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openssl/crypto/ec/ec_point.c
Bodo Möller 7e0c5264e7 Elliptic curves over GF(p), new BIGNUM functions, Montgomery re-implementation. 
These new files will not be included literally in OpenSSL, but I intend
to integrate most of their contents.  Most file names will change,
and when the integration is done, the superfluous files will be deleted.

Submitted by: Lenka Fibikova <fibikova@exp-math.uni-essen.de>
2000-11-26 12:12:35 +00:00

1461 lines
31 KiB
C
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/*
*
* ec_point.c
*
* Elliptic Curve Arithmetic Functions
*
* Copyright (C) Lenka Fibikova 2000
*
*
*/
#include <stdio.h>
#include <stdlib.h>
#include <assert.h>
#include <memory.h>
#include "bn.h"
#include "bn_modfs.h"
#include "bn_mont2.h"
#include "ec.h"
EC_POINT *ECP_new()
{
EC_POINT *ret;
ret=(EC_POINT *)malloc(sizeof(EC_POINT));
if (ret == NULL) return NULL;
ret->X = BN_new();
ret->Y = BN_new();
ret->Z = BN_new();
ret->is_in_mont = 0;
if (ret->X == NULL || ret->Y == NULL || ret->Z == NULL)
{
if (ret->X != NULL) BN_free(ret->X);
if (ret->Y != NULL) BN_free(ret->Y);
if (ret->Z != NULL) BN_free(ret->Z);
free(ret);
return(NULL);
}
return(ret);
}
void ECP_clear_free(EC_POINT *P)
{
if (P == NULL) return;
P->is_in_mont = 0;
if (P->X != NULL) BN_clear_free(P->X);
if (P->Y != NULL) BN_clear_free(P->Y);
if (P->Z != NULL) BN_clear_free(P->Z);
free(P);
}
void ECP_clear_free_precompute(ECP_PRECOMPUTE *prec)
{
int i;
int max;
if (prec == NULL) return;
if (prec->Pi != NULL)
{
max = 1;
max <<= (prec->r - 1);
for (i = 0; i < max; i++)
{
if (prec->Pi[i] != NULL) ECP_clear_free(prec->Pi[i]);
}
}
free(prec);
}
int ECP_is_on_ec(EC_POINT *P, EC *E, BN_CTX *ctx)
{
BIGNUM *n0, *n1, *n2, *p;
int Pnorm;
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);
assert(ctx != NULL);
assert(!P->is_in_mont);
if (ECP_is_infty(P)) return 1;
n0 = ctx->bn[ctx->tos];
n1 = ctx->bn[ctx->tos + 1];
n2 = ctx->bn[ctx->tos + 2];
ctx->tos += 3;
p = E->p;
Pnorm = (ECP_is_norm(P));
if (!Pnorm)
{
if (!BN_mod_mul(n0, P->Z, P->Z, p, ctx)) goto err;
if (!BN_mod_mul(n1, n0, n0, p, ctx)) goto err;
if (!BN_mod_mul(n2, n0, n1, p, ctx)) goto err;
}
if (!BN_mod_mul(n0, P->X, P->X, p, ctx)) goto err;
if (!BN_mod_mul(n0, n0, P->X, p, ctx)) goto err;
if (Pnorm)
{
if (!BN_mod_mul(n1, P->X, E->A, p, ctx)) goto err;
}
else
{
if (!BN_mod_mul(n1, n1, P->X, p, ctx)) goto err;
if (!BN_mod_mul(n1, n1, E->A, p, ctx)) goto err;
}
if (!BN_mod_add(n0, n0, n1, p, ctx)) goto err;
