| /* |
| * Copyright 2001-2018 The OpenSSL Project Authors. All Rights Reserved. |
| * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved |
| * |
| * Licensed under the OpenSSL license (the "License"). You may not use |
| * this file except in compliance with the License. You can obtain a copy |
| * in the file LICENSE in the source distribution or at |
| * https://www.openssl.org/source/license.html |
| */ |
| |
| #include <stdlib.h> |
| |
| #include <openssl/obj_mac.h> |
| #include <openssl/ec.h> |
| #include <openssl/bn.h> |
| #include "internal/refcount.h" |
| #include "internal/ec_int.h" |
| #include "curve448/curve448_lcl.h" |
| |
| #if defined(__SUNPRO_C) |
| # if __SUNPRO_C >= 0x520 |
| # pragma error_messages (off,E_ARRAY_OF_INCOMPLETE_NONAME,E_ARRAY_OF_INCOMPLETE) |
| # endif |
| #endif |
| |
| /* Use default functions for poin2oct, oct2point and compressed coordinates */ |
| #define EC_FLAGS_DEFAULT_OCT 0x1 |
| |
| /* Use custom formats for EC_GROUP, EC_POINT and EC_KEY */ |
| #define EC_FLAGS_CUSTOM_CURVE 0x2 |
| |
| /* Curve does not support signing operations */ |
| #define EC_FLAGS_NO_SIGN 0x4 |
| |
| /* |
| * Structure details are not part of the exported interface, so all this may |
| * change in future versions. |
| */ |
| |
| struct ec_method_st { |
| /* Various method flags */ |
| int flags; |
| /* used by EC_METHOD_get_field_type: */ |
| int field_type; /* a NID */ |
| /* |
| * used by EC_GROUP_new, EC_GROUP_free, EC_GROUP_clear_free, |
| * EC_GROUP_copy: |
| */ |
| int (*group_init) (EC_GROUP *); |
| void (*group_finish) (EC_GROUP *); |
| void (*group_clear_finish) (EC_GROUP *); |
| int (*group_copy) (EC_GROUP *, const EC_GROUP *); |
| /* used by EC_GROUP_set_curve, EC_GROUP_get_curve: */ |
| int (*group_set_curve) (EC_GROUP *, const BIGNUM *p, const BIGNUM *a, |
| const BIGNUM *b, BN_CTX *); |
| int (*group_get_curve) (const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, |
| BN_CTX *); |
| /* used by EC_GROUP_get_degree: */ |
| int (*group_get_degree) (const EC_GROUP *); |
| int (*group_order_bits) (const EC_GROUP *); |
| /* used by EC_GROUP_check: */ |
| int (*group_check_discriminant) (const EC_GROUP *, BN_CTX *); |
| /* |
| * used by EC_POINT_new, EC_POINT_free, EC_POINT_clear_free, |
| * EC_POINT_copy: |
| */ |
| int (*point_init) (EC_POINT *); |
| void (*point_finish) (EC_POINT *); |
| void (*point_clear_finish) (EC_POINT *); |
| int (*point_copy) (EC_POINT *, const EC_POINT *); |
| /*- |
| * used by EC_POINT_set_to_infinity, |
| * EC_POINT_set_Jprojective_coordinates_GFp, |
| * EC_POINT_get_Jprojective_coordinates_GFp, |
| * EC_POINT_set_affine_coordinates, |
| * EC_POINT_get_affine_coordinates, |
| * EC_POINT_set_compressed_coordinates: |
| */ |
| int (*point_set_to_infinity) (const EC_GROUP *, EC_POINT *); |
| int (*point_set_Jprojective_coordinates_GFp) (const EC_GROUP *, |
| EC_POINT *, const BIGNUM *x, |
| const BIGNUM *y, |
| const BIGNUM *z, BN_CTX *); |
| int (*point_get_Jprojective_coordinates_GFp) (const EC_GROUP *, |
| const EC_POINT *, BIGNUM *x, |
| BIGNUM *y, BIGNUM *z, |
| BN_CTX *); |
| int (*point_set_affine_coordinates) (const EC_GROUP *, EC_POINT *, |
| const BIGNUM *x, const BIGNUM *y, |
| BN_CTX *); |
| int (*point_get_affine_coordinates) (const EC_GROUP *, const EC_POINT *, |
| BIGNUM *x, BIGNUM *y, BN_CTX *); |
| int (*point_set_compressed_coordinates) (const EC_GROUP *, EC_POINT *, |
| const BIGNUM *x, int y_bit, |
| BN_CTX *); |
