/* crypto/ec/ec_lcl.h */ /* * Originally written by Bodo Moeller for the OpenSSL project. */ /* ==================================================================== * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in * the documentation and/or other materials provided with the * distribution. * * 3. All advertising materials mentioning features or use of this * software must display the following acknowledgment: * "This product includes software developed by the OpenSSL Project * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" * * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to * endorse or promote products derived from this software without * prior written permission. For written permission, please contact * openssl-core@openssl.org. * * 5. Products derived from this software may not be called "OpenSSL" * nor may "OpenSSL" appear in their names without prior written * permission of the OpenSSL Project. * * 6. Redistributions of any form whatsoever must retain the following * acknowledgment: * "This product includes software developed by the OpenSSL Project * for use in the OpenSSL Toolkit (http://www.openssl.org/)" * * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED * OF THE POSSIBILITY OF SUCH DAMAGE. * ==================================================================== * * This product includes cryptographic software written by Eric Young * (eay@cryptsoft.com). This product includes software written by Tim * Hudson (tjh@cryptsoft.com). * */ /* ==================================================================== * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. * * Portions of the attached software ("Contribution") are developed by * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project. * * The Contribution is licensed pursuant to the OpenSSL open source * license provided above. * * The elliptic curve binary polynomial software is originally written by * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories. * */ #include #include #include /* Structure details are not part of the exported interface, * so all this may change in future versions. */ struct ec_method_st { /* 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_GFp, EC_GROUP_get_curve_GFp, */ /* EC_GROUP_set_curve_GF2m, and EC_GROUP_get_curve_GF2m: */ 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 *); /* 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_GFp, ..._GF2m, * EC_POINT_get_affine_coordinates_GFp, ..._GF2m, * EC_POINT_set_compressed_coordinates_GFp, ..._GF2m: */ 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_POINTs_mul, EC_POINT_mul, EC_POINT_precompute_mult: */ 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 *); /* 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 *); /* 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 *); int (*field_encode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); /* e.g. to Montgomery */ int (*field_decode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); /* e.g. from Montgomery */ int (*field_set_to_one)(const EC_GROUP *, BIGNUM *r, BN_CTX *); } /* EC_METHOD */; 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; void *extra_data; void *(*extra_data_dup_func)(void *); void (*extra_data_free_func)(void *); void (*extra_data_clear_free_func)(void *); /* The following members are handled by the method functions, * even if they appear generic */ BIGNUM field; /* 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. */ unsigned int poly[5]; /* 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. */ BIGNUM a, b; /* 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. */ int a_is_minus3; /* enable optimized point arithmetics for special case */ void *field_data1; /* method-specific (e.g., Montgomery structure) */ void *field_data2; /* method-specific */ int (*field_mod_func)(BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); /* method-specific */ } /* EC_GROUP */; /* Basically a 'mixin' for extra data, but available for EC_GROUPs only * (with visibility limited to 'package' level for now). * We use the function pointers as index for retrieval; this obviates * global ex_data-style index tables. * (Currently, we have one slot only, but is is possible to extend this * if necessary.) */ int EC_GROUP_set_extra_data(EC_GROUP *, void *extra_data, void *(*extra_data_dup_func)(void *), void (*extra_data_free_func)(void *), void (*extra_data_clear_free_func)(void *)); void *EC_GROUP_get_extra_data(const EC_GROUP *, void *(*extra_data_dup_func)(void *), void (*extra_data_free_func)(void *), void (*extra_data_clear_free_func)(void *)); void EC_GROUP_free_extra_data(EC_GROUP *); void EC_GROUP_clear_free_extra_data(EC_GROUP *); struct ec_point_st { const EC_METHOD *meth; /* 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 */ } /* EC_POINT */; /* method functions in ec_mult.c */ 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 *); /* 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 *); /* 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_recp.c */ int ec_GFp_recp_group_init(EC_GROUP *); int ec_GFp_recp_group_set_curve(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_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 *); /* method functions in ecp_nist.c */ int ec_GFp_nist_group_init(EC_GROUP *); int ec_GFp_nist_group_set_curve(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_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 *); /* 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 *); /* method functions in ec2_mult.c */ int ec_GF2m_mont_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_GF2m_mont_precompute_mult(EC_GROUP *group, BN_CTX *ctx);