cipher/hctr: optimization with GCM GF128 method

cipher/benchmark_test.go

@@ -3,12 +3,28 @@ package cipher_test
 import (
 	"crypto/aes"
 	"crypto/cipher"
+	"crypto/rand"
+	"io"
 	"testing"
 
 	smcipher "github.com/emmansun/gmsm/cipher"
 	"github.com/emmansun/gmsm/sm4"
 )
 
+func BenchmarkSM4HCTREncrypt1K(b *testing.B) {
+	var key [16]byte
+	var tweak [32]byte
+	c, _ := sm4.NewCipher(key[:])
+	io.ReadFull(rand.Reader, tweak[:])
+	hctr, _ := smcipher.NewHCTR(c, tweak[:16], tweak[16:])
+	buf := make([]byte, 1024)
+	b.SetBytes(int64(len(buf)))
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		hctr.Encrypt(buf, buf)
+	}
+}
+
 func benchmarkECBEncrypt1K(b *testing.B, block cipher.Block) {
 	buf := make([]byte, 1024)
 	b.SetBytes(int64(len(buf)))

cipher/hctr.go

@@ -37,6 +37,58 @@ type LengthPreservingMode interface {
 	Decrypt(dst, src []byte)
 }
 
+// hctrFieldElement represents a value in GF(2¹²⁸). In order to reflect the HCTR
+// 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 hctrFieldElement struct {
+	low, high uint64
+}
+
+// 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
+}
+
+// hctrAdd adds two elements of GF(2¹²⁸) and returns the sum.
+func hctrAdd(x, y *hctrFieldElement) hctrFieldElement {
+	// Addition in a characteristic 2 field is just XOR.
+	return hctrFieldElement{x.low ^ y.low, x.high ^ y.high}
+}
+
+// hctrDouble returns the result of doubling an element of GF(2¹²⁸).
+func hctrDouble(x *hctrFieldElement) (double hctrFieldElement) {
+	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
+	}
+
+	return
+}
+
+var hctrReductionTable = []uint16{
+	0x0000, 0x1c20, 0x3840, 0x2460, 0x7080, 0x6ca0, 0x48c0, 0x54e0,
+	0xe100, 0xfd20, 0xd940, 0xc560, 0x9180, 0x8da0, 0xa9c0, 0xb5e0,
+}
+
 // hctr represents a Varaible-Input-Length enciphering mode with a specific block cipher,
 // and specific tweak and a hash key. See
 // https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.470.5288
@@ -44,7 +96,9 @@ type LengthPreservingMode interface {
 type hctr struct {
 	cipher _cipher.Block
 	tweak  [blockSize]byte
-	hkey   [blockSize]byte
+	// productTable contains the first sixteen powers of the hash key.
+	// However, they are in bit reversed order.
+	productTable [16]hctrFieldElement
 }
 
 // NewHCTR returns a [LengthPreservingMode] which encrypts/decrypts useing the given [Block]
@@ -55,72 +109,95 @@ func NewHCTR(cipher _cipher.Block, tweak, hkey []byte) (LengthPreservingMode, er
 	}
 	c := &hctr{}
 	c.cipher = cipher
-	copy(c.hkey[:], hkey)
 	copy(c.tweak[:], tweak)
+	// 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 := hctrFieldElement{
+		binary.BigEndian.Uint64(hkey[:8]),
+		binary.BigEndian.Uint64(hkey[8:blockSize]),
+	}
+	c.productTable[reverseBits(1)] = x
+
+	for i := 2; i < 16; i += 2 {
+		c.productTable[reverseBits(i)] = hctrDouble(&c.productTable[reverseBits(i/2)])
+		c.productTable[reverseBits(i+1)] = hctrAdd(&c.productTable[reverseBits(i)], &x)
+	}
 	return c, nil
 }
 
-func _mul2(v *[blockSize]byte) {
-	var carryIn byte
-	for j := range v {
-		carryOut := (v[j] << 7) & 0x80
-		v[j] = (v[j] >> 1) + carryIn
-		carryIn = carryOut
-	}
-	if carryIn != 0 {
-		v[0] ^= 0xE1 //  1<<7 | 1<<6 | 1<<5 | 1
-	}
-}
+// mul sets y to y*H, where H is the GCM key, fixed during NewHCTR.
+func (h *hctr) mul(y *hctrFieldElement) {
+	var z hctrFieldElement
 