| /* used by EC_POINT_point2oct, EC_POINT_oct2point: */ |
| size_t (*point2oct) (const EC_GROUP *, const EC_POINT *, |
| point_conversion_form_t form, unsigned char *buf, |
| size_t len, BN_CTX *); |
| int (*oct2point) (const EC_GROUP *, EC_POINT *, const unsigned char *buf, |
| size_t len, BN_CTX *); |
| /* used by EC_POINT_add, EC_POINT_dbl, ECP_POINT_invert: */ |
| int (*add) (const EC_GROUP *, EC_POINT *r, const EC_POINT *a, |
| const EC_POINT *b, BN_CTX *); |
| int (*dbl) (const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *); |
| int (*invert) (const EC_GROUP *, EC_POINT *, BN_CTX *); |
| /* |
| * used by EC_POINT_is_at_infinity, EC_POINT_is_on_curve, EC_POINT_cmp: |
| */ |
| int (*is_at_infinity) (const EC_GROUP *, const EC_POINT *); |
| int (*is_on_curve) (const EC_GROUP *, const EC_POINT *, BN_CTX *); |
| int (*point_cmp) (const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, |
| BN_CTX *); |
| /* used by EC_POINT_make_affine, EC_POINTs_make_affine: */ |
| int (*make_affine) (const EC_GROUP *, EC_POINT *, BN_CTX *); |
| int (*points_make_affine) (const EC_GROUP *, size_t num, EC_POINT *[], |
| BN_CTX *); |
| /* |
| * used by EC_POINTs_mul, EC_POINT_mul, EC_POINT_precompute_mult, |
| * EC_POINT_have_precompute_mult (default implementations are used if the |
| * 'mul' pointer is 0): |
| */ |
| /*- |
| * mul() calculates the value |
| * |
| * r := generator * scalar |
| * + points[0] * scalars[0] |
| * + ... |
| * + points[num-1] * scalars[num-1]. |
| * |
| * For a fixed point multiplication (scalar != NULL, num == 0) |
| * or a variable point multiplication (scalar == NULL, num == 1), |
| * mul() must use a constant time algorithm: in both cases callers |
| * should provide an input scalar (either scalar or scalars[0]) |
| * in the range [0, ec_group_order); for robustness, implementers |
| * should handle the case when the scalar has not been reduced, but |
| * may treat it as an unusual input, without any constant-timeness |
| * guarantee. |
| */ |
| int (*mul) (const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, |
| size_t num, const EC_POINT *points[], const BIGNUM *scalars[], |
| BN_CTX *); |
| int (*precompute_mult) (EC_GROUP *group, BN_CTX *); |
| int (*have_precompute_mult) (const EC_GROUP *group); |
| /* internal functions */ |
| /* |
| * 'field_mul', 'field_sqr', and 'field_div' 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_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_div) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a, |
| const BIGNUM *b, BN_CTX *); |
| /* e.g. to Montgomery */ |
| int (*field_encode) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a, |
| BN_CTX *); |
| /* e.g. from Montgomery */ |
| int (*field_decode) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a, |
| BN_CTX *); |
| int (*field_set_to_one) (const EC_GROUP *, BIGNUM *r, BN_CTX *); |
| /* private key operations */ |
| size_t (*priv2oct)(const EC_KEY *eckey, unsigned char *buf, size_t len); |
| int (*oct2priv)(EC_KEY *eckey, const unsigned char *buf, size_t len); |
| int (*set_private)(EC_KEY *eckey, const BIGNUM *priv_key); |
| int (*keygen)(EC_KEY *eckey); |
| int (*keycheck)(const EC_KEY *eckey); |
| int (*keygenpub)(EC_KEY *eckey); |
| int (*keycopy)(EC_KEY *dst, const EC_KEY *src); |
| void (*keyfinish)(EC_KEY *eckey); |
| /* custom ECDH operation */ |
| int (*ecdh_compute_key)(unsigned char **pout, size_t *poutlen, |
| const EC_POINT *pub_key, const EC_KEY *ecdh); |
