[secp256k1.git] / src / ecmult_const_impl.h

/**********************************************************************
 * 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_H
#define SECP256K1_ECMULT_CONST_IMPL_H

#include "scalar.h"
#include "group.h"
#include "ecmult_const.h"
#include "ecmult_impl.h"

/* 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..WNAF_SIZE(w)+1) - return_val.
 *  It has 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 always WNAF_SIZE(w) + 1
 *
 *  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;

    int flip;
    int bit;
    secp256k1_scalar neg_s;
    int not_neg_one;
    /* Note that we cannot handle even numbers by negating them to be odd, as is
     * done in other implementations, since if our scalars were specified to have
     * width < 256 for performance reasons, their negations would have width 256
     * and we'd lose any performance benefit. 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, returning a skew value indicating
     * this, and having the caller compensate after doing the multiplication. */

    /* Negative numbers will be negated to keep their bit representation below the maximum width */
    flip = secp256k1_scalar_is_high(&s);
    /* We add 1 to even numbers, 2 to odd ones, noting that negation flips parity */
    bit = flip ^ !secp256k1_scalar_is_even(&s);
    /* 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;

    /* 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;

    int skew_1;
    int wnaf_1[1 + WNAF_SIZE(WINDOW_A - 1)];
#ifdef USE_ENDOMORPHISM
    secp256k1_ge pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)];
    int wnaf_lam[1 + WNAF_SIZE(WINDOW_A - 1)];
    int skew_lam;
    secp256k1_scalar q_1, q_lam;
#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);
    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
    skew_1   = secp256k1_wnaf_const(wnaf_1, 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) */
    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);
#ifdef USE_ENDOMORPHISM
    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);
#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);
        }

        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);
#ifdef USE_ENDOMORPHISM
        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);
#endif
    }

    secp256k1_fe_mul(&r->z, &r->z, &Z);

    {
        /* Correct for wNAF skew */
        secp256k1_ge correction = *a;
        secp256k1_ge_storage correction_1_stor;
#ifdef USE_ENDOMORPHISM
        secp256k1_ge_storage correction_lam_stor;
#endif
        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);
#ifdef USE_ENDOMORPHISM
        secp256k1_ge_to_storage(&correction_lam_stor, a);
#endif
        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);
#ifdef USE_ENDOMORPHISM
        secp256k1_ge_storage_cmov(&correction_lam_stor, &a2_stor, skew_lam == 2);
#endif

        /* Apply the correction */
        secp256k1_ge_from_storage(&correction, &correction_1_stor);
        secp256k1_ge_neg(&correction, &correction);
        secp256k1_gej_add_ge(r, r, &correction);

#ifdef USE_ENDOMORPHISM
        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);
#endif
    }
}

