2 * Copyright (c) 2016 Thomas Pornin <pornin@bolet.org>
4 * Permission is hereby granted, free of charge, to any person obtaining
5 * a copy of this software and associated documentation files (the
6 * "Software"), to deal in the Software without restriction, including
7 * without limitation the rights to use, copy, modify, merge, publish,
8 * distribute, sublicense, and/or sell copies of the Software, and to
9 * permit persons to whom the Software is furnished to do so, subject to
10 * the following conditions:
12 * The above copyright notice and this permission notice shall be
13 * included in all copies or substantial portions of the Software.
15 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
16 * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
17 * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
18 * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
19 * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
20 * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
21 * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
28 * This implementation uses 32-bit multiplications, and only the low
29 * 32 bits for each multiplication result. This is meant primarily for
30 * the ARM Cortex M0 and M0+, whose multiplication opcode does not yield
31 * the upper 32 bits; but it might also be useful on architectures where
32 * access to the upper 32 bits requires use of specific registers that
33 * create contention (e.g. on i386, "mul" necessarily outputs the result
34 * in edx:eax, while "imul" can use any registers but is limited to the
37 * The implementation trick that is used here is bit-reversing (bit 0
38 * is swapped with bit 31, bit 1 with bit 30, and so on). In GF(2)[X],
39 * for all values x and y, we have:
40 * rev32(x) * rev32(y) = rev64(x * y)
41 * In other words, if we bit-reverse (over 32 bits) the operands, then we
42 * bit-reverse (over 64 bits) the result.
46 * Multiplication in GF(2)[X], truncated to its low 32 bits.
48 static inline uint32_t
49 bmul32(uint32_t x, uint32_t y)
51 uint32_t x0, x1, x2, x3;
52 uint32_t y0, y1, y2, y3;
53 uint32_t z0, z1, z2, z3;
55 x0 = x & (uint32_t)0x11111111;
56 x1 = x & (uint32_t)0x22222222;
57 x2 = x & (uint32_t)0x44444444;
58 x3 = x & (uint32_t)0x88888888;
59 y0 = y & (uint32_t)0x11111111;
60 y1 = y & (uint32_t)0x22222222;
61 y2 = y & (uint32_t)0x44444444;
62 y3 = y & (uint32_t)0x88888888;
63 z0 = (x0 * y0) ^ (x1 * y3) ^ (x2 * y2) ^ (x3 * y1);
64 z1 = (x0 * y1) ^ (x1 * y0) ^ (x2 * y3) ^ (x3 * y2);
65 z2 = (x0 * y2) ^ (x1 * y1) ^ (x2 * y0) ^ (x3 * y3);
66 z3 = (x0 * y3) ^ (x1 * y2) ^ (x2 * y1) ^ (x3 * y0);
67 z0 &= (uint32_t)0x11111111;
68 z1 &= (uint32_t)0x22222222;
69 z2 &= (uint32_t)0x44444444;
70 z3 &= (uint32_t)0x88888888;
71 return z0 | z1 | z2 | z3;
75 * Bit-reverse a 32-bit word.
80 #define RMS(m, s) do { \
81 x = ((x & (uint32_t)(m)) << (s)) \
82 | ((x >> (s)) & (uint32_t)(m)); \
89 return (x << 16) | (x >> 16);
94 /* see bearssl_hash.h */
96 br_ghash_ctmul32(void *y, const void *h, const void *data, size_t len)
99 * This implementation is similar to br_ghash_ctmul() except
100 * that we have to do the multiplication twice, with the
101 * "normal" and "bit reversed" operands. Hence we end up with
102 * eighteen 32-bit multiplications instead of nine.