if (Pnorm)
{
if (!BN_mod_add(n0, n0, E->B, p, ctx)) goto err;
}
else
{
if (!BN_mod_mul(n2, n2, E->B, p, ctx)) goto err;
if (!BN_mod_add(n0, n0, n2, p, ctx)) goto err;
}
if (!BN_mod_mul(n1, P->Y, P->Y, p, ctx)) goto err;
if (BN_cmp(n0, n1))
{
ctx->tos -= 3;
return 0;
}
ctx->tos -= 3;
return 1;
err:
ctx->tos -= 3;
return -1;
}
EC_POINT *ECP_generate(BIGNUM *x, BIGNUM *z,EC *E, BN_CTX *ctx)
/* x == NULL || z = 0 -> point of infinity */
/* z == NULL || z = 1 -> normalized */
{
BIGNUM *n0, *n1;
EC_POINT *ret;
int Pnorm, Pinfty, X0, A0;
assert(E != NULL);
assert(E->A != NULL && E->B != NULL && E->p != NULL && E->h != NULL);
assert(ctx != NULL);
Pinfty = (x == NULL);
Pnorm = (z == NULL);
if (!Pnorm)
{
Pnorm = BN_is_one(z);
Pinfty = (Pinfty || BN_is_zero(z));
}
if (Pinfty)
{
if ((ret = ECP_new()) == NULL) return NULL;
if (!BN_zero(ret->Z))
{
ECP_clear_free(ret);
return NULL;
}
return ret;
}
X0 = BN_is_zero(x);
A0 = BN_is_zero(E->A);
if ((ret = ECP_new()) == NULL) return NULL;
ret->is_in_mont = 0;
n0 = ctx->bn[ctx->tos];
n1 = ctx->bn[ctx->tos + 1];
if (!BN_zero(n0)) return NULL;
if (!BN_zero(n1)) return NULL;
ctx->tos += 2;
if (!X0)
{
if (!BN_mod_sqr(n0, x, E->p, ctx)) goto err;
if (!BN_mod_mul(n0, n0, x, E->p, ctx)) goto err; /* x^3 */
}
if (!X0 && !A0)
{
if (!BN_mod_mul(n1, E->A, x, E->p, ctx)) goto err; /* Ax */
if (!BN_mod_add(n0, n0, n1, E->p, ctx)) goto err; /* x^3 + Ax */
}
if (!BN_is_zero(E->B))
if (!BN_mod_add(n0, n0, E->B, E->p, ctx)) goto err; /* x^3 + Ax +B */
if (!BN_mod_sqrt(ret->Y, n0, E->p, ctx)) goto err;
if (BN_copy(ret->X, x) == NULL) goto err;
if (Pnorm)
{
if (!BN_one(ret->Z)) goto err;
}
else
{
if (BN_copy(ret->Z, z) == NULL) goto err;
if (!BN_mod_sqr(n0, z, E->p, ctx)) goto err;
if (!BN_mod_mul(ret->X, ret->X, n0, E->p, ctx)) goto err;
if (!BN_mod_mul(n0, n0, z, E->p, ctx)) goto err;
if (!BN_mod_mul(ret->Y, ret->Y, n0, E->p, ctx)) goto err;
}
#ifdef TEST
if (!ECP_is_on_ec(ret, E, ctx)) goto err;
#endif
ctx->tos -= 2;
return ret;
err:
if (ret != NULL) ECP_clear_free(ret);
ctx->tos -= 2;
return NULL;
}
int ECP_ecp2bin(EC_POINT *P, unsigned char *to, int form)
/* form = 1 ... compressed
2 ... uncompressed
3 ... hybrid */
{
int bytes, bx, by;
assert (P != NULL);
assert (P->X != NULL && P->Y != NULL && P->Z != NULL);
assert (!P->is_in_mont);
assert (ECP_is_norm(P) || ECP_is_infty(P));
assert (to != NULL);
assert (form > 0 && form < 4);
if (BN_is_zero(P->Z))
{
to[0] = 0;
return 1;
}
bx = BN_num_bytes(P->X);
