ghash_ctmul32.c

/*
 * Copyright (c) 2016 Thomas Pornin <[email protected]>
 *
 * Permission is hereby granted, free of charge, to any person obtaining 
 * a copy of this software and associated documentation files (the
 * "Software"), to deal in the Software without restriction, including
 * without limitation the rights to use, copy, modify, merge, publish,
 * distribute, sublicense, and/or sell copies of the Software, and to
 * permit persons to whom the Software is furnished to do so, subject to
 * the following conditions:
 *
 * The above copyright notice and this permission notice shall be 
 * included in all copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, 
 * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
 * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND 
 * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
 * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
 * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
 * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
 * SOFTWARE.
 */

#include "inner.h"

/*
 * This implementation uses 32-bit multiplications, and only the low
 * 32 bits for each multiplication result. This is meant primarily for
 * the ARM Cortex M0 and M0+, whose multiplication opcode does not yield
 * the upper 32 bits; but it might also be useful on architectures where
 * access to the upper 32 bits requires use of specific registers that
 * create contention (e.g. on i386, "mul" necessarily outputs the result
 * in edx:eax, while "imul" can use any registers but is limited to the
 * low 32 bits).
 *
 * The implementation trick that is used here is bit-reversing (bit 0
 * is swapped with bit 31, bit 1 with bit 30, and so on). In GF(2)[X],
 * for all values x and y, we have:
 *    rev32(x) * rev32(y) = rev64(x * y)
 * In other words, if we bit-reverse (over 32 bits) the operands, then we
 * bit-reverse (over 64 bits) the result.
 */

/*
 * Multiplication in GF(2)[X], truncated to its low 32 bits.
 */
static inline uint32_t
bmul32(uint32_t x, uint32_t y)
{
	uint32_t x0, x1, x2, x3;
	uint32_t y0, y1, y2, y3;
	uint32_t z0, z1, z2, z3;

	x0 = x & (uint32_t)0x11111111;
	x1 = x & (uint32_t)0x22222222;
	x2 = x & (uint32_t)0x44444444;
	x3 = x & (uint32_t)0x88888888;
	y0 = y & (uint32_t)0x11111111;
	y1 = y & (uint32_t)0x22222222;
	y2 = y & (uint32_t)0x44444444;
	y3 = y & (uint32_t)0x88888888;
	z0 = (x0 * y0) ^ (x1 * y3) ^ (x2 * y2) ^ (x3 * y1);
	z1 = (x0 * y1) ^ (x1 * y0) ^ (x2 * y3) ^ (x3 * y2);
	z2 = (x0 * y2) ^ (x1 * y1) ^ (x2 * y0) ^ (x3 * y3);
	z3 = (x0 * y3) ^ (x1 * y2) ^ (x2 * y1) ^ (x3 * y0);
	z0 &= (uint32_t)0x11111111;
	z1 &= (uint32_t)0x22222222;
	z2 &= (uint32_t)0x44444444;
	z3 &= (uint32_t)0x88888888;
	return z0 | z1 | z2 | z3;
}

/*
 * Bit-reverse a 32-bit word.
 */
static uint32_t
rev32(uint32_t x)
{
#define RMS(m, s)   do { \
		x = ((x & (uint32_t)(m)) << (s)) \
			| ((x >> (s)) & (uint32_t)(m)); \
	} while (0)

	RMS(0x55555555, 1);
	RMS(0x33333333, 2);
	RMS(0x0F0F0F0F, 4);
	RMS(0x00FF00FF, 8);
	return (x << 16) | (x >> 16);

#undef RMS
}

/* see bearssl_hash.h */
void
br_ghash_ctmul32(void *y, const void *h, const void *data, size_t len)
{
	/*
	 * This implementation is similar to br_ghash_ctmul() except
	 * that we have to do the multiplication twice, with the
	 * "normal" and "bit reversed" operands. Hence we end up with
	 * eighteen 32-bit multiplications instead of nine.
	 */

	const unsigned char *buf, *hb;
	unsigned char *yb;
	uint32_t yw[4];
	uint32_t hw[4], hwr[4];

	buf = data;
	yb = y;
	hb = h;
	yw[3] = br_dec32be(yb);
	yw[2] = br_dec32be(yb + 4);
	yw[1] = br_dec32be(yb + 8);
	yw[0] = br_dec32be(yb + 12);
	hw[3] = br_dec32be(hb);
	hw[2] = br_dec32be(hb + 4);
	hw[1] = br_dec32be(hb + 8);
	hw[0] = br_dec32be(hb + 12);
	hwr[3] = rev32(hw[3]);
	hwr[2] = rev32(hw[2]);
	hwr[1] = rev32(hw[1]);
	hwr[0] = rev32(hw[0]);
	while (len > 0) {
		const unsigned char *src;
		unsigned char tmp[16];
		int i;
		uint32_t a[18], b[18], c[18];
		uint32_t d0, d1, d2, d3, d4, d5, d6, d7;
		uint32_t zw[8];

		if (len >= 16) {
			src = buf;
			buf += 16;
			len -= 16;
		} else {
			memcpy(tmp, buf, len);
			memset(tmp + len, 0, (sizeof tmp) - len);
			src = tmp;
			len = 0;
		}
		yw[3] ^= br_dec32be(src);
		yw[2] ^= br_dec32be(src + 4);
		yw[1] ^= br_dec32be(src + 8);
		yw[0] ^= br_dec32be(src + 12);