| /* Inverse modulo order */ |
| int (*field_inverse_mod_ord)(const EC_GROUP *, BIGNUM *r, |
| const BIGNUM *x, BN_CTX *); |
| int (*blind_coordinates)(const EC_GROUP *group, EC_POINT *p, BN_CTX *ctx); |
| int (*ladder_pre)(const EC_GROUP *group, |
| EC_POINT *r, EC_POINT *s, |
| EC_POINT *p, BN_CTX *ctx); |
| int (*ladder_step)(const EC_GROUP *group, |
| EC_POINT *r, EC_POINT *s, |
| EC_POINT *p, BN_CTX *ctx); |
| int (*ladder_post)(const EC_GROUP *group, |
| EC_POINT *r, EC_POINT *s, |
| EC_POINT *p, BN_CTX *ctx); |
| }; |
| |
| /* |
| * Types and functions to manipulate pre-computed values. |
| */ |
| typedef struct nistp224_pre_comp_st NISTP224_PRE_COMP; |
| typedef struct nistp256_pre_comp_st NISTP256_PRE_COMP; |
| typedef struct nistp521_pre_comp_st NISTP521_PRE_COMP; |
| typedef struct nistz256_pre_comp_st NISTZ256_PRE_COMP; |
| typedef struct ec_pre_comp_st EC_PRE_COMP; |
| |
| struct ec_group_st { |
| const EC_METHOD *meth; |
| EC_POINT *generator; /* optional */ |
| BIGNUM *order, *cofactor; |
| int curve_name; /* optional NID for named curve */ |
| int asn1_flag; /* flag to control the asn1 encoding */ |
| point_conversion_form_t asn1_form; |
| unsigned char *seed; /* optional seed for parameters (appears in |
| * ASN1) */ |
| size_t seed_len; |
| /* |
| * The following members are handled by the method functions, even if |
| * they appear generic |
| */ |
| /* |
| * Field specification. For curves over GF(p), this is the modulus; for |
| * curves over GF(2^m), this is the irreducible polynomial defining the |
| * field. |
| */ |
| BIGNUM *field; |
| /* |
| * Field specification for curves over GF(2^m). The irreducible f(t) is |
| * then of the form: t^poly[0] + t^poly[1] + ... + t^poly[k] where m = |
| * poly[0] > poly[1] > ... > poly[k] = 0. The array is terminated with |
| * poly[k+1]=-1. All elliptic curve irreducibles have at most 5 non-zero |
| * terms. |
| */ |
| int poly[6]; |
| /* |
| * Curve coefficients. (Here the assumption is that BIGNUMs can be used |
| * or abused for all kinds of fields, not just GF(p).) For characteristic |
| * > 3, the curve is defined by a Weierstrass equation of the form y^2 = |
| * x^3 + a*x + b. For characteristic 2, the curve is defined by an |
| * equation of the form y^2 + x*y = x^3 + a*x^2 + b. |
| */ |
| BIGNUM *a, *b; |
| /* enable optimized point arithmetics for special case */ |
| int a_is_minus3; |
| /* method-specific (e.g., Montgomery structure) */ |
| void *field_data1; |
| /* method-specific */ |
| void *field_data2; |
| /* method-specific */ |
| int (*field_mod_func) (BIGNUM *, const BIGNUM *, const BIGNUM *, |
| BN_CTX *); |
| /* data for ECDSA inverse */ |
| BN_MONT_CTX *mont_data; |
| |
| /* |
| * Precomputed values for speed. The PCT_xxx names match the |
| * pre_comp.xxx union names; see the SETPRECOMP and HAVEPRECOMP |
| * macros, below. |
| */ |
| enum { |
| PCT_none, |
| PCT_nistp224, PCT_nistp256, PCT_nistp521, PCT_nistz256, |
| PCT_ec |
| } pre_comp_type; |
| union { |
| NISTP224_PRE_COMP *nistp224; |
| NISTP256_PRE_COMP *nistp256; |
| NISTP521_PRE_COMP *nistp521; |
| NISTZ256_PRE_COMP *nistz256; |
| EC_PRE_COMP *ec; |
| } pre_comp; |
| }; |
| |
| #define SETPRECOMP(g, type, pre) \ |
| g->pre_comp_type = PCT_##type, g->pre_comp.type = pre |
| #define HAVEPRECOMP(g, type) \ |
| g->pre_comp_type == PCT_##type && g->pre_comp.type != NULL |
| |
| struct ec_key_st { |
| const EC_KEY_METHOD *meth; |
