1477 lines
30 KiB
C
1477 lines
30 KiB
C
/*
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*
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* ec_point.c
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*
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* Elliptic Curve Arithmetic Functions
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*
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* Copyright (C) Lenka Fibikova 2000
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*
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*
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*/
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#include <stdio.h>
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#include <stdlib.h>
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#include <assert.h>
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#include <memory.h>
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#include <openssl/bn.h>
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#include "../bn/bn_mont2.h" /* XXX */
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#include "ec.h"
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EC_POINT *ECP_new()
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{
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EC_POINT *ret;
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ret=(EC_POINT *)malloc(sizeof(EC_POINT));
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if (ret == NULL) return NULL;
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ret->X = BN_new();
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ret->Y = BN_new();
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ret->Z = BN_new();
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ret->is_in_mont = 0;
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if (ret->X == NULL || ret->Y == NULL || ret->Z == NULL)
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{
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if (ret->X != NULL) BN_free(ret->X);
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if (ret->Y != NULL) BN_free(ret->Y);
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if (ret->Z != NULL) BN_free(ret->Z);
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free(ret);
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return(NULL);
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}
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return(ret);
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}
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void ECP_clear_free(EC_POINT *P)
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{
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if (P == NULL) return;
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P->is_in_mont = 0;
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if (P->X != NULL) BN_clear_free(P->X);
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if (P->Y != NULL) BN_clear_free(P->Y);
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if (P->Z != NULL) BN_clear_free(P->Z);
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free(P);
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}
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void ECP_clear_free_precompute(ECP_PRECOMPUTE *prec)
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{
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int i;
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int max;
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if (prec == NULL) return;
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if (prec->Pi != NULL)
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{
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max = 1;
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max <<= (prec->r - 1);
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for (i = 0; i < max; i++)
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{
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if (prec->Pi[i] != NULL) ECP_clear_free(prec->Pi[i]);
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}
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}
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free(prec);
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}
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int ECP_is_on_ec(EC_POINT *P, EC *E, BN_CTX *ctx)
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{
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BIGNUM *n0, *n1, *n2, *p;
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int Pnorm;
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int ret = -1;
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assert(P != NULL);
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assert(P->X != NULL && P->Y != NULL && P->Z != NULL);
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assert(E != NULL);
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assert(E->A != NULL && E->B != NULL && E->p != NULL);
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assert(ctx != NULL);
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assert(!P->is_in_mont);
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if (ECP_is_infty(P)) return 1;
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BN_CTX_start(ctx);
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n0 = BN_CTX_get(ctx);
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n1 = BN_CTX_get(ctx);
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n2 = BN_CTX_get(ctx);
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if (n2 == NULL)
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goto err;
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p = E->p;
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Pnorm = (ECP_is_norm(P));
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if (!Pnorm)
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{
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if (!BN_mod_mul(n0, P->Z, P->Z, p, ctx)) goto err;
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if (!BN_mod_mul(n1, n0, n0, p, ctx)) goto err;
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if (!BN_mod_mul(n2, n0, n1, p, ctx)) goto err;
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}
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if (!BN_mod_mul(n0, P->X, P->X, p, ctx)) goto err;
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if (!BN_mod_mul(n0, n0, P->X, p, ctx)) goto err;
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if (Pnorm)
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{
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if (!BN_mod_mul(n1, P->X, E->A, p, ctx)) goto err;