if (form == 1 ) bytes = bx + 1;
else
{
by = BN_num_bytes(P->Y);
bytes = (bx > by ? bx : by);
bytes = bytes * 2 + 1;
}
memset(to, 0, bytes);
switch (form)
{
case 1: to[0] = 2; break;
case 2: to[0] = 4; break;
case 3: to[0] = 6; break;
}
if (form != 2) to[0] += BN_is_bit_set(P->Y, 0);
if ((BN_bn2bin(P->X, to + 1)) != bx) return 0;
if (form != 1)
{
if ((BN_bn2bin(P->Y, to + bx + 1)) != by) return 0;
}
return bytes;
}
int ECP_bin2ecp(unsigned char *from, int len, EC_POINT *P, EC *E, BN_CTX *ctx)
{
int y;
BIGNUM *x;
EC_POINT *pp;
assert (E != NULL);
assert (E->A != NULL && E->B != NULL && E->p != NULL);
assert (!E->is_in_mont);
assert (ctx != NULL);
assert (from != NULL);
assert (P != NULL);
assert (P->X != NULL && P->Y != NULL && P->Z != NULL);
if (len == 1 && from[0] != 0) return 0;
if (len == 0 || len == 1)
{
if (!BN_zero(P->Z)) return 0;
return 1;
}
switch (from[0])
{
case 2:
case 3:
y = from[0] - 2;
if ((x = BN_new()) == NULL) return 0;
if (BN_bin2bn(from + 1, len - 1, x) == NULL) return 0;
pp = ECP_generate(x, NULL, E, ctx);
BN_clear_free(x);
if (pp == NULL) return 0;
ECP_copy(P, pp);
ECP_clear_free(pp);
if (BN_is_bit_set(P->Y, 0) != y)
if (!BN_sub(P->Y, E->p, P->Y)) return 0;
break;
case 4:
case 6:
case 7:
y = (len - 1)/2;
if (BN_bin2bn(from + 1, y, P->X) == NULL) return 0;
if (BN_bin2bn(from + y + 1, y, P->Y) == NULL) return 0;
if (!BN_set_word(P->Z, 1)) return 0;
break;
default:
assert(0);
}
if (!ECP_is_on_ec(P, E, ctx)) return 0;
return 1;
}
int ECP_normalize(EC_POINT *P, EC *E, BN_CTX *ctx)
{
BIGNUM *z, *zm;
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);
assert (ctx != NULL);
if (ECP_is_norm(P)) return 1;
if (ECP_is_infty(P)) return 0;
if ((zm = BN_mod_inverse(P->Z, E->p, ctx)) == NULL) return 0;
assert(!P->is_in_mont);
z = ctx->bn[ctx->tos];
ctx->tos++;
if (!BN_mod_mul(z, zm, zm, E->p, ctx)) goto err;
if (!BN_mod_mul(P->X, P->X, z, E->p, ctx)) goto err;
if (!BN_mod_mul(z, z, zm, E->p, ctx)) goto err;
if (!BN_mod_mul(P->Y, P->Y, z, E->p, ctx)) goto err;
if (!BN_one(P->Z)) goto err;
if (zm != NULL) BN_clear_free(zm);
ctx->tos--;
return 1;
err:
if (zm != NULL) BN_clear_free(zm);
ctx->tos--;
return 0;
}
int ECP_copy(EC_POINT *R, EC_POINT *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);
if (BN_copy(R->X, P->X) == NULL) return 0;
if (BN_copy(R->Y, P->Y) == NULL) return 0;
if (BN_copy(R->Z, P->Z) == NULL) return 0;
R->is_in_mont = P->is_in_mont;
return 1;
}
EC_POINT *ECP_dup(EC_POINT *P)
{
EC_POINT *ret;
ret = ECP_new();
