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+/**********************************************************************
+ * Copyright (c) 2015 Pieter Wuille, Andrew Poelstra *
+ * Distributed under the MIT software license, see the accompanying *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_ECMULT_CONST_IMPL_
+#define _SECP256K1_ECMULT_CONST_IMPL_
+
+#include "scalar.h"
+#include "group.h"
+#include "ecmult_const.h"
+#include "ecmult_impl.h"
+
+#ifdef USE_ENDOMORPHISM
+ #define WNAF_BITS 128
+#else
+ #define WNAF_BITS 256
+#endif
+#define WNAF_SIZE(w) ((WNAF_BITS + (w) - 1) / (w))
+
+/* This is like `ECMULT_TABLE_GET_GE` but is constant time */
+#define ECMULT_CONST_TABLE_GET_GE(r,pre,n,w) do { \
+ int m; \
+ int abs_n = (n) * (((n) > 0) * 2 - 1); \
+ int idx_n = abs_n / 2; \
+ secp256k1_fe neg_y; \
+ VERIFY_CHECK(((n) & 1) == 1); \
+ VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \
+ VERIFY_CHECK((n) <= ((1 << ((w)-1)) - 1)); \
+ VERIFY_SETUP(secp256k1_fe_clear(&(r)->x)); \
+ VERIFY_SETUP(secp256k1_fe_clear(&(r)->y)); \
+ for (m = 0; m < ECMULT_TABLE_SIZE(w); m++) { \
+ /* This loop is used to avoid secret data in array indices. See
+ * the comment in ecmult_gen_impl.h for rationale. */ \
+ secp256k1_fe_cmov(&(r)->x, &(pre)[m].x, m == idx_n); \
+ secp256k1_fe_cmov(&(r)->y, &(pre)[m].y, m == idx_n); \
+ } \
+ (r)->infinity = 0; \
+ secp256k1_fe_negate(&neg_y, &(r)->y, 1); \
+ secp256k1_fe_cmov(&(r)->y, &neg_y, (n) != abs_n); \
+} while(0)
+
+
+/** Convert a number to WNAF notation. The number becomes represented by sum(2^{wi} * wnaf[i], i=0..return_val)
+ * with the following guarantees:
+ * - each wnaf[i] an odd integer between -(1 << w) and (1 << w)
+ * - each wnaf[i] is nonzero
+ * - the number of words set is returned; this is always (WNAF_BITS + w - 1) / w
+ *
+ * Adapted from `The Width-w NAF Method Provides Small Memory and Fast Elliptic Scalar
+ * Multiplications Secure against Side Channel Attacks`, Okeya and Tagaki. M. Joye (Ed.)
+ * CT-RSA 2003, LNCS 2612, pp. 328-443, 2003. Springer-Verlagy Berlin Heidelberg 2003
+ *
+ * Numbers reference steps of `Algorithm SPA-resistant Width-w NAF with Odd Scalar` on pp. 335
+ */
+static int secp256k1_wnaf_const(int *wnaf, secp256k1_scalar s, int w) {
+ int global_sign;
+ int skew = 0;
+ int word = 0;
+ /* 1 2 3 */
+ int u_last;
+ int u;
+
+#ifdef USE_ENDOMORPHISM
+ int flip;
+ int bit;
+ secp256k1_scalar neg_s;
+ int not_neg_one;
+ /* If we are using the endomorphism, we cannot handle even numbers by negating
+ * them, since we are working with 128-bit numbers whose negations would be 256
+ * bits, eliminating the performance advantage. Instead we use a technique from
+ * Section 4.2 of the Okeya/Tagaki paper, which is to add either 1 (for even)
+ * or 2 (for odd) to the number we are encoding, then compensating after the
+ * multiplication. */
+ /* Negative 128-bit numbers will be negated, since otherwise they are 256-bit */
+ flip = secp256k1_scalar_is_high(&s);
+ /* We add 1 to even numbers, 2 to odd ones, noting that negation flips parity */
