From: Bodo Möller Date: Wed, 7 Mar 2001 19:54:35 +0000 (+0000) Subject: Some actual method functions (not enough yet to use the EC library, though), X-Git-Tag: OpenSSL_0_9_6a-beta2~17^2~69 X-Git-Url: https://git.librecmc.org/?a=commitdiff_plain;h=60428dbf0aa0dbacb2e18f7cf846af8d5ebafc82;p=oweals%2Fopenssl.git Some actual method functions (not enough yet to use the EC library, though), including EC arithmetics derived from Lenka Fibikova's code (with some additional optimizations). --- diff --git a/crypto/ec/ec.h b/crypto/ec/ec.h index 01234d714d..cc0dd788bd 100644 --- a/crypto/ec/ec.h +++ b/crypto/ec/ec.h @@ -149,6 +149,7 @@ int EC_POINT_make_affine(const EC_GROUP *, const EC_POINT *, BN_CTX *); /* Error codes for the EC functions. */ /* Function codes. */ +#define EC_F_EC_GFP_SIMPLE_GROUP_SET_GENERATOR 117 #define EC_F_EC_GROUP_CLEAR_FREE 103 #define EC_F_EC_GROUP_COPY 102 #define EC_F_EC_GROUP_FREE 104 diff --git a/crypto/ec/ec_err.c b/crypto/ec/ec_err.c index d0a1b9ae3c..770bce5373 100644 --- a/crypto/ec/ec_err.c +++ b/crypto/ec/ec_err.c @@ -66,6 +66,7 @@ #ifndef OPENSSL_NO_ERR static ERR_STRING_DATA EC_str_functs[]= { +{ERR_PACK(0,EC_F_EC_GFP_SIMPLE_GROUP_SET_GENERATOR,0), "EC_GFP_SIMPLE_GROUP_SET_GENERATOR"}, {ERR_PACK(0,EC_F_EC_GROUP_CLEAR_FREE,0), "EC_GROUP_clear_free"}, {ERR_PACK(0,EC_F_EC_GROUP_COPY,0), "EC_GROUP_copy"}, {ERR_PACK(0,EC_F_EC_GROUP_FREE,0), "EC_GROUP_free"}, diff --git a/crypto/ec/ec_lcl.h b/crypto/ec/ec_lcl.h index 09f749dd3c..231e8ca179 100644 --- a/crypto/ec/ec_lcl.h +++ b/crypto/ec/ec_lcl.h @@ -104,10 +104,10 @@ struct ec_method_st { /* internal functions */ - /* 'field_mult' and 'field_sqr' can be used by 'add' and 'dbl' so that + /* 'field_mul' and 'field_sqr' can be used by 'add' and 'dbl' so that * the same implementations of point operations can be used with different * optimized implementations of expensive field operations: */ - int (*field_mult)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *); + int (*field_mul)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *); int (*field_sqr)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); int (*field_encode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); /* e.g. to Montgomery */ @@ -128,7 +128,6 @@ struct ec_group_st { BIGNUM field; /* Field specification. * For curves over GF(p), this is the modulus. */ - void *field_data; /* method-specific (e.g., Montgomery structure) */ BIGNUM a, b; /* Curve coefficients. * (Here the assumption is that BIGNUMs can be used @@ -141,6 +140,8 @@ struct ec_group_st { EC_POINT *generator; /* optional */ BIGNUM order, cofactor; + + void *field_data; /* method-specific (e.g., Montgomery structure) */ } /* EC_GROUP */; @@ -197,7 +198,7 @@ int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX * int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *); int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *); int ec_GFp_simple_make_affine(const EC_GROUP *, const EC_POINT *, BN_CTX *); -int ec_GFp_simple_field_mult(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *); +int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *); int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); @@ -206,7 +207,8 @@ int ec_GFp_mont_group_init(EC_GROUP *); int