1*0957b409SSimon J. Gerraty /* 2*0957b409SSimon J. Gerraty * Copyright (c) 2016 Thomas Pornin <pornin@bolet.org> 3*0957b409SSimon J. Gerraty * 4*0957b409SSimon J. Gerraty * Permission is hereby granted, free of charge, to any person obtaining 5*0957b409SSimon J. Gerraty * a copy of this software and associated documentation files (the 6*0957b409SSimon J. Gerraty * "Software"), to deal in the Software without restriction, including 7*0957b409SSimon J. Gerraty * without limitation the rights to use, copy, modify, merge, publish, 8*0957b409SSimon J. Gerraty * distribute, sublicense, and/or sell copies of the Software, and to 9*0957b409SSimon J. Gerraty * permit persons to whom the Software is furnished to do so, subject to 10*0957b409SSimon J. Gerraty * the following conditions: 11*0957b409SSimon J. Gerraty * 12*0957b409SSimon J. Gerraty * The above copyright notice and this permission notice shall be 13*0957b409SSimon J. Gerraty * included in all copies or substantial portions of the Software. 14*0957b409SSimon J. Gerraty * 15*0957b409SSimon J. Gerraty * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, 16*0957b409SSimon J. Gerraty * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF 17*0957b409SSimon J. Gerraty * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND 18*0957b409SSimon J. Gerraty * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS 19*0957b409SSimon J. Gerraty * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN 20*0957b409SSimon J. Gerraty * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN 21*0957b409SSimon J. Gerraty * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 22*0957b409SSimon J. Gerraty * SOFTWARE. 23*0957b409SSimon J. Gerraty */ 24*0957b409SSimon J. Gerraty 25*0957b409SSimon J. Gerraty #include "inner.h" 26*0957b409SSimon J. Gerraty 27*0957b409SSimon J. Gerraty /* see inner.h */ 28*0957b409SSimon J. Gerraty void 29*0957b409SSimon J. Gerraty br_i32_muladd_small(uint32_t *x, uint32_t z, const uint32_t *m) 30*0957b409SSimon J. Gerraty { 31*0957b409SSimon J. Gerraty uint32_t m_bitlen; 32*0957b409SSimon J. Gerraty size_t u, mlen; 33*0957b409SSimon J. Gerraty uint32_t a0, a1, b0, hi, g, q, tb; 34*0957b409SSimon J. Gerraty uint32_t chf, clow, under, over; 35*0957b409SSimon J. Gerraty uint64_t cc; 36*0957b409SSimon J. Gerraty 37*0957b409SSimon J. Gerraty /* 38*0957b409SSimon J. Gerraty * We can test on the modulus bit length since we accept to 39*0957b409SSimon J. Gerraty * leak that length. 40*0957b409SSimon J. Gerraty */ 41*0957b409SSimon J. Gerraty m_bitlen = m[0]; 42*0957b409SSimon J. Gerraty if (m_bitlen == 0) { 43*0957b409SSimon J. Gerraty return; 44*0957b409SSimon J. Gerraty } 45*0957b409SSimon J. Gerraty if (m_bitlen <= 32) { 46*0957b409SSimon J. Gerraty x[1] = br_rem(x[1], z, m[1]); 47*0957b409SSimon J. Gerraty return; 48*0957b409SSimon J. Gerraty } 49*0957b409SSimon J. Gerraty mlen = (m_bitlen + 31) >> 5; 50*0957b409SSimon J. Gerraty 51*0957b409SSimon J. Gerraty /* 52*0957b409SSimon J. Gerraty * Principle: we estimate the quotient (x*2^32+z)/m by 53*0957b409SSimon J. Gerraty * doing a 64/32 division with the high words. 54*0957b409SSimon J. Gerraty * 55*0957b409SSimon J. Gerraty * Let: 56*0957b409SSimon J. Gerraty * w = 2^32 57*0957b409SSimon J. Gerraty * a = (w*a0 + a1) * w^N + a2 58*0957b409SSimon J. Gerraty * b = b0 * w^N + b2 59*0957b409SSimon J. Gerraty * such that: 60*0957b409SSimon J. Gerraty * 0 <= a0 < w 61*0957b409SSimon J. Gerraty * 0 <= a1 < w 62*0957b409SSimon J. Gerraty * 0 <= a2 < w^N 63*0957b409SSimon J. Gerraty * w/2 <= b0 < w 64*0957b409SSimon J. Gerraty * 0 <= b2 < w^N 65*0957b409SSimon J. Gerraty * a < w*b 66*0957b409SSimon J. Gerraty * I.e. the two top words of a are a0:a1, the top word of b is 67*0957b409SSimon J. Gerraty * b0, we ensured that b0 is "full" (high bit set), and a is 68*0957b409SSimon J. Gerraty * such that the quotient q = a/b fits on one word (0 <= q < w). 