
z.high >>= 4
z.high |= z.low << 60
z.low >>= 4
z.low ^= uint64(gcmReductionTable[msw]) << 48
// the values in |table| are ordered for
// little-endian bit positions. See the comment
// in NewGCMWithNonceSize.
t := &g.productTable[word&0xf]
z.low ^= t.low
z.high ^= t.high
word >>= 4
*y = z
// updateBlocks extends y with more polynomial terms from blocks, based on
// Horner's rule. There must be a multiple of gcmBlockSize bytes in blocks.
func (g *gcm) updateBlocks(y *gcmFieldElement, blocks []byte) {
for len(blocks) > 0 {
y.low ^= binary.BigEndian.Uint64(blocks)
y.high ^= binary.BigEndian.Uint64(blocks[8:])
blocks = blocks[gcmBlockSize:]
// update extends y with more polynomial terms from data. If data is not a
// multiple of gcmBlockSize bytes long then the remainder is zero padded.
func (g *gcm) update(y *gcmFieldElement, data []byte) {
fullBlocks := (len(data) >> 4) << 4
g.updateBlocks(y, data[:fullBlocks])
if len(data) != fullBlocks {
var partialBlock [gcmBlockSize]byte
copy(partialBlock[:], data[fullBlocks:])
g.updateBlocks(y, partialBlock[:])
// gcmInc32 treats the final four bytes of counterBlock as a big-endian value
// and increments it.
func gcmInc32(counterBlock *[16]byte) {
ctr := counterBlock[len(counterBlock)-4:]
binary.BigEndian.PutUint32(ctr, binary.BigEndian.Uint32(ctr)+1)
// 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):]
// counterCrypt crypts in to out using g.cipher in counter mode.
func (g *gcm) counterCrypt(out, in []byte, counter *[gcmBlockSize]byte) {
var mask [gcmBlockSize]byte
for len(in) >= gcmBlockSize {
g.cipher.Encrypt(mask[:], counter[:])
xorWords(out, in, mask[:])
out = out[gcmBlockSize:]
in = in[gcmBlockSize:]
if len(in) > 0 {
g.cipher.Encrypt(mask[:], counter[:])
xorBytes(out, in, mask[:])
// deriveCounter computes the initial GCM counter state from the given nonce.
// See NIST SP 800-38D, section 7.1. This assumes that counter is filled with
// zeros on entry.
func (g *gcm) deriveCounter(counter *[gcmBlockSize]byte, nonce []byte) {
// GCM has two modes of operation with respect to the initial counter
// state: a "fast path" for 96-bit (12-byte) nonces, and a "slow path"
// for nonces of other lengths. For a 96-bit nonce, the nonce, along
// with a four-byte big-endian counter starting at one, is used
// directly as the starting counter. For other nonce sizes, the counter
// is computed by passing it through the GHASH function.
if len(nonce) == gcmStandardNonceSize {
copy(counter[:], nonce)
counter[gcmBlockSize-1] = 1
} else {
var y gcmFieldElement
g.update(&y, nonce)
y.high ^= uint64(len(nonce)) * 8
binary.BigEndian.PutUint64(counter[:8], y.low)
binary.BigEndian.PutUint64(counter[8:], y.high)
// auth calculates GHASH(ciphertext, additionalData), masks the result with
// tagMask and writes the result to out.
func (g *gcm) auth(out, ciphertext, additionalData []byte, tagMask *[gcmTagSize]byte) {
var y gcmFieldElement
g.update(&y, additionalData)
g.update(&y, ciphertext)
y.low ^= uint64(len(additionalData)) * 8
y.high ^= uint64(len(ciphertext)) * 8
binary.BigEndian.PutUint64(out, y.low)
binary.BigEndian.PutUint64(out[8:], y.high)
xorWords(out, out, tagMask[:])