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}
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else
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{
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if (!BN_mod_mul(n1, n1, P->X, p, ctx)) goto err;
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if (!BN_mod_mul(n1, n1, E->A, p, ctx)) goto err;
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}
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if (!BN_mod_add(n0, n0, n1, p, ctx)) goto err;
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if (Pnorm)
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{
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if (!BN_mod_add(n0, n0, E->B, p, ctx)) goto err;
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}
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else
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{
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if (!BN_mod_mul(n2, n2, E->B, p, ctx)) goto err;
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if (!BN_mod_add(n0, n0, n2, p, ctx)) goto err;
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}
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if (!BN_mod_mul(n1, P->Y, P->Y, p, ctx)) goto err;
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if (BN_cmp(n0, n1))
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ret = 0;
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else
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ret = 1;
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err:
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BN_CTX_end(ctx);
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return ret;
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}
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EC_POINT *ECP_generate(BIGNUM *x, BIGNUM *z,EC *E, BN_CTX *ctx)
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/* x == NULL || z = 0 -> point of infinity */
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/* z == NULL || z = 1 -> normalized */
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{
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BIGNUM *n0, *n1;
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EC_POINT *ret = NULL;
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int Pnorm, Pinfty, X0, A0;
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assert(E != NULL);
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assert(E->A != NULL && E->B != NULL && E->p != NULL && E->h != NULL);
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assert(ctx != NULL);
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Pinfty = (x == NULL);
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Pnorm = (z == NULL);
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if (!Pnorm)
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{
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Pnorm = BN_is_one(z);
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Pinfty = (Pinfty || BN_is_zero(z));
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}
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if (Pinfty)
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{
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if ((ret = ECP_new()) == NULL) return NULL;
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if (!BN_zero(ret->Z))
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{
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ECP_clear_free(ret);
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return NULL;
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}
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return ret;
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}
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X0 = BN_is_zero(x);
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A0 = BN_is_zero(E->A);
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if ((ret = ECP_new()) == NULL) return NULL;
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ret->is_in_mont = 0;
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BN_CTX_start(ctx);
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n0 = BN_CTX_get(ctx);
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n1 = BN_CTX_get(ctx);
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if (n1 == NULL) goto err;
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if (!BN_zero(n0)) goto err;
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if (!BN_zero(n1)) goto err;
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if (!X0)
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{
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if (!BN_mod_sqr(n0, x, E->p, ctx)) goto err;
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if (!BN_mod_mul(n0, n0, x, E->p, ctx)) goto err; /* x^3 */
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}
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if (!X0 && !A0)
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{
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if (!BN_mod_mul(n1, E->A, x, E->p, ctx)) goto err; /* Ax */
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if (!BN_mod_add(n0, n0, n1, E->p, ctx)) goto err; /* x^3 + Ax */
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}
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if (!BN_is_zero(E->B))
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if (!BN_mod_add(n0, n0, E->B, E->p, ctx)) goto err; /* x^3 + Ax +B */
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if (!BN_mod_sqrt(ret->Y, n0, E->p, ctx)) goto err;
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if (BN_copy(ret->X, x) == NULL) goto err;
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if (Pnorm)
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{
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if (!BN_one(ret->Z)) goto err;
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}
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else
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{
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if (BN_copy(ret->Z, z) == NULL) goto err;
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if (!BN_mod_sqr(n0, z, E->p, ctx)) goto err;
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if (!BN_mod_mul(ret->X, ret->X, n0, E->p, ctx)) goto err;
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if (!BN_mod_mul(n0, n0, z, E->p, ctx)) goto err;
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if (!BN_mod_mul(ret->Y, ret->Y, n0, E->p, ctx)) goto err;
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}
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#ifdef TEST