| ENGINE *engine; |
| int version; |
| EC_GROUP *group; |
| EC_POINT *pub_key; |
| BIGNUM *priv_key; |
| unsigned int enc_flag; |
| point_conversion_form_t conv_form; |
| CRYPTO_REF_COUNT references; |
| int flags; |
| CRYPTO_EX_DATA ex_data; |
| CRYPTO_RWLOCK *lock; |
| }; |
| |
| struct ec_point_st { |
| const EC_METHOD *meth; |
| /* NID for the curve if known */ |
| int curve_name; |
| /* |
| * All members except 'meth' are handled by the method functions, even if |
| * they appear generic |
| */ |
| BIGNUM *X; |
| BIGNUM *Y; |
| BIGNUM *Z; /* Jacobian projective coordinates: * (X, Y, |
| * Z) represents (X/Z^2, Y/Z^3) if Z != 0 */ |
| int Z_is_one; /* enable optimized point arithmetics for |
| * special case */ |
| }; |
| |
| static ossl_inline int ec_point_is_compat(const EC_POINT *point, |
| const EC_GROUP *group) |
| { |
| if (group->meth != point->meth |
| || (group->curve_name != 0 |
| && point->curve_name != 0 |
| && group->curve_name != point->curve_name)) |
| return 0; |
| |
| return 1; |
| } |
| |
| NISTP224_PRE_COMP *EC_nistp224_pre_comp_dup(NISTP224_PRE_COMP *); |
| NISTP256_PRE_COMP *EC_nistp256_pre_comp_dup(NISTP256_PRE_COMP *); |
| NISTP521_PRE_COMP *EC_nistp521_pre_comp_dup(NISTP521_PRE_COMP *); |
| NISTZ256_PRE_COMP *EC_nistz256_pre_comp_dup(NISTZ256_PRE_COMP *); |
| NISTP256_PRE_COMP *EC_nistp256_pre_comp_dup(NISTP256_PRE_COMP *); |
| EC_PRE_COMP *EC_ec_pre_comp_dup(EC_PRE_COMP *); |
| |
| void EC_pre_comp_free(EC_GROUP *group); |
| void EC_nistp224_pre_comp_free(NISTP224_PRE_COMP *); |
| void EC_nistp256_pre_comp_free(NISTP256_PRE_COMP *); |
| void EC_nistp521_pre_comp_free(NISTP521_PRE_COMP *); |
| void EC_nistz256_pre_comp_free(NISTZ256_PRE_COMP *); |
| void EC_ec_pre_comp_free(EC_PRE_COMP *); |
| |
| /* |
| * method functions in ec_mult.c (ec_lib.c uses these as defaults if |
| * group->method->mul is 0) |
| */ |
| int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, |
| size_t num, const EC_POINT *points[], const BIGNUM *scalars[], |
| BN_CTX *); |
| int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *); |
| int ec_wNAF_have_precompute_mult(const EC_GROUP *group); |
| |
| /* method functions in ecp_smpl.c */ |
| int ec_GFp_simple_group_init(EC_GROUP *); |
| void ec_GFp_simple_group_finish(EC_GROUP *); |
| void ec_GFp_simple_group_clear_finish(EC_GROUP *); |
| int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *); |
| int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, |
| const BIGNUM *a, const BIGNUM *b, BN_CTX *); |
| int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, |
| BIGNUM *b, BN_CTX *); |
| int ec_GFp_simple_group_get_degree(const EC_GROUP *); |
| int ec_GFp_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *); |
| int ec_GFp_simple_point_init(EC_POINT *); |
| void ec_GFp_simple_point_finish(EC_POINT *); |
| void ec_GFp_simple_point_clear_finish(EC_POINT *); |
| int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *); |
| int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *); |
| int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *, |
| EC_POINT *, const BIGNUM *x, |
| const BIGNUM *y, |
| const BIGNUM *z, BN_CTX *); |
| int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *, |
| const EC_POINT *, BIGNUM *x, |
| BIGNUM *y, BIGNUM *z, |
| BN_CTX *); |
| int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *, |
| const BIGNUM *x, |
| const BIGNUM *y, BN_CTX *); |
| int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *, |