if (ret == NULL) return NULL;
if (!ECP_copy(ret, P))
{
ECP_clear_free(ret);
return(NULL);
}
return(ret);
}
EC_POINT *ECP_minus(EC_POINT *P, BIGNUM *p) /* mont || non-mont */
{
EC_POINT *ret;
assert(P != NULL);
assert(P->X != NULL && P->Y != NULL && P->Z != NULL);
assert(p != NULL);
assert(BN_cmp(P->Y, p) < 0);
ret = ECP_dup(P);
if (ret == NULL) return NULL;
if (BN_is_zero(ret->Y)) return ret;
if (!BN_sub(ret->Y, p, ret->Y))
{
ECP_clear_free(ret);
return NULL;
}
return ret;
}
#ifdef SIMPLE
int ECP_cmp(EC_POINT *P, EC_POINT *Q, BIGNUM *p, BN_CTX *ctx)
/* return values:
-2 ... error
0 ... P = Q
-1 ... P = -Q
1 ... else
*/
{
BIGNUM *n0, *n1, *n2, *n3, *n4;
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(p != NULL);
assert(ctx != NULL);
assert(!P->is_in_mont);
assert(!Q->is_in_mont);
if (ECP_is_infty(P) && ECP_is_infty(Q)) return 0;
if (ECP_is_infty(P) || ECP_is_infty(Q)) return 1;
Pnorm = (ECP_is_norm(P));
Qnorm = (ECP_is_norm(Q));
n0 = ctx->bn[ctx->tos];
n1 = ctx->bn[ctx->tos + 1];
n2 = ctx->bn[ctx->tos + 2];
n3 = ctx->bn[ctx->tos + 3];
n4 = ctx->bn[ctx->tos + 4];
ctx->tos += 5;
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 */
}
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 */
}
if (!BN_mod_sub(n0, n1, n3, p, ctx)) goto err; /* L5 = L1 - L3 */
if (!BN_is_zero(n0))
{
ctx->tos -= 5;
return 1;
}
if (!BN_mod_sub(n0, n2, n4, p, ctx)) goto err; /* L6 = L2 - L4 */
if (!BN_is_zero(n0))
{
ctx->tos -= 5;
return -1;
}
ctx->tos -= 5;
return 0;
err:
ctx->tos -= 5;
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));
n0 = ctx->bn[ctx->tos];
n1 = ctx->bn[ctx->tos + 1];
n2 = ctx->bn[ctx->tos + 2];
n3 = ctx->bn[ctx->tos + 3];
ctx->tos += 4;
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
ctx->tos -= 4;
return 1;
err:
ctx->tos -= 4;
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));
n0 = ctx->bn[ctx->tos];
n1 = ctx->bn[ctx->tos + 1];
n2 = ctx->bn[ctx->tos + 2];
n3 = ctx->bn[ctx->tos + 3];
n4 = ctx->bn[ctx->tos + 4];
n5 = ctx->bn[ctx->tos + 5];
n6 = ctx->bn[ctx->tos + 6];
ctx->tos += 7;
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 */
{
ctx->tos -= 7;
return ECP_double(R, P, E, ctx);
}
else /* P = -Q => P + Q = \infty */
{
ctx->tos -= 7;
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
ctx->tos -= 7;
return 1;
err:
ctx->tos -= 7;
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, ctx)) return 0;
if (!BN_mont_red(P->Y, mont, ctx)) return 0;
if (!BN_mont_red(P->Z, mont, ctx)) 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;