#endif /* SECP256K1_ECMULT_CONST_IMPL_H */
Commit	Line	Data
44015000 AP	1	/**********************************************************************
	2	* Copyright (c) 2015 Pieter Wuille, Andrew Poelstra *
	3	* Distributed under the MIT software license, see the accompanying *
	4	* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
	5	**********************************************************************/
	6
abe2d3e8 DR	7	#ifndef SECP256K1_ECMULT_CONST_IMPL_H
abe2d3e8 DR	8	#define SECP256K1_ECMULT_CONST_IMPL_H
44015000 AP	9
	10	#include "scalar.h"
	11	#include "group.h"
	12	#include "ecmult_const.h"
	13	#include "ecmult_impl.h"
	14
44015000 AP	15	/* This is like `ECMULT_TABLE_GET_GE` but is constant time */
	16	#define ECMULT_CONST_TABLE_GET_GE(r,pre,n,w) do { \
	17	int m; \
	18	int abs_n = (n) * (((n) > 0) * 2 - 1); \
72ae443a	19	int idx_n = abs_n / 2; \
dd891e0e	20	secp256k1_fe neg_y; \
44015000 AP	21	VERIFY_CHECK(((n) & 1) == 1); \
	22	VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \
	23	VERIFY_CHECK((n) <= ((1 << ((w)-1)) - 1)); \
72ae443a PD	24	VERIFY_SETUP(secp256k1_fe_clear(&(r)->x)); \
	25	VERIFY_SETUP(secp256k1_fe_clear(&(r)->y)); \
	26	for (m = 0; m < ECMULT_TABLE_SIZE(w); m++) { \
44015000 AP	27	/* This loop is used to avoid secret data in array indices. See
44015000 AP	28	* the comment in ecmult_gen_impl.h for rationale. */ \
72ae443a PD	29	secp256k1_fe_cmov(&(r)->x, &(pre)[m].x, m == idx_n); \
72ae443a PD	30	secp256k1_fe_cmov(&(r)->y, &(pre)[m].y, m == idx_n); \
44015000 AP	31	} \
44015000 AP	32	(r)->infinity = 0; \
44015000 AP	33	secp256k1_fe_negate(&neg_y, &(r)->y, 1); \
	34	secp256k1_fe_cmov(&(r)->y, &neg_y, (n) != abs_n); \
	35	} while(0)
	36
	37
768514ba JN	38	/** Convert a number to WNAF notation.
	39	* The number becomes represented by sum(2^{wi} * wnaf[i], i=0..WNAF_SIZE(w)+1) - return_val.
	40	* It has the following guarantees:
44015000 AP	41	* - each wnaf[i] an odd integer between -(1 << w) and (1 << w)
44015000 AP	42	* - each wnaf[i] is nonzero
768514ba	43	* - the number of words set is always WNAF_SIZE(w) + 1
44015000 AP	44	*
	45	* Adapted from `The Width-w NAF Method Provides Small Memory and Fast Elliptic Scalar
	46	* Multiplications Secure against Side Channel Attacks`, Okeya and Tagaki. M. Joye (Ed.)
	47	* CT-RSA 2003, LNCS 2612, pp. 328-443, 2003. Springer-Verlagy Berlin Heidelberg 2003
	48	*
	49	* Numbers reference steps of `Algorithm SPA-resistant Width-w NAF with Odd Scalar` on pp. 335
	50	*/
dd891e0e	51	static int secp256k1_wnaf_const(int *wnaf, secp256k1_scalar s, int w) {
cfe0ed91	52	int global_sign;
92e53fc4	53	int skew = 0;
44015000	54	int word = 0;
c6191fde	55
44015000	56	/* 1 2 3 */
92e53fc4	57	int u_last;
44015000	58	int u;
92e53fc4	59
cfe0ed91 GM	60	int flip;
	61	int bit;
	62	secp256k1_scalar neg_s;
	63	int not_neg_one;
c6191fde AP	64	/* Note that we cannot handle even numbers by negating them to be odd, as is
	65	* done in other implementations, since if our scalars were specified to have
	66	* width < 256 for performance reasons, their negations would have width 256
	67	* and we'd lose any performance benefit. Instead, we use a technique from
92e53fc4	68	* Section 4.2 of the Okeya/Tagaki paper, which is to add either 1 (for even)
c6191fde AP	69	* or 2 (for odd) to the number we are encoding, returning a skew value indicating