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if (!ECP_is_on_ec(ret, E, ctx)) goto err;
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#endif
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BN_CTX_end(ctx);
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return ret;
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err:
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if (ret != NULL) ECP_clear_free(ret);
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BN_CTX_end(ctx);
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return NULL;
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}
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int ECP_ecp2bin(EC_POINT *P, unsigned char *to, int form)
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/* form = 1 ... compressed
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2 ... uncompressed
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3 ... hybrid */
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{
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int bytes, bx, by;
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assert (P != NULL);
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assert (P->X != NULL && P->Y != NULL && P->Z != NULL);
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assert (!P->is_in_mont);
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assert (ECP_is_norm(P) || ECP_is_infty(P));
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assert (to != NULL);
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assert (form > 0 && form < 4);
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if (BN_is_zero(P->Z))
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{
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to[0] = 0;
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return 1;
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}
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bx = BN_num_bytes(P->X);
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if (form == 1 ) bytes = bx + 1;
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else
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{
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by = BN_num_bytes(P->Y);
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bytes = (bx > by ? bx : by);
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bytes = bytes * 2 + 1;
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}
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memset(to, 0, bytes);
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switch (form)
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{
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case 1: to[0] = 2; break;
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case 2: to[0] = 4; break;
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case 3: to[0] = 6; break;
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}
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if (form != 2) to[0] += BN_is_bit_set(P->Y, 0);
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if ((BN_bn2bin(P->X, to + 1)) != bx) return 0;
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if (form != 1)
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{
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if ((BN_bn2bin(P->Y, to + bx + 1)) != by) return 0;
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}
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return bytes;
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}
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int ECP_bin2ecp(unsigned char *from, int len, EC_POINT *P, EC *E, BN_CTX *ctx)
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{
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int y;
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BIGNUM *x;
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EC_POINT *pp;
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assert (E != NULL);
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assert (E->A != NULL && E->B != NULL && E->p != NULL);
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assert (!E->is_in_mont);
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assert (ctx != NULL);
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assert (from != NULL);
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assert (P != NULL);
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assert (P->X != NULL && P->Y != NULL && P->Z != NULL);
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if (len == 1 && from[0] != 0) return 0;
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if (len == 0 || len == 1)
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{
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if (!BN_zero(P->Z)) return 0;
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return 1;
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}
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switch (from[0])
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{
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case 2:
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case 3:
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y = from[0] - 2;
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if ((x = BN_new()) == NULL) return 0;
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if (BN_bin2bn(from + 1, len - 1, x) == NULL) return 0;
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pp = ECP_generate(x, NULL, E, ctx);
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BN_clear_free(x);
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if (pp == NULL) return 0;
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ECP_copy(P, pp);
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ECP_clear_free(pp);
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if (BN_is_bit_set(P->Y, 0) != y)
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if (!BN_sub(P->Y, E->p, P->Y)) return 0;
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break;
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case 4:
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case 6:
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case 7:
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y = (len - 1)/2;
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if (BN_bin2bn(from + 1, y, P->X) == NULL) return 0;
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if (BN_bin2bn(from + y + 1, y, P->Y) == NULL) return 0;
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if (!BN_set_word(P->Z, 1)) return 0;
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break;
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default:
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assert(0);
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}
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if (!ECP_is_on_ec(P, E, ctx)) return 0;
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return 1;
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}
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int ECP_normalize(EC_POINT *P, EC *E, BN_CTX *ctx)
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{
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BIGNUM *z, *zm;
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assert (P != NULL);
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assert (P->X != NULL && P->Y != NULL && P->Z != NULL);
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assert (E != NULL);
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assert (E->A != NULL && E->B != NULL && E->p != NULL);
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assert (ctx != NULL);
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if (ECP_is_norm(P)) return 1;
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if (ECP_is_infty(P)) return 0;
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if ((zm = BN_mod_inverse(P->Z, P->Z, E->p, ctx)) == NULL) return 0;
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assert(!P->is_in_mont);
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BN_CTX_start(ctx);
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z = BN_CTX_get(ctx);
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if (z == NULL) goto err;
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if (!BN_mod_mul(z, zm, zm, E->p, ctx)) goto err;
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if (!BN_mod_mul(P->X, P->X, z, E->p, ctx)) goto err;
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if (!BN_mod_mul(z, z, zm, E->p, ctx)) goto err;
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if (!BN_mod_mul(P->Y, P->Y, z, E->p, ctx)) goto err;
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if (!BN_one(P->Z)) goto err;
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if (zm != NULL) BN_clear_free(zm);
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BN_CTX_end(ctx);
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return 1;
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err:
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if (zm != NULL) BN_clear_free(zm);
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BN_CTX_end(ctx);
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return 0;
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}
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int ECP_copy(EC_POINT *R, EC_POINT *P)
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{
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assert(P != NULL);
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assert(P->X != NULL && P->Y != NULL && P->Z != NULL);
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assert(R != NULL);
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assert(R->X != NULL && R->Y != NULL && R->Z != NULL);
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if (BN_copy(R->X, P->X) == NULL) return 0;
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if (BN_copy(R->Y, P->Y) == NULL) return 0;
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if (BN_copy(R->Z, P->Z) == NULL) return 0;
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R->is_in_mont = P->is_in_mont;
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return 1;
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}
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EC_POINT *ECP_dup(EC_POINT *P)
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{
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EC_POINT *ret;
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ret = ECP_new();
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if (ret == NULL) return NULL;
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if (!ECP_copy(ret, P))
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{
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ECP_clear_free(ret);
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return(NULL);
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}
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return(ret);
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}
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EC_POINT *ECP_minus(EC_POINT *P, BIGNUM *p) /* mont || non-mont */
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{
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EC_POINT *ret;
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assert(P != NULL);
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assert(P->X != NULL && P->Y != NULL && P->Z != NULL);
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assert(p != NULL);
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assert(BN_cmp(P->Y, p) < 0);
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ret = ECP_dup(P);
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if (ret == NULL) return NULL;
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if (BN_is_zero(ret->Y)) return ret;
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if (!BN_sub(ret->Y, p, ret->Y))
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{
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ECP_clear_free(ret);
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return NULL;
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}
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return ret;
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}
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#ifdef SIMPLE
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int ECP_cmp(EC_POINT *P, EC_POINT *Q, BIGNUM *p, BN_CTX *ctx)
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/* return values:
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-2 ... error
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0 ... P = Q
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-1 ... P = -Q
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1 ... else
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*/
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{
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BIGNUM *n0, *n1, *n2, *n3, *n4;
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int Pnorm, Qnorm;
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|
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assert(P != NULL);
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assert(P->X != NULL && P->Y != NULL && P->Z != NULL);
