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-/* crypto/ec/ec_lcl.h */
-/*
- * Originally written by Bodo Moeller for the OpenSSL project.
- */
-/* ====================================================================
- * Copyright (c) 1998-2003 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 <stdlib.h>
-
-#include <openssl/obj_mac.h>
-#include <openssl/ec.h>
-#include <openssl/bn.h>
-
-#if defined(__SUNPRO_C)
-# if __SUNPRO_C >= 0x520
-# pragma error_messages (off,E_ARRAY_OF_INCOMPLETE_NONAME,E_ARRAY_OF_INCOMPLETE)
-# endif
-#endif
-
-/* 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_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): */
- 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 *);
-
- 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 */;
-
-typedef struct ec_extra_data_st {
- struct ec_extra_data_st *next;
- void *data;
- void *(*dup_func)(void *);
- void (*free_func)(void *);
- void (*clear_free_func)(void *);
-} EC_EXTRA_DATA; /* used in EC_GROUP */
-
-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;
-
- EC_EXTRA_DATA *extra_data; /* linked list */
-
- /* 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.
- */
-
- int poly[6]; /* 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.
- */
-
- 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 */;
-
-struct ec_key_st {
- int version;
-
- EC_GROUP *group;
-
- EC_POINT *pub_key;
- BIGNUM *priv_key;
-
- unsigned int enc_flag;
- point_conversion_form_t conv_form;
-
- int references;
-
- EC_EXTRA_DATA *method_data;
-} /* EC_KEY */;
-
-/* Basically a 'mixin' for extra data, but available for EC_GROUPs/EC_KEYs 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.
- */
-int EC_EX_DATA_set_data(EC_EXTRA_DATA **, void *data,
- void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
-void *EC_EX_DATA_get_data(const EC_EXTRA_DATA *,
- void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
-void EC_EX_DATA_free_data(EC_EXTRA_DATA **,
- void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
-void EC_EX_DATA_clear_free_data(EC_EXTRA_DATA **,
- void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
-void EC_EX_DATA_free_all_data(EC_EXTRA_DATA **);
-void EC_EX_DATA_clear_free_all_data(EC_EXTRA_DATA **);
-
-
-
-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
- * (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 *);
-
-
-/* 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 *);
-
-
-/* method functions in ec2_mult.c */
-int ec_GF2m_simple_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_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
-int ec_GF2m_have_precompute_mult(const EC_GROUP *group);