/* * Support functions for signatures (hash-to-point, norm). * * ==========================(LICENSE BEGIN)============================ * * Copyright (c) 2017-2019 Falcon Project * * Permission is hereby granted, free of charge, to any person obtaining * a copy of this software and associated documentation files (the * "Software"), to deal in the Software without restriction, including * without limitation the rights to use, copy, modify, merge, publish, * distribute, sublicense, and/or sell copies of the Software, and to * permit persons to whom the Software is furnished to do so, subject to * the following conditions: * * The above copyright notice and this permission notice shall be * included in all copies or substantial portions of the Software. * * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY * CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. * * ===========================(LICENSE END)============================= * * @author Thomas Pornin */ #include "inner.h" /* see inner.h */ void PQCLEAN_FALCON512_CLEAN_hash_to_point( shake256_context *sc, uint16_t *x, unsigned logn, uint8_t *tmp) { /* * Each 16-bit sample is a value in 0..65535. The value is * kept if it falls in 0..61444 (because 61445 = 5*12289) * and rejected otherwise; thus, each sample has probability * about 0.93758 of being selected. * * We want to oversample enough to be sure that we will * have enough values with probability at least 1 - 2^(-256). * Depending on degree N, this leads to the following * required oversampling: * * logn n oversampling * 1 2 65 * 2 4 67 * 3 8 71 * 4 16 77 * 5 32 86 * 6 64 100 * 7 128 122 * 8 256 154 * 9 512 205 * 10 1024 287 * * If logn >= 7, then the provided temporary buffer is large * enough. Otherwise, we use a stack buffer of 63 entries * (i.e. 126 bytes) for the values that do not fit in tmp[]. */ static const uint16_t overtab[] = { 0, /* unused */ 65, 67, 71, 77, 86, 100, 122, 154, 205, 287 }; unsigned n, n2, u, m, p, over; uint16_t *tt1, tt2[63]; /* * We first generate m 16-bit value. Values 0..n-1 go to x[]. * Values n..2*n-1 go to tt1[]. Values 2*n and later go to tt2[]. * We also reduce modulo q the values; rejected values are set * to 0xFFFF. */ n = 1U << logn; n2 = n << 1; over = overtab[logn]; m = n + over; tt1 = (uint16_t *)tmp; for (u = 0; u < m; u ++) { uint8_t buf[2]; uint32_t w, wr; shake256_extract(sc, buf, sizeof buf); w = ((uint32_t)buf[0] << 8) | (uint32_t)buf[1]; wr = w - ((uint32_t)24578 & (((w - 24578) >> 31) - 1)); wr = wr - ((uint32_t)24578 & (((wr - 24578) >> 31) - 1)); wr = wr - ((uint32_t)12289 & (((wr - 12289) >> 31) - 1)); wr |= ((w - 61445) >> 31) - 1; if (u < n) { x[u] = (uint16_t)wr; } else if (u < n2) { tt1[u - n] = (uint16_t)wr; } else { tt2[u - n2] = (uint16_t)wr; } } /* * Now we must "squeeze out" the invalid values. We do this in * a logarithmic sequence of passes; each pass computes where a * value should go, and moves it down by 'p' slots if necessary, * where 'p' uses an increasing powers-of-two scale. It can be * shown that in all cases where the loop decides that a value * has to be moved down by p slots, the destination slot is * "free" (i.e. contains an invalid value). */ for (p = 1; p <= over; p <<= 1) { unsigned v; /* * In the loop below: * * - v contains the index of the final destination of * the value; it is recomputed dynamically based on * whether values are valid or not. * * - u is the index of the value we consider ("source"); * its address is s. * * - The loop may swap the value with the one at index * u-p. The address of the swap destination is d. */ v = 0; for (u = 0; u < m; u ++) { uint16_t *s, *d; unsigned j, sv, dv, mk; if (u < n) { s = &x[u]; } else if (u < n2) { s = &tt1[u - n]; } else { s = &tt2[u - n2]; } sv = *s; /* * The value in sv should ultimately go to * address v, i.e. jump back by u-v slots. */ j = u - v; /* * We increment v for the next iteration, but * only if the source value is valid. The mask * 'mk' is -1 if the value is valid, 0 otherwise, * so we _subtract_ mk. */ mk = (sv >> 15) - 1U; v -= mk; /* * In this loop we consider jumps by p slots; if * u < p then there is nothing more to do. */ if (u < p) { continue; } /* * Destination for the swap: value at address u-p. */ if ((u - p) < n) { d = &x[u - p]; } else if ((u - p) < n2) { d = &tt1[(u - p) - n]; } else { d = &tt2[(u - p) - n2]; } dv = *d; /* * The swap should be performed only if the source * is valid AND the jump j has its 'p' bit set. */ mk &= -(((j & p) + 0x1FF) >> 9); *s = (uint16_t)(sv ^ (mk & (sv ^ dv))); *d = (uint16_t)(dv ^ (mk & (sv ^ dv))); } } } /* see inner.h */ int PQCLEAN_FALCON512_CLEAN_is_short( const int16_t *s1, const int16_t *s2, unsigned logn) { /* * We use the l2-norm. Code below uses only 32-bit operations to * compute the square of the norm with saturation to 2^32-1 if * the value exceeds 2^31-1. */ size_t n, u; uint32_t s, ng; n = (size_t)1 << logn; s = 0; ng = 0; for (u = 0; u < n; u ++) { int32_t z; z = s1[u]; s += (uint32_t)(z * z); ng |= s; z = s2[u]; s += (uint32_t)(z * z); ng |= s; } s |= -(ng >> 31); /* * Acceptance bound on the l2-norm is: * 1.2*1.55*sqrt(q)*sqrt(2*N) * Value 7085 is floor((1.2^2)*(1.55^2)*2*1024). */ return s < (((uint32_t)7085 * (uint32_t)12289) >> (10 - logn)); } /* see inner.h */ int PQCLEAN_FALCON512_CLEAN_is_short_half( uint32_t sqn, const int16_t *s2, unsigned logn) { size_t n, u; uint32_t ng; n = (size_t)1 << logn; ng = -(sqn >> 31); for (u = 0; u < n; u ++) { int32_t z; z = s2[u]; sqn += (uint32_t)(z * z); ng |= sqn; } sqn |= -(ng >> 31); /* * Acceptance bound on the l2-norm is: * 1.2*1.55*sqrt(q)*sqrt(2*N) * Value 7085 is floor((1.2^2)*(1.55^2)*2*1024). */ return sqn < (((uint32_t)7085 * (uint32_t)12289) >> (10 - logn)); }