/* * Copyright (c) 2016 Thomas Pornin * * 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]); }