1 /* 2 * Copyright (c) 2017 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 */ 28 uint32_t 29 br_i31_modpow_opt(uint32_t *x, 30 const unsigned char *e, size_t elen, 31 const uint32_t *m, uint32_t m0i, uint32_t *tmp, size_t twlen) 32 { 33 size_t mlen, mwlen; 34 uint32_t *t1, *t2, *base; 35 size_t u, v; 36 uint32_t acc; 37 int acc_len, win_len; 38 39 /* 40 * Get modulus size. 41 */ 42 mwlen = (m[0] + 63) >> 5; 43 mlen = mwlen * sizeof m[0]; 44 mwlen += (mwlen & 1); 45 t1 = tmp; 46 t2 = tmp + mwlen; 47 48 /* 49 * Compute possible window size, with a maximum of 5 bits. 50 * When the window has size 1 bit, we use a specific code 51 * that requires only two temporaries. Otherwise, for a 52 * window of k bits, we need 2^k+1 temporaries. 53 */ 54 if (twlen < (mwlen << 1)) { 55 return 0; 56 } 57 for (win_len = 5; win_len > 1; win_len --) { 58 if ((((uint32_t)1 << win_len) + 1) * mwlen <= twlen) { 59 break; 60 } 61 } 62 63 /* 64 * Everything is done in Montgomery representation. 65 */ 66 br_i31_to_monty(x, m); 67 68 /* 69 * Compute window contents. If the window has size one bit only, 70 * then t2 is set to x; otherwise, t2[0] is left untouched, and 71 * t2[k] is set to x^k (for k >= 1). 72 */ 73 if (win_len == 1) { 74 memcpy(t2, x, mlen); 75 } else { 76 memcpy(t2 + mwlen, x, mlen); 77 base = t2 + mwlen; 78 for (u = 2; u < ((unsigned)1 << win_len); u ++) { 79 br_i31_montymul(base + mwlen, base, x, m, m0i); 80 base += mwlen; 81 } 82 } 83 84 /* 85 * We need to set x to 1, in Montgomery representation. This can 86 * be done efficiently by setting the high word to 1, then doing 87 * one word-sized shift. 88 */ 89 br_i31_zero(x, m[0]); 90 x[(m[0] + 31) >> 5] = 1; 91 br_i31_muladd_small(x, 0, m); 92 93 /* 94 * We process bits from most to least significant. At each 95 * loop iteration, we have acc_len bits in acc. 96 */ 97 acc = 0; 98 acc_len = 0; 99 while (acc_len > 0 || elen > 0) { 100 int i, k; 101 uint32_t bits; 102 103 /* 104 * Get the next bits. 105 */ 106 k = win_len; 107 if (acc_len < win_len) { 108 if (elen > 0) { 109 acc = (acc << 8) | *e ++; 110 elen --; 111 acc_len += 8; 112 } else { 113 k = acc_len; 114 } 115 } 116 bits = (acc >> (acc_len - k)) & (((uint32_t)1 << k) - 1); 117 acc_len -= k; 118 119 /* 120 * We could get exactly k bits. Compute k squarings. 121 */ 122 for (i = 0; i < k; i ++) { 123 br_i31_montymul(t1, x, x, m, m0i); 124 memcpy(x, t1, mlen); 125 } 126 127 /* 128 * Window lookup: we want to set t2 to the window 129 * lookup value, assuming the bits are non-zero. If 130 * the window length is 1 bit only, then t2 is 131 * already set; otherwise, we do a constant-time lookup. 132 */ 133 if (win_len > 1) { 134 br_i31_zero(t2, m[0]); 135 base = t2 + mwlen; 136 for (u = 1; u < ((uint32_t)1 << k); u ++) { 137 uint32_t mask; 138 139 mask = -EQ(u, bits); 140 for (v = 1; v < mwlen; v ++) { 141 t2[v] |= mask & base[v]; 142 } 143 base += mwlen; 144 } 145 } 146 147 /* 148 * Multiply with the looked-up value. We keep the 149 * product only if the exponent bits are not all-zero. 150 */ 151 br_i31_montymul(t1, x, t2, m, m0i); 152 CCOPY(NEQ(bits, 0), x, t1, mlen); 153 } 154 155 /* 156 * Convert back from Montgomery representation, and exit. 157 */ 158 br_i31_from_monty(x, m, m0i); 159 return 1; 160 } 161