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 */ 28 void 29 br_i32_muladd_small(uint32_t *x, uint32_t z, const uint32_t *m) 30 { 31 uint32_t m_bitlen; 32 size_t u, mlen; 33 uint32_t a0, a1, b0, hi, g, q, tb; 34 uint32_t chf, clow, under, over; 35 uint64_t cc; 36 37 /* 38 * We can test on the modulus bit length since we accept to 39 * leak that length. 40 */ 41 m_bitlen = m[0]; 42 if (m_bitlen == 0) { 43 return; 44 } 45 if (m_bitlen <= 32) { 46 x[1] = br_rem(x[1], z, m[1]); 47 return; 48 } 49 mlen = (m_bitlen + 31) >> 5; 50 51 /* 52 * Principle: we estimate the quotient (x*2^32+z)/m by 53 * doing a 64/32 division with the high words. 54 * 55 * Let: 56 * w = 2^32 57 * a = (w*a0 + a1) * w^N + a2 58 * b = b0 * w^N + b2 59 * such that: 60 * 0 <= a0 < w 61 * 0 <= a1 < w 62 * 0 <= a2 < w^N 63 * w/2 <= b0 < w 64 * 0 <= b2 < w^N 65 * a < w*b 66 * I.e. the two top words of a are a0:a1, the top word of b is 67 * b0, we ensured that b0 is "full" (high bit set), and a is 68 * such that the quotient q = a/b fits on one word (0 <= q < w). 69 * 70 * If a = b*q + r (with 0 <= r < q), we can estimate q by 71 * doing an Euclidean division on the top words: 72 * a0*w+a1 = b0*u + v (with 0 <= v < w) 73 * Then the following holds: 74 * 0 <= u <= w 75 * u-2 <= q <= u 76 */ 77 a0 = br_i32_word(x, m_bitlen - 32); 78 hi = x[mlen]; 79 memmove(x + 2, x + 1, (mlen - 1) * sizeof *x); 80 x[1] = z; 81 a1 = br_i32_word(x, m_bitlen - 32); 82 b0 = br_i32_word(m, m_bitlen - 32); 83 84 /* 85 * We estimate a divisor q. If the quotient returned by br_div() 86 * is g: 87 * -- If a0 == b0 then g == 0; we want q = 0xFFFFFFFF. 88 * -- Otherwise: 89 * -- if g == 0 then we set q = 0; 90 * -- otherwise, we set q = g - 1. 91 * The properties described above then ensure that the true 92 * quotient is q-1, q or q+1. 93 */ 94 g = br_div(a0, a1, b0); 95 q = MUX(EQ(a0, b0), 0xFFFFFFFF, MUX(EQ(g, 0), 0, g - 1)); 96 97 /* 98 * We subtract q*m from x (with the extra high word of value 'hi'). 99 * Since q may be off by 1 (in either direction), we may have to 100 * add or subtract m afterwards. 101 * 102 * The 'tb' flag will be true (1) at the end of the loop if the 103 * result is greater than or equal to the modulus (not counting 104 * 'hi' or the carry). 105 */ 106 cc = 0; 107 tb = 1; 108 for (u = 1; u <= mlen; u ++) { 109 uint32_t mw, zw, xw, nxw; 110 uint64_t zl; 111 112 mw = m[u]; 113 zl = MUL(mw, q) + cc; 114 cc = (uint32_t)(zl >> 32); 115 zw = (uint32_t)zl; 116 xw = x[u]; 117 nxw = xw - zw; 118 cc += (uint64_t)GT(nxw, xw); 119 x[u] = nxw; 120 tb = MUX(EQ(nxw, mw), tb, GT(nxw, mw)); 121 } 122 123 /* 124 * If we underestimated q, then either cc < hi (one extra bit 125 * beyond the top array word), or cc == hi and tb is true (no 126 * extra bit, but the result is not lower than the modulus). In 127 * these cases we must subtract m once. 128 * 129 * Otherwise, we may have overestimated, which will show as 130 * cc > hi (thus a negative result). Correction is adding m once. 131 */ 132 chf = (uint32_t)(cc >> 32); 133 clow = (uint32_t)cc; 134 over = chf | GT(clow, hi); 135 under = ~over & (tb | (~chf & LT(clow, hi))); 136 br_i32_add(x, m, over); 137 br_i32_sub(x, m, under); 138 } 139