diff options
| author | Bodo Möller <bodo@openssl.org> | 2000-11-26 12:12:35 +0000 |
|---|---|---|
| committer | Bodo Möller <bodo@openssl.org> | 2000-11-26 12:12:35 +0000 |
| commit | 7e0c5264e76963b691221082ddb50152c8fc2c75 (patch) | |
| tree | 63e0825c3b07a6cb623407bc3cdf53369631874b /crypto/ec | |
| parent | 73343ac38abfbe34cf889e9da286d5c577ce7973 (diff) | |
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>
Diffstat (limited to 'crypto/ec')
| -rw-r--r-- | crypto/ec/ec.c | 121 | ||||
| -rw-r--r-- | crypto/ec/ec.h | 86 | ||||
| -rw-r--r-- | crypto/ec/ec_point.c | 1461 |
3 files changed, 1668 insertions, 0 deletions
diff --git a/crypto/ec/ec.c b/crypto/ec/ec.c new file mode 100644 index 0000000000..bc689e74f2 --- /dev/null +++ b/crypto/ec/ec.c @@ -0,0 +1,121 @@ +/*
+ *
+ * ec.c
+ *
+ * Elliptic Curve Arithmetic Functions
+ *
+ * Copyright (C) Lenka Fibikova 2000
+ *
+ *
+ */
+
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <assert.h>
+
+#include "ec.h"
+#include "bn_modfs.h"
+
+
+
+EC *EC_new()
+{
+ EC *ret;
+
+ ret=(EC *)malloc(sizeof(EC));
+ if (ret == NULL) return NULL;
+ ret->A = BN_new();
+ ret->B = BN_new();
+ ret->p = BN_new();
+ ret->h = BN_new();
+ ret->is_in_mont = 0;
+
+ if (ret->A == NULL || ret->B == NULL || ret->p == NULL || ret->h == NULL)
+ {
+ if (ret->A != NULL) BN_free(ret->A);
+ if (ret->B != NULL) BN_free(ret->B);
+ if (ret->p != NULL) BN_free(ret->p);
+ if (ret->h != NULL) BN_free(ret->h);
+ free(ret);
+ return(NULL);
+ }
+ return(ret);
+}
+
+
+void EC_clear_free(EC *E)
+{
+ if (E == NULL) return;
+
+ if (E->A != NULL) BN_clear_free(E->A);
+ if (E->B != NULL) BN_clear_free(E->B);
+ if (E->p != NULL) BN_clear_free(E->p);
+ if (E->h != NULL) BN_clear_free(E->h);
+ E->is_in_mont = 0;
+ free(E);
+}
+
+
+#ifdef MONTGOMERY
+int EC_to_montgomery(EC *E, BN_MONTGOMERY *mont, BN_CTX *ctx)
+{
+ assert(E != NULL);
+ assert(E->A != NULL && E->B != NULL && E->p != NULL && E->h != NULL);
+
+ assert(mont != NULL);
+ assert(mont->p != NULL);
+
+ assert(ctx != NULL);
+
+ if (E->is_in_mont) return 1;
+
+ if (!BN_lshift(E->A, E->A, mont->R_num_bits)) return 0;
+ if (!BN_mod(E->A, E->A, mont->p, ctx)) return 0;
+
+ if (!BN_lshift(E->B, E->B, mont->R_num_bits)) return 0;
+ if (!BN_mod(E->B, E->B, mont->p, ctx)) return 0;
+
+ if (!BN_lshift(E->h, E->h, mont->R_num_bits)) return 0;
+ if (!BN_mod(E->h, E->h, mont->p, ctx)) return 0;
+
+ E->is_in_mont = 1;
+ return 1;
+
+}
+
+
+int EC_from_montgomery(EC *E, BN_MONTGOMERY *mont, BN_CTX *ctx)
+{
+ assert(E != NULL);
+ assert(E->A != NULL && E->B != NULL && E->p != NULL && E->h != NULL);
+
+ assert(mont != NULL);
+ assert(mont->p != NULL);
+
+ assert(ctx != NULL);
+
+ if (!E->is_in_mont) return 1;
+
+ if (!BN_mont_red(E->A, mont, ctx)) return 0;
+ if (!BN_mont_red(E->B, mont, ctx)) return 0;
+ if (!BN_mont_red(E->h, mont, ctx)) return 0;
+
+ E->is_in_mont = 0;
+ return 1;
+}
+#endif /* MONTGOMERY */
+
+int EC_set_half(EC *E)
+/* h <- 1/2 mod p = (p + 1)/2 */
+{
+ assert(E != NULL);
+ assert(E->p != NULL);
+ assert(E->h != NULL);
+ assert(!E->is_in_mont);
+
+ if (BN_copy(E->h, E->p) == NULL) return 0;
+ if (!BN_add_word(E->h, 1)) return 0;
+ if (!BN_rshift1(E->h, E->h)) return 0;
+ return 1;
+}