| const EC_POINT *, BIGNUM *x, |
| BIGNUM *y, BN_CTX *); |
| int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *, |
| const BIGNUM *x, int y_bit, |
| BN_CTX *); |
| size_t ec_GFp_simple_point2oct(const EC_GROUP *, const EC_POINT *, |
| point_conversion_form_t form, |
| unsigned char *buf, size_t len, BN_CTX *); |
| int ec_GFp_simple_oct2point(const EC_GROUP *, EC_POINT *, |
| const unsigned char *buf, size_t len, BN_CTX *); |
| int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, |
| const EC_POINT *b, BN_CTX *); |
| int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, |
| BN_CTX *); |
| int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, 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_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, |
| BN_CTX *); |
| int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *); |
| int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num, |
| EC_POINT *[], 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 *); |
| int ec_GFp_simple_blind_coordinates(const EC_GROUP *group, EC_POINT *p, |
| BN_CTX *ctx); |
| int ec_GFp_simple_ladder_pre(const EC_GROUP *group, |
| EC_POINT *r, EC_POINT *s, |
| EC_POINT *p, BN_CTX *ctx); |
| int ec_GFp_simple_ladder_step(const EC_GROUP *group, |
| EC_POINT *r, EC_POINT *s, |
| EC_POINT *p, BN_CTX *ctx); |
| int ec_GFp_simple_ladder_post(const EC_GROUP *group, |
| EC_POINT *r, EC_POINT *s, |
| EC_POINT *p, BN_CTX *ctx); |
| |
| /* method functions in ecp_mont.c */ |
| int ec_GFp_mont_group_init(EC_GROUP *); |
| int ec_GFp_mont_group_set_curve(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_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 *); |
| int ec_GFp_mont_field_set_to_one(const EC_GROUP *, BIGNUM *r, BN_CTX *); |
| |
| /* method functions in ecp_nist.c */ |
| int ec_GFp_nist_group_copy(EC_GROUP *dest, const EC_GROUP *src); |
| int ec_GFp_nist_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, |
| const BIGNUM *b, BN_CTX *); |
| 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 *); |
| |
| /* method functions in ec2_smpl.c */ |
| int ec_GF2m_simple_group_init(EC_GROUP *); |
| void ec_GF2m_simple_group_finish(EC_GROUP *); |
| void ec_GF2m_simple_group_clear_finish(EC_GROUP *); |
| int ec_GF2m_simple_group_copy(EC_GROUP *, const EC_GROUP *); |
| int ec_GF2m_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, |
| const BIGNUM *a, const BIGNUM *b, |
| BN_CTX *); |
| int ec_GF2m_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, |
| BIGNUM *b, BN_CTX *); |
| int ec_GF2m_simple_group_get_degree(const EC_GROUP *); |
| int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *); |
| int ec_GF2m_simple_point_init(EC_POINT *); |
| void ec_GF2m_simple_point_finish(EC_POINT *); |
| void ec_GF2m_simple_point_clear_finish(EC_POINT *); |
| int ec_GF2m_simple_point_copy(EC_POINT *, const EC_POINT *); |
| int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *); |
| int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *, |
| const BIGNUM *x, |
| const BIGNUM *y, BN_CTX *); |
| int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *, |
| const EC_POINT *, BIGNUM *x, |
| BIGNUM *y, BN_CTX *); |
| int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *, |
| const BIGNUM *x, int y_bit, |
| BN_CTX *); |
| size_t ec_GF2m_simple_point2oct(const EC_GROUP *, const EC_POINT *, |
| point_conversion_form_t form, |
| unsigned char *buf, size_t len, BN_CTX *); |