		/*
		 * We are using Karatsuba: the 128x128 multiplication is
		 * reduced to three 64x64 multiplications, hence nine
		 * 32x32 multiplications. With the bit-reversal trick,
		 * we have to perform 18 32x32 multiplications.
		 */

		/*
		 * y[0,1]*h[0,1] -> 0,1,4
		 * y[2,3]*h[2,3] -> 2,3,5
		 * (y[0,1]+y[2,3])*(h[0,1]+h[2,3]) -> 6,7,8
		 */

		a[0] = yw[0];
		a[1] = yw[1];
		a[2] = yw[2];
		a[3] = yw[3];
		a[4] = a[0] ^ a[1];
		a[5] = a[2] ^ a[3];
		a[6] = a[0] ^ a[2];
		a[7] = a[1] ^ a[3];
		a[8] = a[6] ^ a[7];

		a[ 9] = rev32(yw[0]);
		a[10] = rev32(yw[1]);
		a[11] = rev32(yw[2]);
		a[12] = rev32(yw[3]);
		a[13] = a[ 9] ^ a[10];
		a[14] = a[11] ^ a[12];
		a[15] = a[ 9] ^ a[11];
		a[16] = a[10] ^ a[12];
		a[17] = a[15] ^ a[16];

		b[0] = hw[0];
		b[1] = hw[1];
		b[2] = hw[2];
		b[3] = hw[3];
		b[4] = b[0] ^ b[1];
		b[5] = b[2] ^ b[3];
		b[6] = b[0] ^ b[2];
		b[7] = b[1] ^ b[3];
		b[8] = b[6] ^ b[7];

		b[ 9] = hwr[0];
		b[10] = hwr[1];
		b[11] = hwr[2];
		b[12] = hwr[3];
		b[13] = b[ 9] ^ b[10];
		b[14] = b[11] ^ b[12];
		b[15] = b[ 9] ^ b[11];
		b[16] = b[10] ^ b[12];
		b[17] = b[15] ^ b[16];

		for (i = 0; i < 18; i ++) {
			c[i] = bmul32(a[i], b[i]);
		}

		c[4] ^= c[0] ^ c[1];
		c[5] ^= c[2] ^ c[3];
		c[8] ^= c[6] ^ c[7];

		c[13] ^= c[ 9] ^ c[10];
		c[14] ^= c[11] ^ c[12];
		c[17] ^= c[15] ^ c[16];

		/*
		 * y[0,1]*h[0,1] -> 0,9^4,1^13,10
		 * y[2,3]*h[2,3] -> 2,11^5,3^14,12
		 * (y[0,1]+y[2,3])*(h[0,1]+h[2,3]) -> 6,15^8,7^17,16
		 */
		d0 = c[0];
		d1 = c[4] ^ (rev32(c[9]) >> 1);
		d2 = c[1] ^ c[0] ^ c[2] ^ c[6] ^ (rev32(c[13]) >> 1);
		d3 = c[4] ^ c[5] ^ c[8]
			^ (rev32(c[10] ^ c[9] ^ c[11] ^ c[15]) >> 1);
		d4 = c[2] ^ c[1] ^ c[3] ^ c[7]
			^ (rev32(c[13] ^ c[14] ^ c[17]) >> 1);
		d5 = c[5] ^ (rev32(c[11] ^ c[10] ^ c[12] ^ c[16]) >> 1);
		d6 = c[3] ^ (rev32(c[14]) >> 1);
		d7 = rev32(c[12]) >> 1;

		zw[0] = d0 << 1;
		zw[1] = (d1 << 1) | (d0 >> 31);
		zw[2] = (d2 << 1) | (d1 >> 31);
		zw[3] = (d3 << 1) | (d2 >> 31);
		zw[4] = (d4 << 1) | (d3 >> 31);
		zw[5] = (d5 << 1) | (d4 >> 31);
		zw[6] = (d6 << 1) | (d5 >> 31);
		zw[7] = (d7 << 1) | (d6 >> 31);

		for (i = 0; i < 4; i ++) {
			uint32_t lw;

			lw = zw[i];
			zw[i + 4] ^= lw ^ (lw >> 1) ^ (lw >> 2) ^ (lw >> 7);
			zw[i + 3] ^= (lw << 31) ^ (lw << 30) ^ (lw << 25);
		}
		memcpy(yw, zw + 4, sizeof yw);
	}
	br_enc32be(yb, yw[3]);
	br_enc32be(yb + 4, yw[2]);
	br_enc32be(yb + 8, yw[1]);
	br_enc32be(yb + 12, yw[0]);
}