


/**********************************************************************




* Copyright (c) 2015 Pieter Wuille, Andrew Poelstra *




* Distributed under the MIT software license, see the accompanying *




* file COPYING or http://www.opensource.org/licenses/mitlicense.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 Widthw NAF Method Provides Small Memory and Fast Elliptic Scalar




* Multiplications Secure against Side Channel Attacks`, Okeya and Tagaki. M. Joye (Ed.)




* CTRSA 2003, LNCS 2612, pp. 328443, 2003. SpringerVerlagy Berlin Heidelberg 2003




*




* Numbers reference steps of `Algorithm SPAresistant Widthw NAF with Odd Scalar` on pp. 335




*/




static int secp256k1_wnaf_const(int *wnaf, secp256k1_scalar s, int w, int size) {




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.




*




* In fact, we _do_ want to negate numbers to minimize their bitlengths (and in




* particular, to ensure that the outputs from the endomorphismsplit fit into




* 128 bits). If we negate, the parity of our number flips, inverting which of




* {1, 2} we want to add to the scalar when ensuring that it's odd. Further




* complicating things, 1 interacts badly with `secp256k1_scalar_cadd_bit` and




* we need to specialcase it in this logic. */




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 < size) {




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_BITS(size, w));




return skew;




}








static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, const secp256k1_scalar *scalar, int size) {




secp256k1_ge pre_a[ECMULT_TABLE_SIZE(WINDOW_A)];




secp256k1_ge tmpa;




secp256k1_fe Z;








int skew_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 wnaf_1[1 + WNAF_SIZE(WINDOW_A  1)];








int i;




secp256k1_scalar sc = *scalar;








/* build wnaf representation for q. */




int rsize = size;




#ifdef USE_ENDOMORPHISM




if (size > 128) {




rsize = 128;




/* 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, 128);




skew_lam = secp256k1_wnaf_const(wnaf_lam, q_lam, WINDOW_A  1, 128);




} else




#endif




{




skew_1 = secp256k1_wnaf_const(wnaf_1, sc, WINDOW_A  1, size);




#ifdef USE_ENDOMORPHISM




skew_lam = 0;




#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




if (size > 128) {




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_BITS(rsize, 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




if (size > 128) {




i = wnaf_lam[WNAF_SIZE_BITS(rsize, 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_BITS(rsize, 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




if (size > 128) {




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




if (size > 128) {




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 noop) */




secp256k1_ge_storage_cmov(&correction_1_stor, &a2_stor, skew_1 == 2);




#ifdef USE_ENDOMORPHISM




if (size > 128) {




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




if (size > 128) {




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 */