+ bit = flip ^ (s.d[0] & 1);
+ /* We check for negative one, since adding 2 to it will cause an overflow */
+ secp256k1_scalar_negate(&neg_s, &s);
+ not_neg_one = !secp256k1_scalar_is_one(&neg_s);
+ secp256k1_scalar_cadd_bit(&s, bit, not_neg_one);
+ /* If we had negative one, flip == 1, s.d[0] == 0, bit == 1, so caller expects
+ * that we added two to it and flipped it. In fact for -1 these operations are
+ * identical. We only flipped, but since skewing is required (in the sense that
+ * the skew must be 1 or 2, never zero) and flipping is not, we need to change
+ * our flags to claim that we only skewed. */
+ global_sign = secp256k1_scalar_cond_negate(&s, flip);
+ global_sign *= not_neg_one * 2 - 1;
+ skew = 1 << bit;
+#else
+ /* Otherwise, we just negate to force oddness */
+ int is_even = secp256k1_scalar_is_even(&s);
+ global_sign = secp256k1_scalar_cond_negate(&s, is_even);
+#endif
+
+ /* 4 */
+ u_last = secp256k1_scalar_shr_int(&s, w);
+ while (word * w < WNAF_BITS) {
+ int sign;
+ int even;
+
+ /* 4.1 4.4 */
+ u = secp256k1_scalar_shr_int(&s, w);
+ /* 4.2 */
+ even = ((u & 1) == 0);
+ sign = 2 * (u_last > 0) - 1;
+ u += sign * even;
+ u_last -= sign * even * (1 << w);
+
+ /* 4.3, adapted for global sign change */
+ wnaf[word++] = u_last * global_sign;
+
+ u_last = u;
+ }
+ wnaf[word] = u * global_sign;
+
+ VERIFY_CHECK(secp256k1_scalar_is_zero(&s));
+ VERIFY_CHECK(word == WNAF_SIZE(w));
+ return skew;
+}
+
+
+static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, const secp256k1_scalar *scalar) {
+ secp256k1_ge pre_a[ECMULT_TABLE_SIZE(WINDOW_A)];
+ secp256k1_ge tmpa;
+ secp256k1_fe Z;
+
+#ifdef USE_ENDOMORPHISM
+ secp256k1_ge pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)];
+ int wnaf_1[1 + WNAF_SIZE(WINDOW_A - 1)];
+ int wnaf_lam[1 + WNAF_SIZE(WINDOW_A - 1)];
+ int skew_1;
+ int skew_lam;
+ secp256k1_scalar q_1, q_lam;
+#else
+ int wnaf[1 + WNAF_SIZE(WINDOW_A - 1)];
+#endif
+
+ int i;
+ secp256k1_scalar sc = *scalar;
+
+ /* build wnaf representation for q. */
+#ifdef USE_ENDOMORPHISM
+ /* split q into q_1 and q_lam (where q = q_1 + q_lam*lambda, and q_1 and q_lam are ~128 bit) */
+ secp256k1_scalar_split_lambda(&q_1, &q_lam, &sc);
+ /* no need for zero correction when using endomorphism since even
+ * numbers have one added to them anyway */
+ skew_1 = secp256k1_wnaf_const(wnaf_1, q_1, WINDOW_A - 1);
+ skew_lam = secp256k1_wnaf_const(wnaf_lam, q_lam, WINDOW_A - 1);
+#else
+ int is_zero = secp256k1_scalar_is_zero(scalar);
+ /* the wNAF ladder cannot handle zero, so bump this to one .. we will
+ * correct the result after the fact */
+ sc.d[0] += is_zero;
+ VERIFY_CHECK(!secp256k1_scalar_is_zero(&sc));
+
+ secp256k1_wnaf_const(wnaf, sc, WINDOW_A - 1);
+#endif
+
+ /* Calculate odd multiples of a.
+ * All multiples are brought to the same Z 'denominator', which is stored
+ * in Z. Due to secp256k1' isomorphism we can do all operations pretending
+ * that the Z coordinate was 1, use affine addition formulae, and correct
+ * the Z coordinate of the result once at the end.