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assert(Q != NULL);
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assert(Q->X != NULL && Q->Y != NULL && Q->Z != NULL);
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assert(p != NULL);
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assert(ctx != NULL);
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assert(!P->is_in_mont);
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assert(!Q->is_in_mont);
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if (ECP_is_infty(P) && ECP_is_infty(Q)) return 0;
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if (ECP_is_infty(P) || ECP_is_infty(Q)) return 1;
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|
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Pnorm = (ECP_is_norm(P));
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Qnorm = (ECP_is_norm(Q));
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|
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BN_CTX_start(ctx);
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n0 = BN_CTX_get(ctx);
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n1 = BN_CTX_get(ctx);
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n2 = BN_CTX_get(ctx);
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n3 = BN_CTX_get(ctx);
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n4 = BN_CTX_get(ctx);
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if (n4 == NULL) goto err;
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|
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if (Qnorm)
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{
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if (BN_copy(n1, P->X) == NULL) goto err; /* L1 = x_p */
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if (BN_copy(n2, P->Y) == NULL) goto err; /* L2 = y_p */
|
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}
|
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else
|
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{
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if (!BN_sqr(n0, Q->Z, ctx)) goto err;
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if (!BN_mod_mul(n1, P->X, n0, p, ctx)) goto err; /* L1 = x_p * z_q^2 */
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if (!BN_mod_mul(n0, n0, Q->Z, p, ctx)) goto err;
|
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if (!BN_mod_mul(n2, P->Y, n0, p, ctx)) goto err; /* L2 = y_p * z_q^3 */
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}
|
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|
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if (Pnorm)
|
|
{
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if (BN_copy(n3, Q->X) == NULL) goto err; /* L3 = x_q */
|
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if (BN_copy(n4, Q->Y) == NULL) goto err; /* L4 = y_q */
|
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}
|
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else
|
|
{
|
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if (!BN_sqr(n0, P->Z, ctx)) goto err;
|
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if (!BN_mod_mul(n3, Q->X, n0, p, ctx)) goto err; /* L3 = x_q * z_p^2 */
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|
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if (!BN_mod_mul(n0, n0, P->Z, p, ctx)) goto err;
|
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if (!BN_mod_mul(n4, Q->Y, n0, p, ctx)) goto err; /* L4 = y_q * z_p^3 */
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}
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|
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if (!BN_mod_sub(n0, n1, n3, p, ctx)) goto err; /* L5 = L1 - L3 */
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|
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if (!BN_is_zero(n0))
|
|
{
|
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BN_CTX_end(ctx);
|
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return 1;
|
|
}
|
|
|
|
if (!BN_mod_sub(n0, n2, n4, p, ctx)) goto err; /* L6 = L2 - L4 */
|
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|
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if (!BN_is_zero(n0))
|
|
{
|
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BN_CTX_end(ctx);
|
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return -1;
|
|
}
|
|
|
|
BN_CTX_end(ctx);
|
|
return 0;
|
|
|
|
err:
|
|
BN_CTX_end(ctx);
|
|
return -2;
|
|
}
|
|
|
|
|
|
int ECP_double(EC_POINT *R, EC_POINT *P, EC *E, BN_CTX *ctx)
|
|
/* R <- 2P (on E) */
|
|
{
|
|
BIGNUM *n0, *n1, *n2, *n3, *p;
|
|
int Pnorm, A0;
|
|
|
|
assert(P != NULL);
|
|
assert(P->X != NULL && P->Y != NULL && P->Z != NULL);
|
|
|
|
assert(R != NULL);
|
|
assert(R->X != NULL && R->Y != NULL && R->Z != NULL);
|
|
|
|
assert(E != NULL);
|
|
assert(E->A != NULL && E->B != NULL && E->p != NULL && E->h != NULL);
|
|
|
|
assert(ctx != NULL);
|
|
|
|
assert(!P->is_in_mont);
|
|
|
|
if (ECP_is_infty(P))
|
|
{
|
|
if (!BN_zero(R->Z)) return 0;
|
|
return 1;
|
|
}
|
|
|
|
Pnorm = (ECP_is_norm(P));
|
|
A0 = (BN_is_zero(E->A));
|
|
|
|
BN_CTX_start(ctx);
|
|
n0 = BN_CTX_get(ctx);
|
|
n1 = BN_CTX_get(ctx);
|
|
n2 = BN_CTX_get(ctx);
|
|
n3 = BN_CTX_get(ctx);
|
|
if (n3 == NULL) goto err;
|
|
|
|
p = E->p;
|
|
|
|
/* L1 */
|
|
if (Pnorm || A0)
|
|
{
|
|
if (!BN_mod_sqr(n1, P->X, p, ctx)) goto err;
|
|
if (!BN_mul_word(n1, 3)) goto err;
|
|
if (!A0) /* if A = 0: L1 = 3 * x^2 + a * z^4 = 3 * x ^2 */
|
|
if (!BN_mod_add(n1, n1, E->A, p, ctx)) goto err; /* L1 = 3 * x^2 + a * z^4 = 3 * x^2 + a */
|
|
}
|
|
else
|
|
{
|
|
if (!BN_mod_sqr(n0, P->Z, p, ctx)) goto err;
|
|
if (!BN_mod_mul(n0, n0, n0, p, ctx)) goto err;
|
|
if (!BN_mod_mul(n0, n0, E->A, p, ctx)) goto err;
|
|
if (!BN_mod_sqr(n1, P->X, p, ctx)) goto err;
|
|
if (!BN_mul_word(n1, 3)) goto err;
|
|
if (!BN_mod_add(n1, n1, n0, p, ctx)) goto err; /* L1 = 3 * x^2 + a * z^4 */
|
|
}
|
|
|
|
/* Z */
|
|
if (Pnorm)
|
|
{
|
|
if (BN_copy(n0, P->Y) == NULL) goto err;
|
|
}
|
|
else
|
|
{
|
|
if (!BN_mod_mul(n0, P->Y, P->Z, p, ctx)) goto err;
|
|
}
|
|
if (!BN_lshift1(n0, n0)) goto err;
|
|
if (!BN_smod(R->Z, n0, p, ctx)) goto err; /* Z = 2 * y * z */
|
|
|
|
/* L2 */
|
|
if (!BN_mod_sqr(n3, P->Y, p, ctx)) goto err;
|
|
if (!BN_mod_mul(n2, P->X, n3, p, ctx)) goto err;
|
|
if (!BN_lshift(n2, n2, 2)) goto err;
|
|
if (!BN_smod(n2, n2, p, ctx)) goto err; /* L2 = 4 * x * y^2 */
|
|
|
|
/* X */
|
|
if (!BN_lshift1(n0, n2)) goto err;
|
|
if (!BN_mod_sqr(R->X, n1, p, ctx)) goto err;
|
|
if (!BN_mod_sub(R->X, R->X, n0, p, ctx)) goto err; /* X = L1^2 - 2 * L2 */
|
|
|
|
/* L3 */
|
|
if (!BN_mod_sqr(n0, n3, p, ctx)) goto err;
|
|
if (!BN_lshift(n3, n0, 3)) goto err;
|
|
if (!BN_smod(n3, n3, p, ctx)) goto err; /* L3 = 8 * y^4 */
|
|
|
|
/* Y */
|
|