ec_GFp_mont_group_set_curve_GFp(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *); void ec_GFp_mont_group_finish(EC_GROUP *); void ec_GFp_mont_group_clear_finish(EC_GROUP *); -int ec_GFp_mont_field_mult(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *); +int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *); +int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *); int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); @@ -217,7 +219,8 @@ int ec_GFp_recp_group_init(EC_GROUP *); int ec_GFp_recp_group_set_curve_GFp(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *); void ec_GFp_recp_group_finish(EC_GROUP *); void ec_GFp_recp_group_clear_finish(EC_GROUP *); -int ec_GFp_recp_field_mult(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *); +int ec_GFp_recp_group_copy(EC_GROUP *, const EC_GROUP *); +int ec_GFp_recp_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *); int ec_GFp_recp_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); int ec_GFp_recp_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); int ec_GFp_recp_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); @@ -228,7 +231,8 @@ int ec_GFp_nist_group_init(EC_GROUP *); int ec_GFp_nist_group_set_curve_GFp(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *); void ec_GFp_nist_group_finish(EC_GROUP *); void ec_GFp_nist_group_clear_finish(EC_GROUP *); -int ec_GFp_nist_field_mult(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *); +int ec_GFp_nist_group_copy(EC_GROUP *, const EC_GROUP *); +int ec_GFp_nist_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *); int ec_GFp_nist_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); int ec_GFp_nist_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); int ec_GFp_nist_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); diff --git a/crypto/ec/ecp_mont.c b/crypto/ec/ecp_mont.c index 407175fd9a..04d21e5c40 100644 --- a/crypto/ec/ecp_mont.c +++ b/crypto/ec/ecp_mont.c @@ -1,4 +1,3 @@ -/* TODO */ /* crypto/ec/ecp_mont.c */ /* ==================================================================== * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved. @@ -64,7 +63,7 @@ const EC_METHOD *EC_GFp_mont_method(void) ec_GFp_mont_group_set_curve_GFp, ec_GFp_mont_group_finish, ec_GFp_mont_group_clear_finish, - ec_GFp_simple_group_copy, + ec_GFp_mont_group_copy, ec_GFp_simple_group_set_generator, /* TODO: 'set' and 'get' functions for EC_GROUPs */ ec_GFp_simple_point_init, @@ -79,10 +78,52 @@ const EC_METHOD *EC_GFp_mont_method(void) ec_GFp_simple_is_at_infinity, ec_GFp_simple_is_on_curve, ec_GFp_simple_make_affine, - ec_GFp_mont_field_mult, + ec_GFp_mont_field_mul, ec_GFp_mont_field_sqr, ec_GFp_mont_field_encode, ec_GFp_mont_field_decode }; return &ret; } + + +int ec_GFp_mont_group_init(EC_GROUP *group) + { + int ok; + + ok = ec_GFp_simple_group_init(group); + group->field_data = NULL; + return ok; + } + + +int ec_GFp_mont_group_set_curve_GFp(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); +/* TODO */ + + +void ec_GFp_mont_group_finish(EC_GROUP *group); +/* TODO */ + + +void ec_GFp_mont_group_clear_finish(EC_GROUP *group); +/* TODO */ + + +int ec_GFp_mont_group_copy(EC_GROUP *dest, const EC_GROUP *src); +/* TODO */ + + +int ec_GFp_mont_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); +/* TODO */ + + +int ec_GFp_mont_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx); +/* TODO */ + + +int ec_GFp_mont_field_encode(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx); +/* TODO */ + + +int ec_GFp_mont_field_decode(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx); +/* TODO */ diff --git a/crypto/ec/ecp_nist.c b/crypto/ec/ecp_nist.c index f847234faf..16fea7cd55 100644 --- a/crypto/ec/ecp_nist.c +++ b/crypto/ec/ecp_nist.c @@ -1,4 +1,3 @@ -/* TODO */ /* crypto/ec/ecp_nist.c */ /* ==================================================================== * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved. @@ -64,7 +63,7 @@ const EC_METHOD *EC_GFp_nist_method(void) ec_GFp_nist_group_set_curve_GFp, ec_GFp_nist_group_finish, ec_GFp_nist_group_clear_finish, - ec_GFp_simple_group_copy, + ec_GFp_nist_group_copy, ec_GFp_simple_group_set_generator, /* TODO: 'set' and 'get' functions for EC_GROUPs */ ec_GFp_simple_point_init, @@ -79,10 +78,52 @@ const EC_METHOD *EC_GFp_nist_method(void) ec_GFp_simple_is_at_infinity, ec_GFp_simple_is_on_curve, ec_GFp_simple_make_affine, - ec_GFp_nist_field_mult, + ec_GFp_nist_field_mul, ec_GFp_nist_field_sqr, ec_GFp_nist_field_encode, ec_GFp_nist_field_decode }; return &ret; } + + +int ec_GFp_nist_group_init(EC_GROUP *group) + { + int ok; + + ok = ec_GFp_simple_group_init(group); + group->field_data = NULL; + return ok; + } + + +int ec_GFp_nist_group_set_curve_GFp(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); +/* TODO */ + + +void ec_GFp_nist_group_finish(EC_GROUP *group); +/* TODO */ + + +void ec_GFp_nist_group_clear_finish(EC_GROUP *group); +/* TODO */ + + +int ec_GFp_nist_group_copy(EC_GROUP *dest, const EC_GROUP *src); +/* TODO */ + + +int ec_GFp_nist_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); +/* TODO */ + + +int ec_GFp_nist_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx); +/* TODO */ + + +int ec_GFp_nist_field_encode(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx); +/* TODO */ + + +int ec_GFp_nist_field_decode(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx); +/* TODO */ diff --git a/crypto/ec/ecp_recp.c b/crypto/ec/ecp_recp.c index 47c8fdd237..b2a8da92b0 100644 --- a/crypto/ec/ecp_recp.c +++ b/crypto/ec/ecp_recp.c @@ -1,4 +1,3 @@ -/* TODO */ /* crypto/ec/ecp_recp.c */ /* ==================================================================== * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved. @@ -64,7 +63,7 @@ const EC_METHOD *EC_GFp_recp_method(void) ec_GFp_recp_group_set_curve_GFp, ec_GFp_recp_group_finish, ec_GFp_recp_group_clear_finish, - ec_GFp_simple_group_copy, + ec_GFp_recp_group_copy, ec_GFp_simple_group_set_generator, /* TODO: 'set' and 'get' functions for EC_GROUPs */ ec_GFp_simple_point_init, @@ -79,10 +78,52 @@ const EC_METHOD *EC_GFp_recp_method(void) ec_GFp_simple_is_at_infinity, ec_GFp_simple_is_on_curve, ec_GFp_simple_make_affine, - ec_GFp_recp_field_mult, + ec_GFp_recp_field_mul, ec_GFp_recp_field_sqr, ec_GFp_recp_field_encode, ec_GFp_recp_field_decode }; return &ret; } + + +int ec_GFp_recp_group_init(EC_GROUP *group) + { + int ok; + + ok = ec_GFp_simple_group_init(group); + group->field_data = NULL; + return ok; + } + + +int