| int ec_GF2m_simple_oct2point(const EC_GROUP *, EC_POINT *, |
| const unsigned char *buf, size_t len, BN_CTX *); |
| int ec_GF2m_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, |
| const EC_POINT *b, BN_CTX *); |
| int ec_GF2m_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, |
| BN_CTX *); |
| int ec_GF2m_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *); |
| int ec_GF2m_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *); |
| int ec_GF2m_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *); |
| int ec_GF2m_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, |
| BN_CTX *); |
| int ec_GF2m_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *); |
| int ec_GF2m_simple_points_make_affine(const EC_GROUP *, size_t num, |
| EC_POINT *[], BN_CTX *); |
| int ec_GF2m_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, |
| const BIGNUM *b, BN_CTX *); |
| int ec_GF2m_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, |
| BN_CTX *); |
| int ec_GF2m_simple_field_div(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, |
| const BIGNUM *b, BN_CTX *); |
| |
| #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 |
| /* method functions in ecp_nistp224.c */ |
| int ec_GFp_nistp224_group_init(EC_GROUP *group); |
| int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p, |
| const BIGNUM *a, const BIGNUM *n, |
| BN_CTX *); |
| int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group, |
| const EC_POINT *point, |
| BIGNUM *x, BIGNUM *y, |
| BN_CTX *ctx); |
| int ec_GFp_nistp224_mul(const EC_GROUP *group, EC_POINT *r, |
| const BIGNUM *scalar, size_t num, |
| const EC_POINT *points[], const BIGNUM *scalars[], |
| BN_CTX *); |
| int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r, |
| const BIGNUM *scalar, size_t num, |
| const EC_POINT *points[], |
| const BIGNUM *scalars[], BN_CTX *ctx); |
| int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx); |
| int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group); |
| |
| /* method functions in ecp_nistp256.c */ |
| int ec_GFp_nistp256_group_init(EC_GROUP *group); |
| int ec_GFp_nistp256_group_set_curve(EC_GROUP *group, const BIGNUM *p, |
| const BIGNUM *a, const BIGNUM *n, |
| BN_CTX *); |
| int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group, |
| const EC_POINT *point, |
| BIGNUM *x, BIGNUM *y, |
| BN_CTX *ctx); |
| int ec_GFp_nistp256_mul(const EC_GROUP *group, EC_POINT *r, |
| const BIGNUM *scalar, size_t num, |
| const EC_POINT *points[], const BIGNUM *scalars[], |
| BN_CTX *); |
| int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r, |
| const BIGNUM *scalar, size_t num, |
| const EC_POINT *points[], |
| const BIGNUM *scalars[], BN_CTX *ctx); |
| int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx); |
| int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group); |
| |
| /* method functions in ecp_nistp521.c */ |
| int ec_GFp_nistp521_group_init(EC_GROUP *group); |
| int ec_GFp_nistp521_group_set_curve(EC_GROUP *group, const BIGNUM *p, |
| const BIGNUM *a, const BIGNUM *n, |
| BN_CTX *); |
| int ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP *group, |
| const EC_POINT *point, |
| BIGNUM *x, BIGNUM *y, |
| BN_CTX *ctx); |
| int ec_GFp_nistp521_mul(const EC_GROUP *group, EC_POINT *r, |
| const BIGNUM *scalar, size_t num, |
| const EC_POINT *points[], const BIGNUM *scalars[], |
| BN_CTX *); |
| int ec_GFp_nistp521_points_mul(const EC_GROUP *group, EC_POINT *r, |
| const BIGNUM *scalar, size_t num, |