diff --git a/crypto/ec/ec.h b/crypto/ec/ec.h new file mode 100644 index 0000000000..97d55cb2cc --- /dev/null +++ b/crypto/ec/ec.h @@ -0,0 +1,86 @@ +/*
+ *
+ * ec.h
+ *
+ * Elliptic Curve Arithmetic Functions
+ *
+ * Copyright (C) Lenka Fibikova 2000
+ *
+ *
+ */
+
+
+#ifndef HEADER_EC_H
+#define HEADER_EC_H
+
+
+#include "bn.h"
+#include "bn_mont2.h"
+
+typedef struct bn_ec_struct /* E: y^2 = x^3 + Ax + B (mod p) */
+{
+ BIGNUM *A, *B, *p, *h; /* h = 1/2 mod p = (p + 1)/2 */
+ int is_in_mont;
+} EC;
+
+typedef struct bn_ec_point_struct /* P = [X, Y, Z] */
+{
+ BIGNUM *X, *Y, *Z;
+ int is_in_mont;
+} EC_POINT;
+
+typedef struct bn_ecp_precompute_struct /* Pi[i] = [2i + 1]P i = 0..2^{r-1} - 1 */
+{
+ int r;
+ EC_POINT **Pi;
+} ECP_PRECOMPUTE;
+
+
+#define ECP_is_infty(P) (BN_is_zero(P->Z))
+#define ECP_is_norm(P) (BN_is_one(P->Z))
+
+#define ECP_mont_minus(P, mont) (ECP_minus((P), (mont)->p))
+
+
+EC *EC_new();
+void EC_clear_free(EC *E);
+int EC_set_half(EC *E);
+#ifdef MONTGOMERY
+int EC_to_montgomery(EC *E, BN_MONTGOMERY *mont, BN_CTX *ctx);
+int EC_from_montgomery(EC *E, BN_MONTGOMERY *mont, BN_CTX *ctx);
+#endif /* MONTGOMERY */
+
+
+EC_POINT *ECP_new();
+void ECP_clear_free(EC_POINT *P);
+void ECP_clear_free_precompute(ECP_PRECOMPUTE *prec);
+
+EC_POINT *ECP_generate(BIGNUM *x, BIGNUM *z, EC *E, BN_CTX *ctx);
+EC_POINT *ECP_dup(EC_POINT *P);
+int ECP_copy(EC_POINT *R, EC_POINT *P);
+int ECP_normalize(EC_POINT *P, EC *E, BN_CTX *ctx);
+EC_POINT *ECP_minus(EC_POINT *P, BIGNUM *p);
+int ECP_is_on_ec(EC_POINT *P, EC *E, BN_CTX *ctx);
+int ECP_ecp2bin(EC_POINT *P, unsigned char *to, int form); /* form(ANSI 9.62): 1-compressed; 2-uncompressed; 3-hybrid */
+int ECP_bin2ecp(unsigned char *from, int len, EC_POINT *P, EC *E, BN_CTX *ctx);
+
+#ifdef SIMPLE
+int ECP_cmp(EC_POINT *P, EC_POINT *Q, BIGNUM *p, BN_CTX *ctx);
+int ECP_double(EC_POINT *R, EC_POINT *P, EC *E, BN_CTX *ctx);
+int ECP_add(EC_POINT *R, EC_POINT *P, EC_POINT *Q, EC *E, BN_CTX *ctx);
+ECP_PRECOMPUTE *ECP_precompute(int r, EC_POINT *P, EC *E, BN_CTX *ctx);
+int ECP_multiply(EC_POINT *R, BIGNUM *k, ECP_PRECOMPUTE *prec, EC *E, BN_CTX *ctx);
+#endif /* SIMPLE */
+
+#ifdef MONTGOMERY
+int ECP_to_montgomery(EC_POINT *P, BN_MONTGOMERY *mont, BN_CTX *ctx);
+int ECP_from_montgomery(EC_POINT *P, BN_MONTGOMERY *mont, BN_CTX *ctx);
+int ECP_mont_cmp(EC_POINT *P, EC_POINT *Q, BN_MONTGOMERY *mont, BN_CTX *ctx);
+int ECP_mont_double(EC_POINT *R, EC_POINT *P, EC *E, BN_MONTGOMERY *mont, BN_CTX *ctx);
+int ECP_mont_add(EC_POINT *R, EC_POINT *P, EC_POINT *Q, EC *E, BN_MONTGOMERY *mont, BN_CTX *ctx);
+ECP_PRECOMPUTE *ECP_mont_precompute(int r, EC_POINT *P, EC *E, BN_MONTGOMERY *mont, BN_CTX *ctx);
+int ECP_mont_multiply(EC_POINT *R, BIGNUM *k, ECP_PRECOMPUTE *prec, EC *E, BN_MONTGOMERY *mont, BN_CTX *ctx);
+int ECP_mont_multiply2(EC_POINT *R, BIGNUM *k, EC_POINT *P, EC *E, BN_MONTGOMERY *mont, BN_CTX *ctx);
+#endif /* MONTGOMERY */
+
+#endif
\ No newline at end of file diff --git a/crypto/ec/ec_point.c b/crypto/ec/ec_point.c new file mode 100644 index 0000000000..fee5078bf8 --- /dev/null +++ b/crypto/ec/ec_point.c @@ -0,0 +1,1461 @@ +/*
+ *
+ * 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;
+
+ |