ec_GFp_recp_group_set_curve_GFp(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); +/* TODO */ + + +void ec_GFp_recp_group_finish(EC_GROUP *group); +/* TODO */ + + +void ec_GFp_recp_group_clear_finish(EC_GROUP *group); +/* TODO */ + + +int ec_GFp_recp_group_copy(EC_GROUP *dest, const EC_GROUP *src); +/* TODO */ + + +int ec_GFp_recp_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); +/* TODO */ + + +int ec_GFp_recp_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx); +/* TODO */ + + +int ec_GFp_recp_field_encode(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx); +/* TODO */ + + +int ec_GFp_recp_field_decode(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx); +/* TODO */ diff --git a/crypto/ec/ecp_smpl.c b/crypto/ec/ecp_smpl.c index 2d75348923..bae752841a 100644 --- a/crypto/ec/ecp_smpl.c +++ b/crypto/ec/ecp_smpl.c @@ -1,5 +1,6 @@ -/* TODO */ /* crypto/ec/ecp_smpl.c */ +/* Includes code written by Lenka Fibikova + * for the OpenSSL project. */ /* ==================================================================== * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved. * @@ -54,6 +55,8 @@ * */ +#include + #include "ec_lcl.h" @@ -79,10 +82,516 @@ const EC_METHOD *EC_GFp_simple_method(void) ec_GFp_simple_is_at_infinity, ec_GFp_simple_is_on_curve, ec_GFp_simple_make_affine, - ec_GFp_simple_field_mult, + ec_GFp_simple_field_mul, ec_GFp_simple_field_sqr, 0 /* field_encode */, 0 /* field_decode */ }; return &ret; } + + +int ec_GFp_simple_group_init(EC_GROUP *group) + { + BN_init(&group->field); + BN_init(&group->a); + BN_init(&group->b); + group->a_is_minus3 = 0; + group->generator = NULL; + BN_init(&group->order); + BN_init(&group->cofactor); + return 1; + } + + +int ec_GFp_simple_group_set_curve_GFp(EC_GROUP *group, + const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) + { + int ret = 0; + BN_CTX *new_ctx = NULL; + BIGNUM *tmp_a; + + if (ctx == NULL) + { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + BN_CTX_start(ctx); + + tmp_a = BN_CTX_get(ctx); + if (tmp_a == NULL) goto err; + + /* group->field */ + if (!BN_copy(&group->field, p)) goto err; + group->field.neg = 0; + + /* group->a */ + if (!BN_nnmod(tmp_a, a, p, ctx)) goto err; + if (group->meth->field_encode) + { if (!group->meth->field_encode(group, &group->a, tmp_a, ctx)) goto err; } + else + if (!BN_copy(&group->a, tmp_a)) goto err; + + /* group->b */ + if (!BN_nnmod(&group->b, b, p, ctx)) goto err; + if (group->meth->field_encode) + if (!group->meth->field_encode(group, &group->b, &group->b, ctx)) goto err; + + /* group->a_is_minus3 */ + if (!BN_add_word(tmp_a, 3)) goto err; + group->a_is_minus3 = (0 == BN_cmp(tmp_a, &group->field)); + + ret = 1; + + err: + BN_CTX_end(ctx); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + return ret; + } + + +void ec_GFp_simple_group_finish(EC_GROUP *group) + { + BN_free(&group->field); + BN_free(&group->a); + BN_free(&group->b); + if (group->generator != NULL) + EC_POINT_free(group->generator); + BN_free(&group->order); + BN_free(&group->cofactor); + } + + +void ec_GFp_simple_group_clear_finish(EC_GROUP *group) + { + BN_clear_free(&group->field); + BN_clear_free(&group->a); + BN_clear_free(&group->b); + if (group->generator != NULL) + { + EC_POINT_clear_free(group->generator); + group->generator = NULL; + } + BN_clear_free(&group->order); + BN_clear_free(&group->cofactor); + } + + +int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src) + { + if (!BN_copy(&dest->field, &src->field)) return 0; + if (!BN_copy(&dest->a, &src->a)) return 0; + if (!BN_copy(&dest->b, &src->b)) return 0; + + dest->a_is_minus3 = src->a_is_minus3; + + if (src->generator != NULL) + { + if (dest->generator == NULL) + { + dest->generator = EC_POINT_new(dest); + if (dest->generator == NULL) return 0; + } + if (!EC_POINT_copy(dest->generator, src->generator)) return 0; + } + else + { + /* src->generator == NULL */ + if (dest->generator != NULL) + { + EC_POINT_clear_free(dest->generator); + dest->generator = NULL; + } + } + + if (!BN_copy(&dest->order, &src->order)) return 0; + if (!BN_copy(&dest->cofactor, &src->cofactor)) return 0; + + return 1; + } + + +int ec_GFp_simple_group_set_generator(EC_GROUP *group, const EC_POINT *generator, + const BIGNUM *order, const BIGNUM *cofactor) + { + if (generator) + { + ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_GENERATOR, ERR_R_PASSED_NULL_PARAMETER); + return 0 ; + } + + if (group->generator == NULL) + { + group->generator = EC_POINT_new(group); + if (group->generator == NULL) return 0; + } + if (!EC_POINT_copy(group->generator, generator)) return 0; + + if (order != NULL) + { if (!BN_copy(&group->order, order)) return 0; } + else + { if (!BN_zero(&group->order)) return 0; } + + if (cofactor != NULL) + { if (!BN_copy(&group->cofactor, cofactor)) return 0; } + else + { if (!BN_zero(&group->cofactor)) return 0; } + + return 1; + } + + +/* TODO: 'set' and 'get' functions for EC_GROUPs */ + + +int ec_GFp_simple_point_init(EC_POINT *point) + { + BN_init(&point->X); + BN_init(&point->Y); + BN_init(&point->Z); + point->Z_is_one = 0; + + return 1; + } + + +void ec_GFp_simple_point_finish(EC_POINT *point) + { + BN_free(&point->X); + BN_free(&point->Y); + BN_free(&point->Z); + } + + +void ec_GFp_simple_point_clear_finish(EC_POINT *point) + { + BN_clear_free(&point->X); + BN_clear_free(&point->Y); + BN_clear_free(&point->Z); + point->Z_is_one = 0; + } + + +int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src) + { + if (!BN_copy(&dest->X, &src->X)) return 0; + if (!BN_copy(&dest->Y, &src->Y)) return 0; + if (!BN_copy(&dest->Z, &src->Z)) return 0; + dest->Z_is_one = src->Z_is_one; + + return 1; + } + + +/* TODO: 'set' and 'get' functions for EC_POINTs */ + + +size_t ec_GFp_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form, + unsigned char *buf, size_t len, BN_CTX *ctx); +/* TODO */ + + +int ec_GFp_simple_oct2point(const EC_GROUP *group, EC_POINT *point, + const unsigned char *buf, size_t len, BN_CTX *); +/* TODO */ + + +int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx) + { + int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); + int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); + const BIGNUM *p; + BN_CTX *new_ctx = NULL; + BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6; + int ret = 0; + + if (a == b) + return EC_POINT_dbl(group, r, a, ctx); + if (EC_POINT_is_at_infinity(group, a)) + return EC_POINT_copy(r, b); + if (EC_POINT_is_at_infinity(group, b)) + return EC_POINT_copy(r, a); + + field_mul = group->meth->field_mul; + field_sqr = group->meth->field_sqr; + p = &group->field; + + if (ctx == NULL) + { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + 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 end; + + /* n1, n2 */ + if (b->Z_is_one) + { + if (!BN_copy(n1, &a->X)) goto end; + if (!BN_copy(n2, &a->Y)) goto end; + /* n1 = X_a */ + /* n2 = Y_a */ + } + else + { + if (!field_sqr(group, n0, &b->Z, ctx)) goto end; + if (!field_mul(group, n1, &a->X, n0, ctx)) goto end; + /* n1 = X_a * Z_b^2 */ + + if (!field_mul(group, n0, n0, &b->Z, ctx)) goto end; + if (!field_mul(group, n2, &a->Y, n0, ctx)) goto end; + /* n2 = Y_a * Z_b^3 */ + } + + /* n3, n4 */ + if (a->Z_is_one) + { + if (!BN_copy(n3, &b->X)) goto end; + if (!BN_copy(n4, &b->Y)) goto end; + /* n3 = X_b */ + /* n4 = Y_b */ + } + else + { + if (!field_sqr(group, n0, &a->Z, ctx)) goto end; + if (!field_mul(group, n3, &b->X, n0, ctx)) goto end; + /* n3 = X_b * Z_a^2 */ + + if (!field_mul(group, n0, n0, &a->Z, ctx)) goto end; + if (!field_mul(group, n4, &b->Y, n0, ctx)) goto end; + /* n4 = Y_b * Z_a^3 */ + } + + /* n5, n6 */ + if (!BN_mod_sub_quick(n5, n1, n3, p)) goto end; + if (!BN_mod_sub_quick(n6, n2, n4, p)) goto end; + /* n5 = n1 - n3 */ + /* n6 = n2 - n4 */ + + if (BN_is_zero(n5)) + { + if (BN_is_zero(n6)) + { + /* a is the same point as b */ + BN_CTX_end(ctx); + ctx = NULL; + ret = EC_POINT_dbl(group, r, a, ctx); + goto end; + } + else + { + /* a is the inverse of b */ + if (!BN_zero(&r->Z)) goto end; + r->Z_is_one = 0; + ret = 1; + goto end; + } + } + + /* 'n7', 'n8' */ + if (!BN_mod_add_quick(n1, n1, n3, p)) goto end; + if (!BN_mod_add_quick(n2, n2, n4, p)) goto end; + /* 'n7' = n1 + n3 */ + /* 'n8' = n2 + n4 */ + + /* Z_r */ + if (a->Z_is_one && b->Z_is_one) + { + if (!BN_copy(&r->Z, n5)) goto end; + } + else + { + if (a->Z_is_one) + { if (!BN_copy(n0, &b->Z)) goto end; } + else if (b->Z_is_one) + { if (!BN_copy(n0, &a->Z)) goto end; } + else + { if (!field_mul(group, n0, &a->Z, &b->Z, ctx)) goto end; } + if (!field_mul(group, &r->Z, n0, n5, ctx)) goto end; + } + r->Z_is_one = 0; + /* Z_r = Z_a * Z_b * n5 */ + + /* X_r */ + if (!field_sqr(group, n0, n6, ctx)) goto end; + if (!field_sqr(group, n4, n5, ctx)) goto end; + if (!field_mul(group, n3, n1, n4, ctx)) goto end; + if (!BN_mod_sub_quick(&r->X, n0, n3, p)) goto end; + /* X_r = n6^2 - n5^2 * 'n7' */ + + /* 'n9' */ + if (!BN_mod_lshift1_quick(n0, &r->X, p)) goto end; + if (!BN_mod_sub_quick(n0, n3, n0, p)) goto end; + /* n9 = n5^2 * 'n7' - 2 * X_r */ + + /* Y_r */ + if (!field_mul(group, n0, n0, n6, ctx)) goto end; + if (!field_mul(group, n5, n4, n5, ctx)) goto end; /* now n5 is n5^3 */ + if (!field_mul(group, n1, n2, n5, ctx)) goto end; + if (!BN_mod_sub_quick(n0, n0, n1, p)) goto end; + if (BN_is_odd(n0)) + if (!BN_add(n0, n0, p)) goto end; + /* now 0 <= n0 < 2*p, and n0 is even */ + if (!BN_rshift1(&r->Y, n0)) goto end; + /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */ + + ret = 1; + + end: + if (ctx) /* otherwise we already called BN_CTX_end */ + BN_CTX_end(ctx); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + return ret; + } + + +int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx) + { + int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); + int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); + const