| const EC_POINT *points[], |
| const BIGNUM *scalars[], BN_CTX *ctx); |
| int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx); |
| int ec_GFp_nistp521_have_precompute_mult(const EC_GROUP *group); |
| |
| /* utility functions in ecp_nistputil.c */ |
| void ec_GFp_nistp_points_make_affine_internal(size_t num, void *point_array, |
| size_t felem_size, |
| void *tmp_felems, |
| void (*felem_one) (void *out), |
| int (*felem_is_zero) (const void |
| *in), |
| void (*felem_assign) (void *out, |
| const void |
| *in), |
| void (*felem_square) (void *out, |
| const void |
| *in), |
| void (*felem_mul) (void *out, |
| const void |
| *in1, |
| const void |
| *in2), |
| void (*felem_inv) (void *out, |
| const void |
| *in), |
| void (*felem_contract) (void |
| *out, |
| const |
| void |
| *in)); |
| void ec_GFp_nistp_recode_scalar_bits(unsigned char *sign, |
| unsigned char *digit, unsigned char in); |
| #endif |
| int ec_group_simple_order_bits(const EC_GROUP *group); |
| |
| #ifdef ECP_NISTZ256_ASM |
| /** Returns GFp methods using montgomery multiplication, with x86-64 optimized |
| * P256. See http://eprint.iacr.org/2013/816. |
| * \return EC_METHOD object |
| */ |
| const EC_METHOD *EC_GFp_nistz256_method(void); |
| #endif |
| |
| size_t ec_key_simple_priv2oct(const EC_KEY *eckey, |
| unsigned char *buf, size_t len); |
| int ec_key_simple_oct2priv(EC_KEY *eckey, const unsigned char *buf, size_t len); |
| int ec_key_simple_generate_key(EC_KEY *eckey); |
| int ec_key_simple_generate_public_key(EC_KEY *eckey); |
| int ec_key_simple_check_key(const EC_KEY *eckey); |
| |
| /* EC_METHOD definitions */ |
| |
| struct ec_key_method_st { |
| const char *name; |
| int32_t flags; |
| int (*init)(EC_KEY *key); |
| void (*finish)(EC_KEY *key); |
| int (*copy)(EC_KEY *dest, const EC_KEY *src); |
| int (*set_group)(EC_KEY *key, const EC_GROUP *grp); |
| int (*set_private)(EC_KEY *key, const BIGNUM *priv_key); |
| int (*set_public)(EC_KEY *key, const EC_POINT *pub_key); |
| int (*keygen)(EC_KEY *key); |
| int (*compute_key)(unsigned char **pout, size_t *poutlen, |
| const EC_POINT *pub_key, const EC_KEY *ecdh); |
| int (*sign)(int type, const unsigned char *dgst, int dlen, unsigned char |
| *sig, unsigned int *siglen, const BIGNUM *kinv, |
| const BIGNUM *r, EC_KEY *eckey); |
| int (*sign_setup)(EC_KEY *eckey, BN_CTX *ctx_in, BIGNUM **kinvp, |
| BIGNUM **rp); |
| ECDSA_SIG *(*sign_sig)(const unsigned char *dgst, int dgst_len, |
| const BIGNUM *in_kinv, const BIGNUM *in_r, |
| EC_KEY *eckey); |
| |
| int (*verify)(int type, const unsigned char *dgst, int dgst_len, |
| const unsigned char *sigbuf, int sig_len, EC_KEY *eckey); |
| int (*verify_sig)(const unsigned char *dgst, int dgst_len, |
| const ECDSA_SIG *sig, EC_KEY *eckey); |
| }; |
| |
| #define EC_KEY_METHOD_DYNAMIC 1 |
| |
| int ossl_ec_key_gen(EC_KEY *eckey); |
| int ossl_ecdh_compute_key(unsigned char **pout, size_t *poutlen, |
| const EC_POINT *pub_key, const EC_KEY *ecdh); |
| int ecdh_simple_compute_key(unsigned char **pout, size_t *poutlen, |
| const EC_POINT *pub_key, const EC_KEY *ecdh); |
| |
| struct ECDSA_SIG_st { |
| BIGNUM *r; |
| BIGNUM *s; |
| }; |
| |
| int ossl_ecdsa_sign_setup(EC_KEY *eckey, BN_CTX *ctx_in, BIGNUM **kinvp, |
| BIGNUM **rp); |
| int ossl_ecdsa_sign(int type, const unsigned char *dgst, int dlen, |
| unsigned char *sig, unsigned int *siglen, |
| const BIGNUM *kinv, const BIGNUM *r, EC_KEY *eckey); |