n0 = ctx->bn[ctx->tos];
n1 = ctx->bn[ctx->tos + 1];
n2 = ctx->bn[ctx->tos + 2];
n3 = ctx->bn[ctx->tos + 3];
n4 = ctx->bn[ctx->tos + 4];
n5 = ctx->bn[ctx->tos + 5];
ctx->tos += 6;
p = mont->p;
if (!BN_mont_mod_mul(n5, Q->Z, Q->Z, mont, ctx)) goto err;
if (!BN_mont_mod_mul(n1, P->X, n5, mont, ctx)) goto err; /* L1 = x_p * z_q^2 */
if (!BN_mont_mod_mul(n0, n5, Q->Z, mont, ctx)) goto err;
if (!BN_mont_mod_mul(n2, P->Y, n0, mont, ctx)) goto err; /* L2 = y_p * z_q^3 */
if (!BN_mont_mod_mul(n5, P->Z, P->Z, mont, ctx)) goto err;
if (!BN_mont_mod_mul(n3, Q->X, n5, mont, ctx)) goto err; /* L3 = x_q * z_p^2 */
if (!BN_mont_mod_mul(n0, n5, P->Z, mont, ctx)) goto err;
if (!BN_mont_mod_mul(n4, Q->Y, n0, mont, ctx)) goto err; /* L4 = y_q * z_p^3 */
if (!BN_mont_mod_sub(n0, n1, n3, mont)) goto err; /* L5 = L1 - L3 */
if (!BN_is_zero(n0))
{
ctx->tos -= 6;
return 1;
}
if (!BN_mont_mod_sub(n0, n2, n4, mont)) goto err; /* L6 = L2 - L4 */
if (!BN_is_zero(n0))
{
ctx->tos -= 6;
return -1;
}
ctx->tos -= 6;
return 0;
err:
ctx->tos -= 6;
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;
}
n0 = ctx->bn[ctx->tos];
n1 = ctx->bn[ctx->tos + 1];
n2 = ctx->bn[ctx->tos + 2];
n3 = ctx->bn[ctx->tos + 3];
ctx->tos += 4;
p = E->p;
/* L1 */
if (!BN_mont_mod_mul(n0, P->Z, P->Z, mont, ctx)) goto err;
if (!BN_mont_mod_mul(n2, n0, n0, mont, ctx)) goto err;
if (!BN_mont_mod_mul(n0, n2, E->A, mont, ctx)) goto err;
if (!BN_mont_mod_mul(n1, P->X, P->X, mont, ctx)) goto err;
if (!BN_mont_mod_lshift1(n2, n1, mont)) goto err;
if (!BN_mont_mod_add(n1, n1, n2, mont)) goto err;
if (!BN_mont_mod_add(n1, n1, n0, mont)) goto err; /* L1 = 3 * x^2 + a * z^4 */
/* Z */
if (!BN_mont_mod_mul(n0, P->Y, P->Z, mont, ctx)) goto err;
if (!BN_mont_mod_lshift1(R->Z, n0, mont)) goto err; /* Z = 2 * y * z */
/* L2 */
if (!BN_mont_mod_mul(n3, P->Y, P->Y, mont, ctx)) goto err;
if (!BN_mont_mod_mul(n2, P->X, n3, mont, ctx)) goto err;
if (!BN_mont_mod_lshift(n2, n2, 2, mont)) goto err; /* L2 = 4 * x * y^2 */
/* X */
if (!BN_mont_mod_lshift1(n0, n2, mont)) goto err;
if (!BN_mont_mod_mul(R->X, n1, n1, mont, ctx)) goto err;
if (!BN_mont_mod_sub(R->X, R->X, n0, mont)) goto err; /* X = L1^2 - 2 * L2 */
/* L3 */
if (!BN_mont_mod_mul(n0, n3, n3, mont, ctx)) goto err;
if (!BN_mont_mod_lshift(n3, n0, 3, mont)) goto err; /* L3 = 8 * y^4 */
/* Y */
if (!BN_mont_mod_sub(n2, n2, R->X, mont)) goto err;
if (!BN_mont_mod_mul(n0, n1, n2, mont, ctx)) goto err;
if (!BN_mont_mod_sub(R->Y, n0, n3, mont)) goto err; /* Y = L1 * (L2 - X) - L3 */