if (!BN_mod_sub(n0, n2, R->X, p, ctx)) goto err;
|
|
if (!BN_mod_mul(n0, n1, n0, p, ctx)) goto err;
|
|
if (!BN_mod_sub(R->Y, n0, n3, p, ctx)) goto err; /* Y = L1 * (L2 - X) - L3 */
|
|
|
|
|
|
#ifdef TEST
|
|
if (!ECP_is_on_ec(R, E, ctx)) return 0;
|
|
#endif
|
|
|
|
BN_CTX_end(ctx);
|
|
return 1;
|
|
|
|
err:
|
|
BN_CTX_end(ctx);
|
|
return 0;
|
|
}
|
|
|
|
|
|
int ECP_add(EC_POINT *R, EC_POINT *P, EC_POINT *Q, EC *E, BN_CTX *ctx)
|
|
/* R <- P + Q (on E) */
|
|
{
|
|
BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6, *p;
|
|
int Pnorm, Qnorm;
|
|
|
|
assert(P != NULL);
|
|
assert(P->X != NULL && P->Y != NULL && P->Z != NULL);
|
|
|
|
assert(Q != NULL);
|
|
assert(Q->X != NULL && Q->Y != NULL && Q->Z != NULL);
|
|
|
|
assert(R != NULL);
|
|
assert(R->X != NULL && R->Y != NULL && R->Z != NULL);
|
|
|
|
assert(E != NULL);
|
|
assert(E->A != NULL && E->B != NULL && E->p != NULL && E->h != NULL);
|
|
assert(!BN_is_zero(E->h));;
|
|
|
|
assert(ctx != NULL);
|
|
|
|
assert(!P->is_in_mont);
|
|
assert(!Q->is_in_mont);
|
|
|
|
if (P == Q) return ECP_double(R, P, E, ctx);
|
|
|
|
if (ECP_is_infty(P)) return ECP_copy(R, Q);
|
|
if (ECP_is_infty(Q)) return ECP_copy(R, P);
|
|
|
|
Pnorm = (ECP_is_norm(P));
|
|
Qnorm = (ECP_is_norm(Q));
|
|
|
|
BN_CTX_start(ctx);
|
|
n0 = BN_CTX_get(ctx);
|
|
n1 = BN_CTX_get(ctx);
|
|
n2 = BN_CTX_get(ctx);
|
|
n3 = BN_CTX_get(ctx);
|
|
n4 = BN_CTX_get(ctx);
|
|
n5 = BN_CTX_get(ctx);
|
|
n6 = BN_CTX_get(ctx);
|
|
if (n6 == NULL) goto err;
|
|
|
|
p = E->p;
|
|
|
|
/* L1; L2 */
|
|
if (Qnorm)
|
|
{
|
|
if (BN_copy(n1, P->X) == NULL) goto err; /* L1 = x_p */
|
|
if (BN_copy(n2, P->Y) == NULL) goto err; /* L2 = y_p */
|
|
}
|
|
else
|
|
{
|
|
if (!BN_sqr(n0, Q->Z, ctx)) goto err;
|
|
if (!BN_mod_mul(n1, P->X, n0, p, ctx)) goto err; /* L1 = x_p * z_q^2 */
|
|
|
|
if (!BN_mod_mul(n0, n0, Q->Z, p, ctx)) goto err;
|
|
if (!BN_mod_mul(n2, P->Y, n0, p, ctx)) goto err; /* L2 = y_p * z_q^3 */
|
|
}
|
|
|
|
/* L3; L4 */
|
|
if (Pnorm)
|
|
{
|
|
if (BN_copy(n3, Q->X) == NULL) goto err; /* L3 = x_q */
|
|
if (BN_copy(n4, Q->Y) == NULL) goto err; /* L4 = y_q */
|
|
}
|
|
else
|
|
{
|
|
if (!BN_sqr(n0, P->Z, ctx)) goto err;
|
|
if (!BN_mod_mul(n3, Q->X, n0, p, ctx)) goto err; /* L3 = x_q * z_p^2 */
|
|
|
|
if (!BN_mod_mul(n0, n0, P->Z, p, ctx)) goto err;
|
|
if (!BN_mod_mul(n4, Q->Y, n0, p, ctx)) goto err; /* L4 = y_q * z_p^3 */
|
|
}
|
|
|
|
/* L5; L6 */
|
|
if (!BN_mod_sub(n5, n1, n3, p, ctx)) goto err; /* L5 = L1 - L3 */
|
|
if (!BN_mod_sub(n6, n2, n4, p, ctx)) goto err; /* L6 = L2 - L4 */
|
|
|
|
/* pata */
|
|
if (BN_is_zero(n5))
|
|
{
|
|
if (BN_is_zero(n6)) /* P = Q => P + Q = 2P */
|
|
{
|
|
BN_CTX_end(ctx);
|
|
return ECP_double(R, P, E, ctx);
|
|
}
|
|
else /* P = -Q => P + Q = \infty */
|
|
{
|
|
BN_CTX_end(ctx);
|
|
if (!BN_zero(R->Z)) return 0;
|
|
return 1;
|
|
}
|
|
}
|
|
|
|
/* L7; L8 */
|
|
if (!BN_mod_add(n1, n1, n3, p, ctx)) goto err; /* L7 = L1 + L3 */
|
|
if (!BN_mod_add(n2, n2, n4, p, ctx)) goto err; /* L8 = L2 + L4 */
|
|
|
|
/* Z */
|
|
if (Pnorm)
|
|
{
|
|
if (BN_copy(n0, Q->Z) == NULL) goto err;
|
|
}
|
|
else
|
|
{
|
|
if (!BN_mod_mul(n0, P->Z, Q->Z, p, ctx)) goto err;
|
|
}
|
|
if (!BN_mod_mul(R->Z, n0, n5, p, ctx)) goto err; /* Z = z_p * z_q * L_5 */
|
|
|
|
/* X */
|
|
if (!BN_mod_sqr(n0, n6, p, ctx)) goto err;
|
|
if (!BN_mod_sqr(n4, n5, p, ctx)) goto err;
|
|
if (!BN_mod_mul(n3, n1, n4, p, ctx)) goto err;
|
|
if (!BN_mod_sub(R->X, n0, n3, p, ctx)) goto err; /* X = L6^2 - L5^2 * L7 */
|
|
|
|
/* L9 */
|
|
if (!BN_lshift1(n0, R->X)) goto err;
|
|
if (!BN_mod_sub(n0, n3, n0, p, ctx)) goto err; /* L9 = L5^2 * L7 - 2X */
|
|
|
|
/* Y */
|
|
if (!BN_mod_mul(n0, n0, n6, p, ctx)) goto err;
|
|
if (!BN_mod_mul(n5, n4, n5, p, ctx)) goto err;
|
|
if (!BN_mod_mul(n1, n2, n5, p, ctx)) goto err;
|
|
if (!BN_mod_sub(n0, n0, n1, p, ctx)) goto err;
|
|
if (!BN_mod_mul(R->Y, n0, E->h, p, ctx)) goto err; /* Y = (L6 * L9 - L8 * L5^3) / 2 */
|
|
|
|
|
|
|
|
#ifdef TEST
|
|
if (!ECP_is_on_ec(R, E, ctx)) return 0;
|
|
#endif
|
|
|
|
BN_CTX_end(ctx);
|
|
return 1;
|
|
|
|
err:
|
|
BN_CTX_end(cxt);
|
|
return 0;
|
|
}
|
|
|
|
|
|
ECP_PRECOMPUTE *ECP_precompute(int r, EC_POINT *P, EC *E, BN_CTX *ctx)
|
|
{
|
|
ECP_PRECOMPUTE *ret;
|
|
EC_POINT *P2;
|
|
int i, max;
|
|
|
|
assert(r > 2);
|
|
assert(!P->is_in_mont);
|
|
assert(!E->is_in_mont);
|
|
|
|
ret=(ECP_PRECOMPUTE *)malloc(sizeof(ECP_PRECOMPUTE));
|
|
if (ret == NULL) return NULL;
|
|
|
|
max = 1;
|
|
max <<= (r - 1);
|
|
|
|
ret->r = 0;
|
|
|
|
ret->Pi=(EC_POINT **)malloc(sizeof(EC_POINT *) * max);
|
|
if (ret->Pi == NULL) goto err;
|
|
|
|
|
|
/* P2 = [2]P */
|
|
if ((P2 = ECP_new()) == NULL) goto err;
|
|
if (!ECP_double(P2, P, E, ctx)) goto err;
|
|
|
|
/* P_0 = P */
|
|
if((ret->Pi[0] = ECP_dup(P)) == NULL) goto err;
|
|
|
|
|
|
/* P_i = P_(i-1) + P2 */
|
|
for (i = 1; i < max; i++)
|
|
{
|
|
if ((ret->Pi[i] = ECP_new()) == NULL) goto err;
|
|
|
|
if (!ECP_add(ret->Pi[i], P2, ret->Pi[i - 1], E, ctx)) goto err;
|
|
}
|
|
|
|
ret->r = r;
|
|
ECP_clear_free(P2);
|
|
|
|
return ret;
|
|
|
|
err:
|
|
ECP_clear_free(P2);
|
|
ECP_clear_free_precompute(ret);
|
|
return NULL;
|
|
}
|
|
|
|
|
|
int ECP_multiply(EC_POINT *R, BIGNUM *k, ECP_PRECOMPUTE *prec, EC *E, BN_CTX *ctx)
|
|
/* R = [k]P */
|
|
{
|
|
int j;
|
|
int t, nextw, h, r;
|
|
|
|
assert(R != NULL);
|
|
assert(R->X != NULL && R->Y != NULL && R->Z != NULL);
|
|
|
|
assert(E != NULL);
|
|
assert(E->A != NULL && E->B != NULL && E->p != NULL && E->h != NULL);
|
|
|
|
assert(k != NULL);
|
|
assert(!k->neg);
|
|
|
|
assert(ctx != NULL);
|
|
assert(prec != NULL);
|
|
|
|
assert(!E->is_in_mont);
|
|
|
|
if (BN_is_zero(k))
|
|
{
|
|
if (!BN_zero(R->Z)) return 0;
|
|
R->is_in_mont = 0;
|
|
return 1;
|
|
}
|
|
|
|
|
|
j = BN_num_bits(k);
|
|
j--;
|
|
|
|
r = prec->r;
|
|
|
|
if (!BN_zero(R->Z)) return 0;
|
|
R->is_in_mont = 0;
|
|
|
|
while(j >= 0)
|
|
{
|
|
if (!BN_is_bit_set(k, j))
|
|
{
|
|
if (!ECP_double(R, R, E, ctx)) return 0;
|
|
j--;
|
|
}
|
|
else
|
|
{
|
|
nextw = j - r;
|
|
if (nextw < -1) nextw = -1;
|
|
t = nextw + 1;
|
|
while(!BN_is_bit_set(k, t))
|
|
t++;
|
|
|
|
if (!ECP_double(R, R, E, ctx)) return 0;
|
|
|
|
j--;
|
|
if (j < t) h = 0;
|
|
else
|
|
{
|
|
h = 1;
|
|
for(; j > t; j--)
|
|
{
|
|
h <<= 1;
|
|
if (BN_is_bit_set(k, j)) h++;
|
|
if (!ECP_double(R, R, E, ctx)) return 0;
|
|
}
|
|
if (!ECP_double(R, R, E, ctx)) return 0;
|
|
j--;
|
|
}
|
|
|
|
if (!ECP_add(R, R, prec->Pi[h], E, ctx)) return 0;
|
|
|
|
for (; j > nextw; j--)
|
|
{
|
|
if (!ECP_double(R, R, E, ctx)) return 0;
|
|
}
|
|
|
|
}
|
|
}
|
|
|
|
return 1;
|
|
}
|
|
|
|
#endif /* SIMPLE */
|
|
|
|
|
|
#ifdef MONTGOMERY
|
|
|
|
int ECP_to_montgomery(EC_POINT *P, BN_MONTGOMERY *mont, BN_CTX *ctx)
|
|
{
|
|
assert(P != NULL);
|
|
