| /* Originally written by Bodo Moeller for the OpenSSL project. |
| * ==================================================================== |
| * Copyright (c) 1998-2005 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 |
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| * 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) |
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| * 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. */ |
| |
| #ifndef OPENSSL_HEADER_EC_INTERNAL_H |
| #define OPENSSL_HEADER_EC_INTERNAL_H |
| |
| #include <openssl/base.h> |
| |
| #include <openssl/bn.h> |
| #include <openssl/ex_data.h> |
| #include <openssl/thread.h> |
| #include <openssl/type_check.h> |
| |
| #include "../bn/internal.h" |
| |
| #if defined(__cplusplus) |
| extern "C" { |
| #endif |
| |
| |
| // Cap the size of all field elements and scalars, including custom curves, to |
| // 66 bytes, large enough to fit secp521r1 and brainpoolP512r1, which appear to |
| // be the largest fields anyone plausibly uses. |
| #define EC_MAX_SCALAR_BYTES 66 |
| #define EC_MAX_SCALAR_WORDS ((66 + BN_BYTES - 1) / BN_BYTES) |
| |
| OPENSSL_COMPILE_ASSERT(EC_MAX_SCALAR_WORDS <= BN_SMALL_MAX_WORDS, |
| bn_small_functions_applicable); |
| |
| // An EC_SCALAR is an integer fully reduced modulo the order. Only the first |
| // |order->width| words are used. An |EC_SCALAR| is specific to an |EC_GROUP| |
| // and must not be mixed between groups. |
| typedef union { |
| // bytes is the representation of the scalar in little-endian order. |
| uint8_t bytes[EC_MAX_SCALAR_BYTES]; |
| BN_ULONG words[EC_MAX_SCALAR_WORDS]; |
| } EC_SCALAR; |
| |
| // An EC_FELEM represents a field element. Only the first |field->width| words |
| // are used. An |EC_FELEM| is specific to an |EC_GROUP| and must not be mixed |
| // between groups. Additionally, the representation (whether or not elements are |
| // represented in Montgomery-form) may vary between |EC_METHOD|s. |
| typedef union { |
| // bytes is the representation of the field element in little-endian order. |
| uint8_t bytes[EC_MAX_SCALAR_BYTES]; |
| BN_ULONG words[EC_MAX_SCALAR_WORDS]; |
| } EC_FELEM; |
| |
| // An EC_RAW_POINT represents an elliptic curve point. Unlike |EC_POINT|, it is |
| // a plain struct which can be stack-allocated and needs no cleanup. It is |
| // specific to an |EC_GROUP| and must not be mixed between groups. |
| typedef struct { |
| EC_FELEM X, Y, Z; |
| // X, Y, and Z are Jacobian projective coordinates. They represent |
| // (X/Z^2, Y/Z^3) if Z != 0 and the point at infinity otherwise. |
| } EC_RAW_POINT; |
| |
| struct ec_method_st { |
| int (*group_init)(EC_GROUP *); |
| void (*group_finish)(EC_GROUP *); |
| int (*group_set_curve)(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, |
| const BIGNUM *b, BN_CTX *); |
| int (*point_get_affine_coordinates)(const EC_GROUP *, const EC_RAW_POINT *, |
| BIGNUM *x, BIGNUM *y); |
| |
| // Computes |r = g_scalar*generator + p_scalar*p| if |g_scalar| and |p_scalar| |
| // are both non-null. Computes |r = g_scalar*generator| if |p_scalar| is null. |
| // Computes |r = p_scalar*p| if g_scalar is null. At least one of |g_scalar| |
| // and |p_scalar| must be non-null, and |p| must be non-null if |p_scalar| is |
| // non-null. |
| void (*mul)(const EC_GROUP *group, EC_RAW_POINT *r, const EC_SCALAR *g_scalar, |
| const EC_RAW_POINT *p, const EC_SCALAR *p_scalar); |
| // mul_public performs the same computation as mul. It further assumes that |
| // the inputs are public so there is no concern about leaking their values |
| // through timing. |
| void (*mul_public)(const EC_GROUP *group, EC_RAW_POINT *r, |
| const EC_SCALAR *g_scalar, const EC_RAW_POINT *p, |
| const EC_SCALAR *p_scalar); |
| |
| // felem_mul and felem_sqr implement multiplication and squaring, |