+ */
+ secp256k1_gej_set_ge(r, a);
+ secp256k1_ecmult_odd_multiples_table_globalz_windowa(pre_a, &Z, r);
+ for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
+ secp256k1_fe_normalize_weak(&pre_a[i].y);
+ }
+#ifdef USE_ENDOMORPHISM
+ for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
+ secp256k1_ge_mul_lambda(&pre_a_lam[i], &pre_a[i]);
+ }
+#endif
+
+ /* first loop iteration (separated out so we can directly set r, rather
+ * than having it start at infinity, get doubled several times, then have
+ * its new value added to it) */
+#ifdef USE_ENDOMORPHISM
+ i = wnaf_1[WNAF_SIZE(WINDOW_A - 1)];
+ VERIFY_CHECK(i != 0);
+ ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, i, WINDOW_A);
+ secp256k1_gej_set_ge(r, &tmpa);
+
+ i = wnaf_lam[WNAF_SIZE(WINDOW_A - 1)];
+ VERIFY_CHECK(i != 0);
+ ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a_lam, i, WINDOW_A);
+ secp256k1_gej_add_ge(r, r, &tmpa);
+#else
+ i = wnaf[WNAF_SIZE(WINDOW_A - 1)];
+ VERIFY_CHECK(i != 0);
+ ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, i, WINDOW_A);
+ secp256k1_gej_set_ge(r, &tmpa);
+#endif
+ /* remaining loop iterations */
+ for (i = WNAF_SIZE(WINDOW_A - 1) - 1; i >= 0; i--) {
+ int n;
+ int j;
+ for (j = 0; j < WINDOW_A - 1; ++j) {
+ secp256k1_gej_double_nonzero(r, r, NULL);
+ }
+#ifdef USE_ENDOMORPHISM
+ n = wnaf_1[i];
+ ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, n, WINDOW_A);
+ VERIFY_CHECK(n != 0);
+ secp256k1_gej_add_ge(r, r, &tmpa);
+
+ n = wnaf_lam[i];
+ ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a_lam, n, WINDOW_A);
+ VERIFY_CHECK(n != 0);
+ secp256k1_gej_add_ge(r, r, &tmpa);
+#else
+ n = wnaf[i];
+ VERIFY_CHECK(n != 0);
+ ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, n, WINDOW_A);
+ secp256k1_gej_add_ge(r, r, &tmpa);
+#endif
+ }
+
+ secp256k1_fe_mul(&r->z, &r->z, &Z);
+
+#ifdef USE_ENDOMORPHISM
+ {
+ /* Correct for wNAF skew */
+ secp256k1_ge correction = *a;
+ secp256k1_ge_storage correction_1_stor;
+ secp256k1_ge_storage correction_lam_stor;
+ secp256k1_ge_storage a2_stor;
+ secp256k1_gej tmpj;
+ secp256k1_gej_set_ge(&tmpj, &correction);
+ secp256k1_gej_double_var(&tmpj, &tmpj, NULL);
+ secp256k1_ge_set_gej(&correction, &tmpj);
+ secp256k1_ge_to_storage(&correction_1_stor, a);
+ secp256k1_ge_to_storage(&correction_lam_stor, a);
+ secp256k1_ge_to_storage(&a2_stor, &correction);
+
+ /* For odd numbers this is 2a (so replace it), for even ones a (so no-op) */
+ secp256k1_ge_storage_cmov(&correction_1_stor, &a2_stor, skew_1 == 2);
+ secp256k1_ge_storage_cmov(&correction_lam_stor, &a2_stor, skew_lam == 2);
+
+ /* Apply the correction */
+ secp256k1_ge_from_storage(&correction, &correction_1_stor);
+ secp256k1_ge_neg(&correction, &correction);
+ secp256k1_gej_add_ge(r, r, &correction);
+
+ secp256k1_ge_from_storage(&correction, &correction_lam_stor);
+ secp256k1_ge_neg(&correction, &correction);
+ secp256k1_ge_mul_lambda(&correction, &correction);
+ secp256k1_gej_add_ge(r, r, &correction);
+ }
+#else
+ /* correct for zero */
+ r->infinity |= is_zero;
+#endif
+}
+
+#endif