| ECDSA_SIG *ossl_ecdsa_sign_sig(const unsigned char *dgst, int dgst_len, |
| const BIGNUM *in_kinv, const BIGNUM *in_r, |
| EC_KEY *eckey); |
| int ossl_ecdsa_verify(int type, const unsigned char *dgst, int dgst_len, |
| const unsigned char *sigbuf, int sig_len, EC_KEY *eckey); |
| int ossl_ecdsa_verify_sig(const unsigned char *dgst, int dgst_len, |
| const ECDSA_SIG *sig, EC_KEY *eckey); |
| |
| int ED25519_sign(uint8_t *out_sig, const uint8_t *message, size_t message_len, |
| const uint8_t public_key[32], const uint8_t private_key[32]); |
| int ED25519_verify(const uint8_t *message, size_t message_len, |
| const uint8_t signature[64], const uint8_t public_key[32]); |
| void ED25519_public_from_private(uint8_t out_public_key[32], |
| const uint8_t private_key[32]); |
| |
| int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32], |
| const uint8_t peer_public_value[32]); |
| void X25519_public_from_private(uint8_t out_public_value[32], |
| const uint8_t private_key[32]); |
| |
| /*- |
| * This functions computes a single point multiplication over the EC group, |
| * using, at a high level, a Montgomery ladder with conditional swaps, with |
| * various timing attack defenses. |
| * |
| * It performs either a fixed point multiplication |
| * (scalar * generator) |
| * when point is NULL, or a variable point multiplication |
| * (scalar * point) |
| * when point is not NULL. |
| * |
| * `scalar` cannot be NULL and should be in the range [0,n) otherwise all |
| * constant time bets are off (where n is the cardinality of the EC group). |
| * |
| * This function expects `group->order` and `group->cardinality` to be well |
| * defined and non-zero: it fails with an error code otherwise. |
| * |
| * NB: This says nothing about the constant-timeness of the ladder step |
| * implementation (i.e., the default implementation is based on EC_POINT_add and |
| * EC_POINT_dbl, which of course are not constant time themselves) or the |
| * underlying multiprecision arithmetic. |
| * |
| * The product is stored in `r`. |
| * |
| * This is an internal function: callers are in charge of ensuring that the |
| * input parameters `group`, `r`, `scalar` and `ctx` are not NULL. |
| * |
| * Returns 1 on success, 0 otherwise. |
| */ |
| int ec_scalar_mul_ladder(const EC_GROUP *group, EC_POINT *r, |
| const BIGNUM *scalar, const EC_POINT *point, |
| BN_CTX *ctx); |
| |
| int ec_point_blind_coordinates(const EC_GROUP *group, EC_POINT *p, BN_CTX *ctx); |
| |
| static ossl_inline int ec_point_ladder_pre(const EC_GROUP *group, |
| EC_POINT *r, EC_POINT *s, |
| EC_POINT *p, BN_CTX *ctx) |
| { |
| if (group->meth->ladder_pre != NULL) |
| return group->meth->ladder_pre(group, r, s, p, ctx); |
| |
| if (!EC_POINT_copy(s, p) |
| || !EC_POINT_dbl(group, r, s, ctx)) |
| return 0; |
| |
| return 1; |
| } |
| |
| static ossl_inline int ec_point_ladder_step(const EC_GROUP *group, |
| EC_POINT *r, EC_POINT *s, |
| EC_POINT *p, BN_CTX *ctx) |
| { |
| if (group->meth->ladder_step != NULL) |
| return group->meth->ladder_step(group, r, s, p, ctx); |
| |
| if (!EC_POINT_add(group, s, r, s, ctx) |
| || !EC_POINT_dbl(group, r, r, ctx)) |
| return 0; |
| |
| return 1; |
| |
| } |
| |
| static ossl_inline int ec_point_ladder_post(const EC_GROUP *group, |
| EC_POINT *r, EC_POINT *s, |
| EC_POINT *p, BN_CTX *ctx) |
| { |
| if (group->meth->ladder_post != NULL) |
| return group->meth->ladder_post(group, r, s, p, ctx); |
| |
| return 1; |
| } |