| // respectively, so that the generic |EC_POINT_add| and |EC_POINT_dbl| |
| // implementations can work both with |EC_GFp_mont_method| and the tuned |
| // operations. |
| // |
| // TODO(davidben): This constrains |EC_FELEM|'s internal representation, adds |
| // many indirect calls in the middle of the generic code, and a bunch of |
| // conversions. If p224-64.c were easily convertable to Montgomery form, we |
| // could say |EC_FELEM| is always in Montgomery form. If we exposed the |
| // internal add and double implementations in each of the curves, we could |
| // give |EC_POINT| an |EC_METHOD|-specific representation and |EC_FELEM| is |
| // purely a |EC_GFp_mont_method| type. |
| void (*felem_mul)(const EC_GROUP *, EC_FELEM *r, const EC_FELEM *a, |
| const EC_FELEM *b); |
| void (*felem_sqr)(const EC_GROUP *, EC_FELEM *r, const EC_FELEM *a); |
| |
| int (*bignum_to_felem)(const EC_GROUP *group, EC_FELEM *out, |
| const BIGNUM *in); |
| int (*felem_to_bignum)(const EC_GROUP *group, BIGNUM *out, |
| const EC_FELEM *in); |
| |
| // scalar_inv_mont sets |out| to |in|^-1, where both input and output are in |
| // Montgomery form. |
| void (*scalar_inv_montgomery)(const EC_GROUP *group, EC_SCALAR *out, |
| const EC_SCALAR *in); |
| |
| } /* EC_METHOD */; |
| |
| const EC_METHOD *EC_GFp_mont_method(void); |
| |
| struct ec_group_st { |
| const EC_METHOD *meth; |
| |
| // Unlike all other |EC_POINT|s, |generator| does not own |generator->group| |
| // to avoid a reference cycle. |
| EC_POINT *generator; |
| BIGNUM order; |
| |
| int curve_name; // optional NID for named curve |
| |
| BN_MONT_CTX *order_mont; // data for ECDSA inverse |
| |
| // The following members are handled by the method functions, |
| // even if they appear generic |
| |
| BIGNUM field; // For curves over GF(p), this is the modulus. |
| |
| EC_FELEM a, b; // Curve coefficients. |
| |
| int a_is_minus3; // enable optimized point arithmetics for special case |
| |
| CRYPTO_refcount_t references; |
| |
| BN_MONT_CTX *mont; // Montgomery structure. |
| |
| EC_FELEM one; // The value one. |
| } /* EC_GROUP */; |
| |
| struct ec_point_st { |
| // group is an owning reference to |group|, unless this is |
| // |group->generator|. |
| EC_GROUP *group; |
| EC_RAW_POINT raw; |
| } /* EC_POINT */; |
| |
| EC_GROUP *ec_group_new(const EC_METHOD *meth); |
| |
| // ec_bignum_to_felem converts |in| to an |EC_FELEM|. It returns one on success |
| // and zero if |in| is out of range. |
| int ec_bignum_to_felem(const EC_GROUP *group, EC_FELEM *out, const BIGNUM *in); |
| |
| // ec_felem_to_bignum converts |in| to a |BIGNUM|. It returns one on success and |
| // zero on allocation failure. |
| int ec_felem_to_bignum(const EC_GROUP *group, BIGNUM *out, const EC_FELEM *in); |
| |
| // ec_felem_neg sets |out| to -|a|. |
| void ec_felem_neg(const EC_GROUP *group, EC_FELEM *out, const EC_FELEM *a); |
| |
| // ec_felem_add sets |out| to |a| + |b|. |
| void ec_felem_add(const EC_GROUP *group, EC_FELEM *out, const EC_FELEM *a, |
| const EC_FELEM *b); |
| |
| // ec_felem_add sets |out| to |a| - |b|. |
| void ec_felem_sub(const EC_GROUP *group, EC_FELEM *out, const EC_FELEM *a, |
| const EC_FELEM *b); |
| |
| // ec_felem_non_zero_mask returns all ones if |a| is non-zero and all zeros |
| // otherwise. |
| BN_ULONG ec_felem_non_zero_mask(const EC_GROUP *group, const EC_FELEM *a); |
| |
| // ec_felem_select, in constant time, sets |out| to |a| if |mask| is all ones |
| // and |b| if |mask| is all zeros. |
| void ec_felem_select(const EC_GROUP *group, EC_FELEM *out, BN_ULONG mask, |
| const EC_FELEM *a, const EC_FELEM *b); |
| |
| // ec_felem_equal returns one if |a| and |b| are equal and zero otherwise. It |
| // treats |a| and |b| as public and does *not* run in constant time. |
| int ec_felem_equal(const EC_GROUP *group, const EC_FELEM *a, const EC_FELEM *b); |
| |