assert(P->X != NULL && P->Y != NULL && P->Z != NULL);
|
|
|
|
assert(mont != NULL);
|
|
assert(mont->p != NULL);
|
|
|
|
assert(ctx != NULL);
|
|
|
|
if (P->is_in_mont) return 1;
|
|
|
|
if (!BN_lshift(P->X, P->X, mont->R_num_bits)) return 0;
|
|
if (!BN_mod(P->X, P->X, mont->p, ctx)) return 0;
|
|
|
|
if (!BN_lshift(P->Y, P->Y, mont->R_num_bits)) return 0;
|
|
if (!BN_mod(P->Y, P->Y, mont->p, ctx)) return 0;
|
|
|
|
if (!BN_lshift(P->Z, P->Z, mont->R_num_bits)) return 0;
|
|
if (!BN_mod(P->Z, P->Z, mont->p, ctx)) return 0;
|
|
|
|
P->is_in_mont = 1;
|
|
return 1;
|
|
}
|
|
|
|
|
|
int ECP_from_montgomery(EC_POINT *P, BN_MONTGOMERY *mont, BN_CTX *ctx)
|
|
{
|
|
|
|
assert(P != NULL);
|
|
assert(P->X != NULL && P->Y != NULL && P->Z != NULL);
|
|
|
|
assert(mont != NULL);
|
|
assert(mont->p != NULL);
|
|
|
|
assert(ctx != NULL);
|
|
|
|
if (!P->is_in_mont) return 1;
|
|
|
|
if (!BN_mont_red(P->X, mont)) return 0;
|
|
if (!BN_mont_red(P->Y, mont)) return 0;
|
|
if (!BN_mont_red(P->Z, mont)) return 0;
|
|
|
|
P->is_in_mont = 0;
|
|
return 1;
|
|
}
|
|
|
|
|
|
int ECP_mont_cmp(EC_POINT *P, EC_POINT *Q, BN_MONTGOMERY *mont, BN_CTX *ctx)
|
|
/* return values:
|
|
-2 ... error
|
|
0 ... P = Q
|
|
-1 ... P = -Q
|
|
1 ... else
|
|
*/
|
|
{
|
|
BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *p;
|
|
|
|
assert(P != NULL);
|
|
assert(P->X != NULL && P->Y != NULL && P->Z != NULL);
|
|
|
|
assert(Q != NULL);
|
|
assert(Q->X != NULL && Q->Y != NULL && Q->Z != NULL);
|
|
|
|
assert(mont != NULL);
|
|
assert(mont->p != NULL);
|
|
|
|
assert(ctx != NULL);
|
|
|
|
if (!P->is_in_mont)
|
|
if (!ECP_to_montgomery(P, mont, ctx)) return 0;
|
|
|
|
if (!Q->is_in_mont)
|
|
if (!ECP_to_montgomery(Q, mont, ctx)) return 0;
|
|
|
|
|
|
if (ECP_is_infty(P) && ECP_is_infty(Q)) return 0;
|
|
if (ECP_is_infty(P) || ECP_is_infty(Q)) return 1;
|
|
|
|
|
|
BN_CTX_start(ctx);
|
|
n0 = BN_CTX_get(ctx);
|
|
n1 = BN_CTX_get(ctx);
|
|
n2 = BN_CTX_get(ctx);
|
|
n3 = BN_CTX_get(ctx);
|
|
n4 = BN_CTX_get(ctx);
|
|
n5 = BN_CTX_get(ctx);
|
|
if (n5 == 0) goto err;
|
|
|
|
|
|
p = mont->p;
|
|
|
|
|
|
if (!BN_mont_mod_mul(n5, Q->Z, Q->Z, mont)) goto err;
|
|
if (!BN_mont_mod_mul(n1, P->X, n5, mont)) goto err; /* L1 = x_p * z_q^2 */
|
|
|
|
if (!BN_mont_mod_mul(n0, n5, Q->Z, mont)) goto err;
|
|
if (!BN_mont_mod_mul(n2, P->Y, n0, mont)) goto err; /* L2 = y_p * z_q^3 */
|
|
|
|
if (!BN_mont_mod_mul(n5, P->Z, P->Z, mont)) goto err;
|
|
if (!BN_mont_mod_mul(n3, Q->X, n5, mont)) goto err; /* L3 = x_q * z_p^2 */
|
|
|
|
if (!BN_mont_mod_mul(n0, n5, P->Z, mont)) goto err;
|
|
if (!BN_mont_mod_mul(n4, Q->Y, n0, mont)) goto err; /* L4 = y_q * z_p^3 */
|
|
|
|
|
|
if (!BN_mod_sub_quick(n0, n1, n3, p)) goto err; /* L5 = L1 - L3 */
|
|
|
|
if (!BN_is_zero(n0))
|
|
{
|
|
BN_CTX_end(ctx);
|
|
return 1;
|
|
}
|
|
|
|
if (!BN_mod_sub_quick(n0, n2, n4, p)) goto err; /* L6 = L2 - L4 */
|
|
|
|
if (!BN_is_zero(n0))
|
|
{
|
|
BN_CTX_end(ctx);
|
|
return -1;
|
|
}
|
|
|
|
BN_CTX_end(ctx);
|
|
return 0;
|
|
|
|
err:
|
|
BN_CTX_end(ctx);
|
|
return -2;
|
|
}
|
|
|
|
|
|
int ECP_mont_double(EC_POINT *R, EC_POINT *P, EC *E, BN_MONTGOMERY *mont, BN_CTX *ctx)
|
|
/* R <- 2P (on E) */
|
|
{
|
|
BIGNUM *n0, *n1, *n2, *n3, *p;
|
|
|
|
assert(P != NULL);
|
|
assert(P->X != NULL && P->Y != NULL && P->Z != NULL);
|
|
|
|
assert(R != NULL);
|
|
assert(R->X != NULL && R->Y != NULL && R->Z != NULL);
|
|
|
|
assert(E != NULL);
|
|
assert(E->A != NULL && E->B != NULL && E->p != NULL && E->h != NULL);
|
|
|
|
assert(ctx != NULL);
|
|
|
|
if (!P->is_in_mont)
|
|
if (!ECP_to_montgomery(P, mont, ctx)) return 0;
|
|
|
|
if (!E->is_in_mont)
|
|
if (!EC_to_montgomery(E, mont, ctx)) return 0;
|
|
|
|
R->is_in_mont = 1;
|
|
|
|
if (ECP_is_infty(P))
|
|
{
|
|
if (!BN_zero(R->Z)) return 0;
|
|
return 1;
|
|
}
|
|
|
|
|
|
BN_CTX_start(ctx);
|
|
n0 = BN_CTX_get(ctx);
|
|
n1 = BN_CTX_get(ctx);
|
|
n2 = BN_CTX_get(ctx);
|
|
n3 = BN_CTX_get(ctx);
|
|
if (n3 == 0) goto err;
|
|
|
|
p = E->p;
|
|
|
|
/* L1 */
|
|
if (!BN_mont_mod_mul(n0, P->Z, P->Z, mont)) goto err;
|
|
if (!BN_mont_mod_mul(n2, n0, n0, mont)) goto err;
|
|
if (!BN_mont_mod_mul(n0, n2, E->A, mont)) goto err;
|
|
if (!BN_mont_mod_mul(n1, P->X, P->X, mont)) goto err;
|
|
if (!BN_mod_lshift1_quick(n2, n1, p)) goto err;
|
|
if (!BN_mod_add_quick(n1, n1, n2, p)) goto err;
|
|
if (!BN_mod_add_quick(n1, n1, n0, p)) goto err; /* L1 = 3 * x^2 + a * z^4 */
|
|
|
|
/* Z */
|
|
if (!BN_mont_mod_mul(n0, P->Y, P->Z, mont)) goto err;
|
|
if (!BN_mod_lshift1_quick(R->Z, n0, p)) goto err; /* Z = 2 * y * z */
|
|
|
|
/* L2 */
|
|
if (!BN_mont_mod_mul(n3, P->Y, P->Y, mont)) goto err;
|
|
if (!BN_mont_mod_mul(n2, P->X, n3, mont)) goto err;
|
|
if (!BN_mod_lshift_quick(n2, n2, 2, p)) goto err; /* L2 = 4 * x * y^2 */
|
|
|
|
/* X */
|
|
if (!BN_mod_lshift1_quick(n0, n2, p)) goto err;
|
|
if (!BN_mont_mod_mul(R->X, n1, n1, mont)) goto err;
|
|
if (!BN_mod_sub_quick(R->X, R->X, n0, p)) goto err; /* X = L1^2 - 2 * L2 */
|
|
|
|
/* L3 */
|
|
if (!BN_mont_mod_mul(n0, n3, n3, mont)) goto err;
|
|
if (!BN_mod_lshift_quick(n3, n0, 3, p)) goto err; /* L3 = 8 * y^4 */
|
|
|
|
|
|
/* Y */
|
|
if (!BN_mod_sub_quick(n2, n2, R->X, p)) goto err;
|
|
if (!BN_mont_mod_mul(n0, n1, n2, mont)) goto err;
|
|
if (!BN_mod_sub_quick(R->Y, n0, n3, p)) goto err; /* Y = L1 * (L2 - X) - L3 */
|
|
|
|
BN_CTX_end(ctx);
|
|
return 1;
|
|
|
|
err:
|
|
BN_CTX_end(ctx);
|
|
return 0;
|
|
}
|
|
|
|
|
|
int ECP_mont_add(EC_POINT *R, EC_POINT *P, EC_POINT *Q, EC *E, BN_MONTGOMERY *mont, BN_CTX *ctx)
|
|
/* R <- P + Q (on E) */
|
|
{
|
|
BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6, *p;
|
|
|
|
assert(P != NULL);
|
|
assert(P->X != NULL && P->Y != NULL && P->Z != NULL);
|
|
|
|
assert(Q != NULL);
|
|
assert(Q->X != NULL && Q->Y != NULL && Q->Z != NULL);
|
|
|
|
assert(R != NULL);
|
|
assert(R->X != NULL && R->Y != NULL && R->Z != NULL);
|
|
|
|
assert(E != NULL);
|
|
assert(E->A != NULL && E->B != NULL && E->p != NULL && E->h != NULL);
|
|
assert(!BN_is_zero(E->h));;
|
|
|
|
assert(ctx != NULL);
|
|
|
|
if (!Q->is_in_mont)
|
|
if (!ECP_to_montgomery(Q, mont, ctx)) return 0;
|
|
|
|
if (!P->is_in_mont)
|
|
if (!ECP_to_montgomery(P, mont, ctx)) return 0;
|
|
|
|
if (!E->is_in_mont)
|
|
if (!EC_to_montgomery(E, mont, ctx)) return 0;
|
|
|
|
if (P == Q) return ECP_mont_double(R, P, E, mont, ctx);
|
|
|
|
if (ECP_is_infty(P)) return ECP_copy(R, Q);
|
|
if (ECP_is_infty(Q)) return ECP_copy(R, P);
|
|
|
|
|
|
BN_CTX_start(ctx);
|
|
n0 = BN_CTX_get(ctx);
|
|
n1 = BN_CTX_get(ctx);
|
|
n2 = BN_CTX_get(ctx);
|
|
n3 = BN_CTX_get(ctx);
|
|
n4 = BN_CTX_get(ctx);
|
|
n5 = BN_CTX_get(ctx);
|
|
n6 = BN_CTX_get(ctx);
|
|
if (n6 == NULL) goto err;
|
|
|
|
|
|
p = E->p;
|
|
|
|
R->is_in_mont = 1;
|
|
|
|
/* L1; L2 */
|
|
if (!BN_mont_mod_mul(n6, Q->Z, Q->Z, mont)) goto err;