BIGNUM *p; + BN_CTX *new_ctx = NULL; + BIGNUM *n0, *n1, *n2, *n3; + int ret = 0; + + if (EC_POINT_is_at_infinity(group, a)) + { + if (!BN_zero(&r->Z)) return 0; + r->Z_is_one = 0; + return 1; + } + + field_mul = group->meth->field_mul; + field_sqr = group->meth->field_sqr; + p = &group->field; + + if (ctx == NULL) + { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + 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; + + /* TODO: optimization for group->a_is_minus3 */ + + /* n1 */ + if (a->Z_is_one) + { + if (!field_sqr(group, n0, &a->X, ctx)) goto err; + if (!BN_mod_lshift1_quick(n1, n0, p)) goto err; + if (!BN_mod_add_quick(n0, n0, n1, p)) goto err; + if (!BN_mod_add_quick(n1, n0, &group->a, p)) goto err; + /* n1 = 3 * X_a^2 + a_curve */ + } + else if (group->a_is_minus3) + { + if (!field_sqr(group, n1, &a->Z, ctx)) goto err; + if (!BN_mod_add_quick(n0, &a->X, n1, p)) goto err; + if (!BN_mod_sub_quick(n2, &a->X, n1, p)) goto err; + if (!field_mul(group, n1, n0, n2, ctx)) goto err; + if (!BN_mod_lshift1_quick(n0, n1, p)) goto err; + if (!BN_mod_add_quick(n1, n0, n1, p)) goto err; + /* n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2) + * = 3 * X_a^2 - 3 * Z_a^4 */ + } + else + { + if (!field_sqr(group, n0, &a->X, ctx)) goto err; + if (!BN_mod_lshift1_quick(n1, n0, p)) goto err; + if (!BN_mod_add_quick(n0, n0, n1, p)) goto err; + if (!field_sqr(group, n1, &a->Z, ctx)) goto err; + if (!field_sqr(group, n1, n1, ctx)) goto err; + if (!field_mul(group, n1, n1, &group->a, ctx)) goto err; + if (!BN_mod_add_quick(n1, n1, n0, p)) goto err; + /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */ + } + + /* Z_r */ + if (a->Z_is_one) + { + if (!BN_copy(n0, &a->Y)) goto err; + } + else + { + if (!field_mul(group, n0, &a->Y, &a->Z, ctx)) goto err; + } + if (!BN_mod_lshift1_quick(&r->Z, n0, p)) goto err; + r->Z_is_one = 0; + /* Z_r = 2 * Y_a * Z_a */ + + /* n2 */ + if (!field_sqr(group, n3, &a->Y, ctx)) goto err; + if (!field_mul(group, n2, &a->X, n3, ctx)) goto err; + if (!BN_mod_lshift_quick(n2, n2, 2, p)) goto err; + /* n2 = 4 * X_a * Y_a^2 */ + + /* X_r */ + if (!BN_mod_lshift1_quick(n0, n2, p)) goto err; + if (!field_sqr(group, &r->X, n1, ctx)) goto err; + if (!BN_mod_sub_quick(&r->X, &r->X, n0, p)) goto err; + /* X_r = n1^2 - 2 * n2 */ + + /* n3 */ + if (!field_sqr(group, n0, n3, ctx)) goto err; + if (!BN_mod_lshift_quick(n3, n0, 3, p)) goto err; + /* n3 = 8 * Y_a^4 */ + + /* Y_r */ + if (!BN_mod_sub_quick(n0, n2, &r->X, p)) goto err; + if (!field_mul(group, n0, n1, n0, ctx)) goto err; + if (!BN_mod_sub_quick(&r->Y, n0, n3, p)) goto err; + /* Y_r = n1 * (n2 - X_r) - n3 */ + + ret = 1; + + err: + BN_CTX_end(ctx); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + return ret; + } + + +int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point) + { + return BN_is_zero(&point->Z); + } + + +int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx); +/* TODO */ + + +int ec_GFp_simple_make_affine(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx); +/* TODO */ + + +int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) + { + return BN_mod_mul(r, a, b, &group->field, ctx); + } + + +int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx) + { + return BN_mod_sqr(r, a, &group->field, ctx); + }