	70	* this, and having the caller compensate after doing the multiplication. */
	71
	72	/* Negative numbers will be negated to keep their bit representation below the maximum width */
cfe0ed91	73	flip = secp256k1_scalar_is_high(&s);
92e53fc4	74	/* We add 1 to even numbers, 2 to odd ones, noting that negation flips parity */
83836a95	75	bit = flip ^ !secp256k1_scalar_is_even(&s);
92e53fc4	76	/* We check for negative one, since adding 2 to it will cause an overflow */
92e53fc4 AP	77	secp256k1_scalar_negate(&neg_s, &s);
	78	not_neg_one = !secp256k1_scalar_is_one(&neg_s);
	79	secp256k1_scalar_cadd_bit(&s, bit, not_neg_one);
	80	/* If we had negative one, flip == 1, s.d[0] == 0, bit == 1, so caller expects
	81	* that we added two to it and flipped it. In fact for -1 these operations are
	82	* identical. We only flipped, but since skewing is required (in the sense that
	83	* the skew must be 1 or 2, never zero) and flipping is not, we need to change
	84	* our flags to claim that we only skewed. */
	85	global_sign = secp256k1_scalar_cond_negate(&s, flip);
	86	global_sign = not_neg_one 2 - 1;
	87	skew = 1 << bit;
92e53fc4	88
44015000	89	/* 4 */
92e53fc4	90	u_last = secp256k1_scalar_shr_int(&s, w);
44015000 AP	91	while (word * w < WNAF_BITS) {
	92	int sign;
	93	int even;
	94
	95	/* 4.1 4.4 */
	96	u = secp256k1_scalar_shr_int(&s, w);
	97	/* 4.2 */
	98	even = ((u & 1) == 0);
	99	sign = 2 * (u_last > 0) - 1;
	100	u += sign * even;
	101	u_last -= sign * even * (1 << w);
	102
	103	/* 4.3, adapted for global sign change */
	104	wnaf[word++] = u_last * global_sign;
	105
	106	u_last = u;
	107	}
	108	wnaf[word] = u * global_sign;
	109
	110	VERIFY_CHECK(secp256k1_scalar_is_zero(&s));
	111	VERIFY_CHECK(word == WNAF_SIZE(w));
92e53fc4	112	return skew;
44015000 AP	113	}
	114
	115
dd891e0e PW	116	static void secp256k1_ecmult_const(secp256k1_gej r, const secp256k1_ge a, const secp256k1_scalar *scalar) {
	117	secp256k1_ge pre_a[ECMULT_TABLE_SIZE(WINDOW_A)];
	118	secp256k1_ge tmpa;
	119	secp256k1_fe Z;
44015000	120
c6191fde AP	121	int skew_1;
c6191fde AP	122	int wnaf_1[1 + WNAF_SIZE(WINDOW_A - 1)];
92e53fc4	123	#ifdef USE_ENDOMORPHISM
dd891e0e	124	secp256k1_ge pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)];
92e53fc4	125	int wnaf_lam[1 + WNAF_SIZE(WINDOW_A - 1)];
92e53fc4	126	int skew_lam;
dd891e0e	127	secp256k1_scalar q_1, q_lam;
92e53fc4	128	#endif
44015000 AP	129
44015000 AP	130	int i;
dd891e0e	131	secp256k1_scalar sc = *scalar;
92e53fc4 AP	132
	133	/* build wnaf representation for q. */
	134	#ifdef USE_ENDOMORPHISM
	135	/* split q into q_1 and q_lam (where q = q_1 + q_lamlambda, and q_1 and q_lam are ~128 bit) /
	136	secp256k1_scalar_split_lambda(&q_1, &q_lam, &sc);
92e53fc4 AP	137	skew_1 = secp256k1_wnaf_const(wnaf_1, q_1, WINDOW_A - 1);
	138	skew_lam = secp256k1_wnaf_const(wnaf_lam, q_lam, WINDOW_A - 1);
	139	#else
c6191fde	140	skew_1 = secp256k1_wnaf_const(wnaf_1, sc, WINDOW_A - 1);
92e53fc4	141	#endif
44015000 AP	142
	143	/* Calculate odd multiples of a.
	144	* All multiples are brought to the same Z 'denominator', which is stored
	145	* in Z. Due to secp256k1' isomorphism we can do all operations pretending
	146	* that the Z coordinate was 1, use affine addition formulae, and correct
	147	* the Z coordinate of the result once at the end.
	148	*/
	149	secp256k1_gej_set_ge(r, a);
	150	secp256k1_ecmult_odd_multiples_table_globalz_windowa(pre_a, &Z, r);