|
|
if (!BN_mont_mod_mul(n1, P->X, n6, mont)) goto err; /* L1 = x_p * z_q^2 */
|
|
|
|
if (!BN_mont_mod_mul(n0, n6, Q->Z, mont)) goto err;
|
|
if (!BN_mont_mod_mul(n2, P->Y, n0, mont)) goto err; /* L2 = y_p * z_q^3 */
|
|
|
|
|
|
/* L3; L4 */
|
|
if (!BN_mont_mod_mul(n6, P->Z, P->Z, mont)) goto err;
|
|
if (!BN_mont_mod_mul(n3, Q->X, n6, mont)) goto err; /* L3 = x_q * z_p^2 */
|
|
|
|
if (!BN_mont_mod_mul(n0, n6, P->Z, mont)) goto err;
|
|
if (!BN_mont_mod_mul(n4, Q->Y, n0, mont)) goto err; /* L4 = y_q * z_p^3 */
|
|
|
|
|
|
/* L5; L6 */
|
|
if (!BN_mod_sub_quick(n5, n1, n3, p)) goto err; /* L5 = L1 - L3 */
|
|
if (!BN_mod_sub_quick(n6, n2, n4, p)) goto err; /*L6 = L2 - L4 */
|
|
|
|
|
|
/* pata */
|
|
if (BN_is_zero(n5))
|
|
{
|
|
if (BN_is_zero(n6)) /* P = Q => P + Q = 2P */
|
|
{
|
|
BN_CTX_end(ctx);
|
|
return ECP_mont_double(R, P, E, mont, ctx);
|
|
}
|
|
else /* P = -Q => P + Q = \infty */
|
|
{
|
|
BN_CTX_end(ctx);
|
|
if (!BN_zero(R->Z)) return 0;
|
|
return 1;
|
|
}
|
|
}
|
|
|
|
/* L7; L8 */
|
|
if (!BN_mod_add_quick(n1, n1, n3, p)) goto err; /* L7 = L1 + L3 */
|
|
if (!BN_mod_add_quick(n2, n2, n4, p)) goto err; /* L8 = L2 + L4 */
|
|
|
|
|
|
/* Z */
|
|
if (!BN_mont_mod_mul(n0, P->Z, Q->Z, mont)) goto err;
|
|
if (!BN_mont_mod_mul(R->Z, n0, n5, mont)) goto err; /* Z = z_p * z_q * L_5 */
|
|
|
|
|
|
/* X */
|
|
if (!BN_mont_mod_mul(n0, n6, n6, mont)) goto err;
|
|
if (!BN_mont_mod_mul(n4, n5, n5, mont)) goto err;
|
|
if (!BN_mont_mod_mul(n3, n1, n4, mont)) goto err;
|
|
if (!BN_mod_sub_quick(R->X, n0, n3, p)) goto err; /* X = L6^2 - L5^2 * L7 */
|
|
|
|
|
|
/* L9 */
|
|
if (!BN_mod_lshift1_quick(n0, R->X, p)) goto err;
|
|
if (!BN_mod_sub_quick(n3, n3, n0, p)) goto err; /* L9 = L5^2 * L7 - 2X */
|
|
|
|
|
|
/* Y */
|
|
if (!BN_mont_mod_mul(n0, n3, n6, mont)) goto err;
|
|
if (!BN_mont_mod_mul(n6, n4, n5, mont)) goto err;
|
|
if (!BN_mont_mod_mul(n1, n2, n6, mont)) goto err;
|
|
if (!BN_mod_sub_quick(n0, n0, n1, p)) goto err;
|
|
if (!BN_mont_mod_mul(R->Y, n0, E->h, mont)) goto err; /* Y = (L6 * L9 - L8 * L5^3) / 2 */
|
|
|
|
|
|
BN_CTX_end(ctx);
|
|
return 1;
|
|
|
|
err:
|
|
BN_CTX_end(ctx);
|
|
return 0;
|
|
}
|
|
|
|
|
|
ECP_PRECOMPUTE *ECP_mont_precompute(int r, EC_POINT *P, EC *E, BN_MONTGOMERY *mont, BN_CTX *ctx)
|
|
{
|
|
ECP_PRECOMPUTE *ret;
|
|
EC_POINT *P2;
|
|
int i, max;
|
|
|
|
assert(r > 2);
|
|
assert(r < sizeof(unsigned int) * 8 - 1);
|
|
|
|
assert(mont != NULL);
|
|
assert(mont->p != NULL);
|
|
|
|
if (!P->is_in_mont)
|
|
if (!ECP_to_montgomery(P, mont, ctx)) return 0;
|
|
|
|
if (!E->is_in_mont)
|
|
if (!EC_to_montgomery(E, mont, ctx)) return 0;
|
|
|
|
ret=(ECP_PRECOMPUTE *)malloc(sizeof(ECP_PRECOMPUTE));
|
|
if (ret == NULL) return NULL;
|
|
|
|
max = 1;
|
|
max <<= (r - 1);
|
|
|
|
ret->r = 0;
|
|
|
|
ret->Pi=(EC_POINT **)malloc(sizeof(EC_POINT *) * max);
|
|
if (ret->Pi == NULL) goto err;
|
|
|
|
|
|
/* P2 = [2]P */
|
|
if ((P2 = ECP_new()) == NULL) goto err;
|
|
if (!ECP_mont_double(P2, P, E, mont, ctx)) goto err;
|
|
|
|
/* P_0 = P */
|
|
if((ret->Pi[0] = ECP_dup(P)) == NULL) goto err;
|
|
|
|
|
|
/* P_i = P_(i-1) + P2 */
|
|
for (i = 1; i < max; i++)
|
|
{
|
|
if ((ret->Pi[i] = ECP_new()) == NULL) goto err;
|
|
if (!ECP_mont_add(ret->Pi[i], P2, ret->Pi[i - 1], E, mont, ctx)) goto err;
|
|
}
|
|
|
|
ret->r = r;
|
|
ECP_clear_free(P2);
|
|
|
|
return ret;
|
|
|
|
err:
|
|
ECP_clear_free(P2);
|
|
ECP_clear_free_precompute(ret);
|
|
return NULL;
|
|
}
|
|
|
|
|
|
int ECP_mont_multiply(EC_POINT *R, BIGNUM *k, ECP_PRECOMPUTE *prec, EC *E, BN_MONTGOMERY *mont, BN_CTX *ctx)
|
|
/* R = [k]P P = prec->Pi[0]*/
|
|
{
|
|
int j;
|
|
int t, nextw, h, r;
|
|
|
|
assert(R != NULL);
|
|
assert(R->X != NULL && R->Y != NULL && R->Z != NULL);
|
|
|
|
assert(E != NULL);
|
|
assert(E->A != NULL && E->B != NULL && E->p != NULL && E->h != NULL);
|
|
|
|
assert(k != NULL);
|
|
assert(!k->neg);
|
|
|
|
assert(ctx != NULL);
|
|
assert(prec != NULL);
|
|
|
|
assert(mont != NULL);
|
|
assert(mont->p != NULL);
|
|
|
|
if (!E->is_in_mont)
|
|
if (!EC_to_montgomery(E, mont, ctx)) return 0;
|
|
|
|
|
|
if (BN_is_zero(k))
|
|
{
|
|
if (!BN_zero(R->Z)) return 0;
|
|
R->is_in_mont = 1;
|
|
return 1;
|
|
}
|
|
|
|
j = BN_num_bits(k);
|
|
j--;
|
|
|
|
r = prec->r;
|
|
|
|
if (!BN_zero(R->Z)) return 0;
|
|
R->is_in_mont = 1;
|
|
|
|
while(j >= 0)
|
|
{
|
|
if (!BN_is_bit_set(k, j))
|
|
{
|
|
if (!ECP_mont_double(R, R, E, mont, ctx)) return 0;
|
|
j--;
|
|
}
|
|
else
|
|
{
|
|
nextw = j - r;
|
|
if (nextw < -1) nextw = -1;
|
|
t = nextw + 1;
|
|
while(!BN_is_bit_set(k, t))
|
|
t++;
|
|
|
|
if (!ECP_mont_double(R, R, E, mont, ctx)) return 0;
|
|
|
|
j--;
|
|
if (j < t) h = 0;
|
|
else
|
|
{
|
|
h = 1;
|
|
for(; j > t; j--)
|
|
{
|
|
h <<= 1;
|
|
if (BN_is_bit_set(k, j)) h++;
|
|
if (!ECP_mont_double(R, R, E, mont, ctx)) return 0;
|
|
}
|
|
if (!ECP_mont_double(R, R, E, mont, ctx)) return 0;
|
|
j--;
|
|
}
|
|
|
|
if (!ECP_mont_add(R, R, prec->Pi[h], E, mont, ctx)) return 0;
|
|
|
|
for (; j > nextw; j--)
|
|
{
|
|
if (!ECP_mont_double(R, R, E, mont, ctx)) return 0;
|
|
}
|
|
|
|
}
|
|
}
|
|
|
|
return 1;
|
|
}
|
|
|
|
|
|
int ECP_mont_multiply2(EC_POINT *R, BIGNUM *k, EC_POINT *P, EC *E, BN_MONTGOMERY *mont, BN_CTX *ctx)
|
|
/* R = [k]P */
|
|
{
|
|
int j, hj, kj;
|
|
BIGNUM *h;
|
|
EC_POINT *mP;
|
|
|
|
assert(R != NULL);
|
|
assert(R->X != NULL && R->Y != NULL && R->Z != NULL);
|
|
|
|
assert(P != NULL);
|
|
assert(P->X != NULL && P->Y != NULL && P->Z != NULL);
|
|
|
|
assert(E != NULL);
|
|
assert(E->A != NULL && E->B != NULL && E->p != NULL && E->h != NULL);
|
|
|
|
assert(k != NULL);
|
|
assert(!k->neg);
|
|
|
|
assert(ctx != NULL);
|
|
|
|
assert(mont != NULL);
|
|
assert(mont->p != NULL);
|
|
|
|
if (!E->is_in_mont)
|
|
if (!EC_to_montgomery(E, mont, ctx)) return 0;
|
|
|
|
if (!P->is_in_mont)
|
|
if (!ECP_to_montgomery(P, mont, ctx)) return 0;
|
|
|
|
|
|
if (BN_is_zero(k))
|
|
{
|
|
if (!BN_zero(R->Z)) return 0;
|
|
R->is_in_mont = 1;
|
|
return 1;
|
|
}
|
|
|
|
if ((h = BN_dup(k)) == NULL) return 0;
|
|
|
|
if (!BN_lshift1(h, h)) goto err;
|
|
if (!BN_add(h, h, k)) goto err;
|
|
|
|
if (!ECP_copy(R, P)) goto err;
|
|
if ((mP = ECP_mont_minus(P, mont)) == NULL) goto err;
|
|
|
|
for(j = BN_num_bits(h) - 2; j > 0; j--)
|
|
{
|
|
if (!ECP_mont_double(R, R, E, mont, ctx)) goto err;
|
|
kj = BN_is_bit_set(k, j);
|
|
hj = BN_is_bit_set(h, j);
|
|
if (hj == 1 && kj == 0)
|
|
if (!ECP_mont_add(R, R, P, E, mont, ctx)) goto err;
|
|
if (hj == 0 && kj == 1)
|
|
if (!ECP_mont_add(R, R, mP, E, mont, ctx)) goto err;
|
|
}
|
|
|
|
if (h != NULL) BN_free(h);
|
|
if (mP != NULL) ECP_clear_free(mP);
|
|
return 1;
|
|
|
|
err:
|
|
if (h != NULL) BN_free(h);
|
|
if (mP != NULL) ECP_clear_free(mP);
|
|
return 0;
|
|
}
|
|
|
|
#endif /* MONTGOMERY */
|