1/* 2 * Copyright (c) 2016 Thomas Pornin <pornin@bolet.org> 3 * 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: 11 * 12 * The above copyright notice and this permission notice shall be 13 * included in all copies or substantial portions of the Software. 14 * 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 22 * SOFTWARE. 23 */ 24 25#include "inner.h" 26 27/* see inner.h */ 28void 29br_i31_montymul(uint32_t *d, const uint32_t *x, const uint32_t *y, 30 const uint32_t *m, uint32_t m0i) 31{ 32 /* 33 * Each outer loop iteration computes: 34 * d <- (d + xu*y + f*m) / 2^31 35 * We have xu <= 2^31-1 and f <= 2^31-1. 36 * Thus, if d <= 2*m-1 on input, then: 37 * 2*m-1 + 2*(2^31-1)*m <= (2^32)*m-1 38 * and the new d value is less than 2*m. 39 * 40 * We represent d over 31-bit words, with an extra word 'dh' 41 * which can thus be only 0 or 1. 42 */ 43 size_t len, len4, u, v; 44 uint32_t dh; 45 46 len = (m[0] + 31) >> 5; 47 len4 = len & ~(size_t)3; 48 br_i31_zero(d, m[0]); 49 dh = 0; 50 for (u = 0; u < len; u ++) { 51 /* 52 * The carry for each operation fits on 32 bits: 53 * d[v+1] <= 2^31-1 54 * xu*y[v+1] <= (2^31-1)*(2^31-1) 55 * f*m[v+1] <= (2^31-1)*(2^31-1) 56 * r <= 2^32-1 57 * (2^31-1) + 2*(2^31-1)*(2^31-1) + (2^32-1) = 2^63 - 2^31 58 * After division by 2^31, the new r is then at most 2^32-1 59 * 60 * Using a 32-bit carry has performance benefits on 32-bit 61 * systems; however, on 64-bit architectures, we prefer to 62 * keep the carry (r) in a 64-bit register, thus avoiding some 63 * "clear high bits" operations. 64 */ 65 uint32_t f, xu; 66#if BR_64 67 uint64_t r; 68#else 69 uint32_t r; 70#endif 71 72 xu = x[u + 1]; 73 f = MUL31_lo((d[1] + MUL31_lo(x[u + 1], y[1])), m0i); 74 75 r = 0; 76 for (v = 0; v < len4; v += 4) { 77 uint64_t z; 78 79 z = (uint64_t)d[v + 1] + MUL31(xu, y[v + 1]) 80 + MUL31(f, m[v + 1]) + r; 81 r = z >> 31; 82 d[v + 0] = (uint32_t)z & 0x7FFFFFFF; 83 z = (uint64_t)d[v + 2] + MUL31(xu, y[v + 2]) 84 + MUL31(f, m[v + 2]) + r; 85 r = z >> 31; 86 d[v + 1] = (uint32_t)z & 0x7FFFFFFF; 87 z = (uint64_t)d[v + 3] + MUL31(xu, y[v + 3]) 88 + MUL31(f, m[v + 3]) + r; 89 r = z >> 31; 90 d[v + 2] = (uint32_t)z & 0x7FFFFFFF; 91 z = (uint64_t)d[v + 4] + MUL31(xu, y[v + 4]) 92 + MUL31(f, m[v + 4]) + r; 93 r = z >> 31; 94 d[v + 3] = (uint32_t)z & 0x7FFFFFFF; 95 } 96 for (; v < len; v ++) { 97 uint64_t z; 98 99 z = (uint64_t)d[v + 1] + MUL31(xu, y[v + 1]) 100 + MUL31(f, m[v + 1]) + r; 101 r = z >> 31; 102 d[v] = (uint32_t)z & 0x7FFFFFFF; 103 } 104 105 /* 106 * Since the new dh can only be 0 or 1, the addition of 107 * the old dh with the carry MUST fit on 32 bits, and 108 * thus can be done into dh itself. 109 */ 110 dh += r; 111 d[len] = dh & 0x7FFFFFFF; 112 dh >>= 31; 113 } 114 115 /* 116 * We must write back the bit length because it was overwritten in 117 * the loop (not overwriting it would require a test in the loop, 118 * which would yield bigger and slower code). 119 */ 120 d[0] = m[0]; 121 122 /* 123 * d[] may still be greater than m[] at that point; notably, the 124 * 'dh' word may be non-zero. 125 */ 126 br_i31_sub(d, m, NEQ(dh, 0) | NOT(br_i31_sub(d, m, 0))); 127} 128