105 const unsigned char *buf, *hb;
108 uint32_t hw[4], hwr[4];
113 yw[3] = br_dec32be(yb);
114 yw[2] = br_dec32be(yb + 4);
115 yw[1] = br_dec32be(yb + 8);
116 yw[0] = br_dec32be(yb + 12);
117 hw[3] = br_dec32be(hb);
118 hw[2] = br_dec32be(hb + 4);
119 hw[1] = br_dec32be(hb + 8);
120 hw[0] = br_dec32be(hb + 12);
121 hwr[3] = rev32(hw[3]);
122 hwr[2] = rev32(hw[2]);
123 hwr[1] = rev32(hw[1]);
124 hwr[0] = rev32(hw[0]);
126 const unsigned char *src;
127 unsigned char tmp[16];
129 uint32_t a[18], b[18], c[18];
130 uint32_t d0, d1, d2, d3, d4, d5, d6, d7;
138 memcpy(tmp, buf, len);
139 memset(tmp + len, 0, (sizeof tmp) - len);
143 yw[3] ^= br_dec32be(src);
144 yw[2] ^= br_dec32be(src + 4);
145 yw[1] ^= br_dec32be(src + 8);
146 yw[0] ^= br_dec32be(src + 12);
149 * We are using Karatsuba: the 128x128 multiplication is
150 * reduced to three 64x64 multiplications, hence nine
151 * 32x32 multiplications. With the bit-reversal trick,
152 * we have to perform 18 32x32 multiplications.
156 * y[0,1]*h[0,1] -> 0,1,4
157 * y[2,3]*h[2,3] -> 2,3,5
158 * (y[0,1]+y[2,3])*(h[0,1]+h[2,3]) -> 6,7,8
171 a[ 9] = rev32(yw[0]);
172 a[10] = rev32(yw[1]);
173 a[11] = rev32(yw[2]);
174 a[12] = rev32(yw[3]);
175 a[13] = a[ 9] ^ a[10];
176 a[14] = a[11] ^ a[12];
177 a[15] = a[ 9] ^ a[11];
178 a[16] = a[10] ^ a[12];
179 a[17] = a[15] ^ a[16];
195 b[13] = b[ 9] ^ b[10];
196 b[14] = b[11] ^ b[12];
197 b[15] = b[ 9] ^ b[11];
198 b[16] = b[10] ^ b[12];
199 b[17] = b[15] ^ b[16];
201 for (i = 0; i < 18; i ++) {
202 c[i] = bmul32(a[i], b[i]);
209 c[13] ^= c[ 9] ^ c[10];
210 c[14] ^= c[11] ^ c[12];
211 c[17] ^= c[15] ^ c[16];
214 * y[0,1]*h[0,1] -> 0,9^4,1^13,10
215 * y[2,3]*h[2,3] -> 2,11^5,3^14,12
216 * (y[0,1]+y[2,3])*(h[0,1]+h[2,3]) -> 6,15^8,7^17,16
219 d1 = c[4] ^ (rev32(c[9]) >> 1);
220 d2 = c[1] ^ c[0] ^ c[2] ^ c[6] ^ (rev32(c[13]) >> 1);
221 d3 = c[4] ^ c[5] ^ c[8]
222 ^ (rev32(c[10] ^ c[9] ^ c[11] ^ c[15]) >> 1);
223 d4 = c[2] ^ c[1] ^ c[3] ^ c[7]
224 ^ (rev32(c[13] ^ c[14] ^ c[17]) >> 1);
225 d5 = c[5] ^ (rev32(c[11] ^ c[10] ^ c[12] ^ c[16]) >> 1);
226 d6 = c[3] ^ (rev32(c[14]) >> 1);
227 d7 = rev32(c[12]) >> 1;
230 zw[1] = (d1 << 1) | (d0 >> 31);
231 zw[2] = (d2 << 1) | (d1 >> 31);
232 zw[3] = (d3 << 1) | (d2 >> 31);
233 zw[4] = (d4 << 1) | (d3 >> 31);
234 zw[5] = (d5 << 1) | (d4 >> 31);
235 zw[6] = (d6 << 1) | (d5 >> 31);
236 zw[7] = (d7 << 1) | (d6 >> 31);
238 for (i = 0; i < 4; i ++) {
242 zw[i + 4] ^= lw ^ (lw >> 1) ^ (lw >> 2) ^ (lw >> 7);
243 zw[i + 3] ^= (lw << 31) ^ (lw << 30) ^ (lw << 25);
245 memcpy(yw, zw + 4, sizeof yw);
247 br_enc32be(yb, yw[3]);
248 br_enc32be(yb + 4, yw[2]);
249 br_enc32be(yb + 8, yw[1]);
250 br_enc32be(yb + 12, yw[0]);