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+#include "inner.h"
+
+/*
+ * 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 <thomas.pornin@nccgroup.com>
+ */
+
+
+/* see inner.h */
+void
+PQCLEAN_FALCON1024_CLEAN_hash_to_point_vartime(
+ inner_shake256_context *sc,
+ uint16_t *x, unsigned logn) {
+ /*
+ * This is the straightforward per-the-spec implementation. It
+ * is not constant-time, thus it might reveal information on the
+ * plaintext (at least, enough to check the plaintext against a
+ * list of potential plaintexts) in a scenario where the
+ * attacker does not have access to the signature value or to
+ * the public key, but knows the nonce (without knowledge of the
+ * nonce, the hashed output cannot be matched against potential
+ * plaintexts).
+ */
+ size_t n;
+
+ n = (size_t)1 << logn;
+ while (n > 0) {
+ uint8_t buf[2];
+ uint32_t w;
+
+ inner_shake256_extract(sc, (void *)buf, sizeof buf);
+ w = ((unsigned)buf[0] << 8) | (unsigned)buf[1];
+ if (w < 61445) {
+ while (w >= 12289) {
+ w -= 12289;
+ }
+ *x ++ = (uint16_t)w;
+ n --;
+ }
+ }
+}
+
+/* see inner.h */
+void
+PQCLEAN_FALCON1024_CLEAN_hash_to_point_ct(
+ inner_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;
+
+ inner_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_FALCON1024_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_FALCON1024_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));
+}