ctx->tos -= 4;
return 1;
err:
ctx->tos -= 4;
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);
n0 = ctx->bn[ctx->tos];
n1 = ctx->bn[ctx->tos + 1];
n2 = ctx->bn[ctx->tos + 2];
n3 = ctx->bn[ctx->tos + 3];
n4 = ctx->bn[ctx->tos + 4];
n5 = ctx->bn[ctx->tos + 5];
n6 = ctx->bn[ctx->tos + 6];
ctx->tos += 7;
p = E->p;
R->is_in_mont = 1;
/* L1; L2 */
if (!BN_mont_mod_mul(n6, Q->Z, Q->Z, mont, ctx)) goto err;
if (!BN_mont_mod_mul(n1, P->X, n6, mont, ctx)) goto err; /* L1 = x_p * z_q^2 */
if (!BN_mont_mod_mul(n0, n6, Q->Z, mont, ctx)) goto err;
if (!BN_mont_mod_mul(n2, P->Y, n0, mont, ctx)) goto err; /* L2 = y_p * z_q^3 */
/* L3; L4 */
if (!BN_mont_mod_mul(n6, P->Z, P->Z, mont, ctx)) goto err;
if (!BN_mont_mod_mul(n3, Q->X, n6, mont, ctx)) goto err; /* L3 = x_q * z_p^2 */
if (!BN_mont_mod_mul(n0, n6, P->Z, mont, ctx)) goto err;
if (!BN_mont_mod_mul(n4, Q->Y, n0, mont, ctx)) goto err; /* L4 = y_q * z_p^3 */
/* L5; L6 */
if (!BN_mont_mod_sub(n5, n1, n3, mont)) goto err; /* L5 = L1 - L3 */
if (!BN_mont_mod_sub(n6, n2, n4, mont)) goto err; /*L6 = L2 - L4 */
/* pata */
if (BN_is_zero(n5))
{
if (BN_is_zero(n6)) /* P = Q => P + Q = 2P */
{
ctx->tos -= 7;
return ECP_mont_double(R, P, E, mont, ctx);
}
else /* P = -Q => P + Q = \infty */
{
ctx->tos -= 7;
if (!BN_zero(R->Z)) return 0;
return 1;
}
}
/* L7; L8 */
if (!BN_mont_mod_add(n1, n1, n3, mont)) goto err; /* L7 = L1 + L3 */
if (!BN_mont_mod_add(n2, n2, n4, mont)) goto err; /* L8 = L2 + L4 */
/* Z */
if (!BN_mont_mod_mul(n0, P->Z, Q->Z, mont, ctx)) goto err;
if (!BN_mont_mod_mul(R->Z, n0, n5, mont, ctx)) goto err; /* Z = z_p * z_q * L_5 */
/* X */
if (!BN_mont_mod_mul(n0, n6, n6, mont, ctx)) goto err;
if (!BN_mont_mod_mul(n4, n5, n5, mont, ctx)) goto err;
if (!BN_mont_mod_mul(n3, n1, n4, mont, ctx)) goto err;
if (!BN_mont_mod_sub(R->X, n0, n3, mont)) goto err; /* X = L6^2 - L5^2 * L7 */
/* L9 */
if (!BN_mont_mod_lshift1(n0, R->X, mont)) goto err;
if (!BN_mont_mod_sub(n3, n3, n0, mont)) goto err; /* L9 = L5^2 * L7 - 2X */
/* Y */
if (!BN_mont_mod_mul(n0, n3, n6, mont, ctx)) goto err;
if (!BN_mont_mod_mul(n6, n4, n5, mont, ctx)) goto err;
if (!BN_mont_mod_mul(n1, n2, n6, mont, ctx)) goto err;
if (!BN_mont_mod_sub(n0, n0, n1, mont)) goto err;
if (!BN_mont_mod_mul(R->Y, n0, E->h, mont, ctx)) goto err; /* Y = (L6 * L9 - L8 * L5^3) / 2 */
ctx->tos -= 7;
return 1;
err:
ctx->tos -= 7;
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 */
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