69*0957b409SSimon J. Gerraty * 70*0957b409SSimon J. Gerraty * If a = b*q + r (with 0 <= r < q), we can estimate q by 71*0957b409SSimon J. Gerraty * doing an Euclidean division on the top words: 72*0957b409SSimon J. Gerraty * a0*w+a1 = b0*u + v (with 0 <= v < w) 73*0957b409SSimon J. Gerraty * Then the following holds: 74*0957b409SSimon J. Gerraty * 0 <= u <= w 75*0957b409SSimon J. Gerraty * u-2 <= q <= u 76*0957b409SSimon J. Gerraty */ 77*0957b409SSimon J. Gerraty a0 = br_i32_word(x, m_bitlen - 32); 78*0957b409SSimon J. Gerraty hi = x[mlen]; 79*0957b409SSimon J. Gerraty memmove(x + 2, x + 1, (mlen - 1) * sizeof *x); 80*0957b409SSimon J. Gerraty x[1] = z; 81*0957b409SSimon J. Gerraty a1 = br_i32_word(x, m_bitlen - 32); 82*0957b409SSimon J. Gerraty b0 = br_i32_word(m, m_bitlen - 32); 83*0957b409SSimon J. Gerraty 84*0957b409SSimon J. Gerraty /* 85*0957b409SSimon J. Gerraty * We estimate a divisor q. If the quotient returned by br_div() 86*0957b409SSimon J. Gerraty * is g: 87*0957b409SSimon J. Gerraty * -- If a0 == b0 then g == 0; we want q = 0xFFFFFFFF. 88*0957b409SSimon J. Gerraty * -- Otherwise: 89*0957b409SSimon J. Gerraty * -- if g == 0 then we set q = 0; 90*0957b409SSimon J. Gerraty * -- otherwise, we set q = g - 1. 91*0957b409SSimon J. Gerraty * The properties described above then ensure that the true 92*0957b409SSimon J. Gerraty * quotient is q-1, q or q+1. 93*0957b409SSimon J. Gerraty */ 94*0957b409SSimon J. Gerraty g = br_div(a0, a1, b0); 95*0957b409SSimon J. Gerraty q = MUX(EQ(a0, b0), 0xFFFFFFFF, MUX(EQ(g, 0), 0, g - 1)); 96*0957b409SSimon J. Gerraty 97*0957b409SSimon J. Gerraty /* 98*0957b409SSimon J. Gerraty * We subtract q*m from x (with the extra high word of value 'hi'). 99*0957b409SSimon J. Gerraty * Since q may be off by 1 (in either direction), we may have to 100*0957b409SSimon J. Gerraty * add or subtract m afterwards. 101*0957b409SSimon J. Gerraty * 102*0957b409SSimon J. Gerraty * The 'tb' flag will be true (1) at the end of the loop if the 103*0957b409SSimon J. Gerraty * result is greater than or equal to the modulus (not counting 104*0957b409SSimon J. Gerraty * 'hi' or the carry). 105*0957b409SSimon J. Gerraty */ 106*0957b409SSimon J. Gerraty cc = 0; 107*0957b409SSimon J. Gerraty tb = 1; 108*0957b409SSimon J. Gerraty for (u = 1; u <= mlen; u ++) { 109*0957b409SSimon J. Gerraty uint32_t mw, zw, xw, nxw; 110*0957b409SSimon J. Gerraty uint64_t zl; 111*0957b409SSimon J. Gerraty 112*0957b409SSimon J. Gerraty mw = m[u]; 113*0957b409SSimon J. Gerraty zl = MUL(mw, q) + cc; 114*0957b409SSimon J. Gerraty cc = (uint32_t)(zl >> 32); 115*0957b409SSimon J. Gerraty zw = (uint32_t)zl; 116*0957b409SSimon J. Gerraty xw = x[u]; 117*0957b409SSimon J. Gerraty nxw = xw - zw; 118*0957b409SSimon J. Gerraty cc += (uint64_t)GT(nxw, xw); 119*0957b409SSimon J. Gerraty x[u] = nxw; 120*0957b409SSimon J. Gerraty tb = MUX(EQ(nxw, mw), tb, GT(nxw, mw)); 121*0957b409SSimon J. Gerraty } 122*0957b409SSimon J. Gerraty 123*0957b409SSimon J. Gerraty /* 124*0957b409SSimon J. Gerraty * If we underestimated q, then either cc < hi (one extra bit 125*0957b409SSimon J. Gerraty * beyond the top array word), or cc == hi and tb is true (no 126*0957b409SSimon J. Gerraty * extra bit, but the result is not lower than the modulus). In 127*0957b409SSimon J. Gerraty * these cases we must subtract m once. 128*0957b409SSimon J. Gerraty * 129*0957b409SSimon J. Gerraty * Otherwise, we may have overestimated, which will show as 130*0957b409SSimon J. Gerraty * cc > hi (thus a negative result). Correction is adding m once. 131*0957b409SSimon J. Gerraty */ 132*0957b409SSimon J. Gerraty chf = (uint32_t)(cc >> 32); 133*0957b409SSimon J. Gerraty clow = (uint32_t)cc; 134*0957b409SSimon J. Gerraty over = chf | GT(clow, hi); 135*0957b409SSimon J. Gerraty under = ~over & (tb | (~chf & LT(clow, hi))); 136*0957b409SSimon J. Gerraty br_i32_add(x, m, over); 137*0957b409SSimon J. Gerraty br_i32_sub(x, m, under); 138*0957b409SSimon J. Gerraty } 139