-// mul sets y to y*hkey.
-func (h *hctr) mul(y *[blockSize]byte) {
-	var z [blockSize]byte
-	for _, i := range h.hkey {
-		for k := 0; k < 8; k++ {
-			if (i>>(7-k))&1 == 1 {
-				subtle.XORBytes(z[:], z[:], y[:])
-			}
-			_mul2(y)
+	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 hash key.
+		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(hctrReductionTable[msw]) << 48
+
+			// the values in |table| are ordered for
+			// little-endian bit positions. See the comment
+			// in NewGCMWithNonceSize.
+			t := &h.productTable[word&0xf]
+
+			z.low ^= t.low
+			z.high ^= t.high
+			word >>= 4
 		}
 	}
-	copy(y[:], z[:])
+
+	*y = z
+}
+
+func (h *hctr) updateBlock(block []byte, y *hctrFieldElement) {
+	y.low ^= binary.BigEndian.Uint64(block)
+	y.high ^= binary.BigEndian.Uint64(block[8:blockSize])
+	h.mul(y)	
 }
 
 // Universal Hash Function.
 // Chapter 3.3 in https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.470.5288.
-func (h *hctr) uhash(m []byte, dst *[blockSize]byte) {
-	for k := 0; k < blockSize; k++ {
-		dst[k] = 0
-	}
+func (h *hctr) uhash(m []byte, out *[blockSize]byte) {
+	var y hctrFieldElement
 	msg := m
+	// update blocks
 	for len(msg) >= blockSize {
-		subtle.XORBytes(dst[:], dst[:], msg[:blockSize])
-		h.mul(dst)
+		h.updateBlock(msg, &y)
 		msg = msg[blockSize:]
 	}
-	var v [blockSize]byte
+	// update partial block & tweak
 	if len(msg) > 0 {
-		copy(v[:], msg)
-		copy(v[len(msg):], h.tweak[:])
-		subtle.XORBytes(dst[:], dst[:], v[:])
-		h.mul(dst)
-		copy(v[:], h.tweak[len(msg):])
+		var partialBlock [blockSize]byte
+		copy(partialBlock[:], msg)
+		copy(partialBlock[len(msg):], h.tweak[:])
+		h.updateBlock(partialBlock[:], &y)
+
+		copy(partialBlock[:], h.tweak[len(msg):])
 		for i := len(msg); i < blockSize; i++ {
-			v[i] = 0
-		}
-		subtle.XORBytes(dst[:], dst[:], v[:])
-		h.mul(dst)
-		for i := 0; i < len(msg); i++ {
-			v[i] = 0
+			partialBlock[i] = 0
 		}
+		h.updateBlock(partialBlock[:], &y)
 	} else {
-		subtle.XORBytes(dst[:], dst[:], h.tweak[:])
-		h.mul(dst)
+		h.updateBlock(h.tweak[:], &y)
 	}
-	// (|M|)₂
-	binary.BigEndian.PutUint64(v[8:], uint64(len(m)+blockSize)<<3)
-	subtle.XORBytes(dst[:], dst[:], v[:])
-	h.mul(dst)
+	// update bit string length (|M|)₂
+	y.high ^= uint64(len(m)+blockSize) * 8
+	h.mul(&y)
+	// output result
+	binary.BigEndian.PutUint64(out[:], y.low)
+	binary.BigEndian.PutUint64(out[8:], y.high)
 }
 
 func (h *hctr) Encrypt(ciphertext, plaintext []byte) {
@@ -135,7 +212,6 @@ func (h *hctr) Encrypt(ciphertext, plaintext []byte) {
 	}
 
 	var z1, z2 [blockSize]byte
-
 	// a) z1 generation
 	h.uhash(plaintext[blockSize:], &z1)
 	subtle.XORBytes(z1[:], z1[:], plaintext[:blockSize])