72ae443a PD	151	for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
	152	secp256k1_fe_normalize_weak(&pre_a[i].y);
	153	}
92e53fc4 AP	154	#ifdef USE_ENDOMORPHISM
	155	for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
	156	secp256k1_ge_mul_lambda(&pre_a_lam[i], &pre_a[i]);
	157	}
	158	#endif
44015000 AP	159
	160	/* first loop iteration (separated out so we can directly set r, rather
	161	* than having it start at infinity, get doubled several times, then have
	162	* its new value added to it) */
92e53fc4 AP	163	i = wnaf_1[WNAF_SIZE(WINDOW_A - 1)];
	164	VERIFY_CHECK(i != 0);
	165	ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, i, WINDOW_A);
	166	secp256k1_gej_set_ge(r, &tmpa);
c6191fde	167	#ifdef USE_ENDOMORPHISM
92e53fc4 AP	168	i = wnaf_lam[WNAF_SIZE(WINDOW_A - 1)];
	169	VERIFY_CHECK(i != 0);
	170	ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a_lam, i, WINDOW_A);
	171	secp256k1_gej_add_ge(r, r, &tmpa);
92e53fc4	172	#endif
44015000 AP	173	/* remaining loop iterations */
	174	for (i = WNAF_SIZE(WINDOW_A - 1) - 1; i >= 0; i--) {
	175	int n;
	176	int j;
	177	for (j = 0; j < WINDOW_A - 1; ++j) {
	178	secp256k1_gej_double_nonzero(r, r, NULL);
	179	}
c6191fde	180
92e53fc4 AP	181	n = wnaf_1[i];
	182	ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, n, WINDOW_A);
	183	VERIFY_CHECK(n != 0);
	184	secp256k1_gej_add_ge(r, r, &tmpa);
c6191fde	185	#ifdef USE_ENDOMORPHISM
92e53fc4 AP	186	n = wnaf_lam[i];
	187	ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a_lam, n, WINDOW_A);
	188	VERIFY_CHECK(n != 0);
	189	secp256k1_gej_add_ge(r, r, &tmpa);
92e53fc4	190	#endif
44015000 AP	191	}
	192
	193	secp256k1_fe_mul(&r->z, &r->z, &Z);
	194
92e53fc4 AP	195	{
92e53fc4 AP	196	/* Correct for wNAF skew */
dd891e0e PW	197	secp256k1_ge correction = *a;
dd891e0e PW	198	secp256k1_ge_storage correction_1_stor;
c6191fde	199	#ifdef USE_ENDOMORPHISM
dd891e0e	200	secp256k1_ge_storage correction_lam_stor;
c6191fde	201	#endif
dd891e0e PW	202	secp256k1_ge_storage a2_stor;
dd891e0e PW	203	secp256k1_gej tmpj;
92e53fc4 AP	204	secp256k1_gej_set_ge(&tmpj, &correction);
	205	secp256k1_gej_double_var(&tmpj, &tmpj, NULL);
	206	secp256k1_ge_set_gej(&correction, &tmpj);
	207	secp256k1_ge_to_storage(&correction_1_stor, a);
c6191fde	208	#ifdef USE_ENDOMORPHISM
92e53fc4	209	secp256k1_ge_to_storage(&correction_lam_stor, a);
c6191fde	210	#endif
92e53fc4 AP	211	secp256k1_ge_to_storage(&a2_stor, &correction);
	212
	213	/* For odd numbers this is 2a (so replace it), for even ones a (so no-op) */
	214	secp256k1_ge_storage_cmov(&correction_1_stor, &a2_stor, skew_1 == 2);
c6191fde	215	#ifdef USE_ENDOMORPHISM
92e53fc4	216	secp256k1_ge_storage_cmov(&correction_lam_stor, &a2_stor, skew_lam == 2);
c6191fde	217	#endif
92e53fc4 AP	218
	219	/* Apply the correction */
	220	secp256k1_ge_from_storage(&correction, &correction_1_stor);
	221	secp256k1_ge_neg(&correction, &correction);
	222	secp256k1_gej_add_ge(r, r, &correction);
	223
c6191fde	224	#ifdef USE_ENDOMORPHISM
92e53fc4 AP	225	secp256k1_ge_from_storage(&correction, &correction_lam_stor);
	226	secp256k1_ge_neg(&correction, &correction);
	227	secp256k1_ge_mul_lambda(&correction, &correction);
	228	secp256k1_gej_add_ge(r, r, &correction);
92e53fc4	229	#endif
c6191fde	230	}
44015000 AP	231	}
44015000 AP	232
abe2d3e8	233	#endif /* SECP256K1_ECMULT_CONST_IMPL_H */