| // ec_bignum_to_scalar converts |in| to an |EC_SCALAR| and writes it to |
| // |*out|. It returns one on success and zero if |in| is out of range. |
| OPENSSL_EXPORT int ec_bignum_to_scalar(const EC_GROUP *group, EC_SCALAR *out, |
| const BIGNUM *in); |
| |
| // ec_random_nonzero_scalar sets |out| to a uniformly selected random value from |
| // 1 to |group->order| - 1. It returns one on success and zero on error. |
| int ec_random_nonzero_scalar(const EC_GROUP *group, EC_SCALAR *out, |
| const uint8_t additional_data[32]); |
| |
| // ec_scalar_add sets |r| to |a| + |b|. |
| void ec_scalar_add(const EC_GROUP *group, EC_SCALAR *r, const EC_SCALAR *a, |
| const EC_SCALAR *b); |
| |
| // ec_scalar_to_montgomery sets |r| to |a| in Montgomery form. |
| void ec_scalar_to_montgomery(const EC_GROUP *group, EC_SCALAR *r, |
| const EC_SCALAR *a); |
| |
| // ec_scalar_to_montgomery sets |r| to |a| converted from Montgomery form. |
| void ec_scalar_from_montgomery(const EC_GROUP *group, EC_SCALAR *r, |
| const EC_SCALAR *a); |
| |
| // ec_scalar_mul_montgomery sets |r| to |a| * |b| where inputs and outputs are |
| // in Montgomery form. |
| void ec_scalar_mul_montgomery(const EC_GROUP *group, EC_SCALAR *r, |
| const EC_SCALAR *a, const EC_SCALAR *b); |
| |
| // ec_scalar_mul_montgomery sets |r| to |a|^-1 where inputs and outputs are in |
| // Montgomery form. |
| void ec_scalar_inv_montgomery(const EC_GROUP *group, EC_SCALAR *r, |
| const EC_SCALAR *a); |
| |
| // ec_point_mul_scalar sets |r| to generator * |g_scalar| + |p| * |
| // |p_scalar|. Unlike other functions which take |EC_SCALAR|, |g_scalar| and |
| // |p_scalar| need not be fully reduced. They need only contain as many bits as |
| // the order. |
| int ec_point_mul_scalar(const EC_GROUP *group, EC_POINT *r, |
| const EC_SCALAR *g_scalar, const EC_POINT *p, |
| const EC_SCALAR *p_scalar, BN_CTX *ctx); |
| |
| // ec_point_mul_scalar_public performs the same computation as |
| // ec_point_mul_scalar. It further assumes that the inputs are public so |
| // there is no concern about leaking their values through timing. |
| OPENSSL_EXPORT int ec_point_mul_scalar_public( |
| const EC_GROUP *group, EC_POINT *r, const EC_SCALAR *g_scalar, |
| const EC_POINT *p, const EC_SCALAR *p_scalar, BN_CTX *ctx); |
| |
| void ec_GFp_simple_mul(const EC_GROUP *group, EC_RAW_POINT *r, |
| const EC_SCALAR *g_scalar, const EC_RAW_POINT *p, |
| const EC_SCALAR *p_scalar); |
| |
| // ec_compute_wNAF writes the modified width-(w+1) Non-Adjacent Form (wNAF) of |
| // |scalar| to |out|. |out| must have room for |bits| + 1 elements, each of |
| // which will be either zero or odd with an absolute value less than 2^w |
| // satisfying |
| // scalar = \sum_j out[j]*2^j |
| // where at most one of any w+1 consecutive digits is non-zero |
| // with the exception that the most significant digit may be only |
| // w-1 zeros away from that next non-zero digit. |
| void ec_compute_wNAF(const EC_GROUP *group, int8_t *out, |
| const EC_SCALAR *scalar, size_t bits, int w); |
| |
| void ec_GFp_simple_mul_public(const EC_GROUP *group, EC_RAW_POINT *r, |
| const EC_SCALAR *g_scalar, const EC_RAW_POINT *p, |
| const EC_SCALAR *p_scalar); |
| |
| // method functions in simple.c |
| int ec_GFp_simple_group_init(EC_GROUP *); |
| void ec_GFp_simple_group_finish(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); |
| unsigned ec_GFp_simple_group_get_degree(const EC_GROUP *); |
| void ec_GFp_simple_point_init(EC_RAW_POINT *); |
| void ec_GFp_simple_point_copy(EC_RAW_POINT *, const EC_RAW_POINT *); |
| void ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_RAW_POINT *); |
| int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_RAW_POINT *, |
| const BIGNUM *x, |
| const BIGNUM *y); |
| void ec_GFp_simple_add(const EC_GROUP *, EC_RAW_POINT *r, const EC_RAW_POINT *a, |
| const EC_RAW_POINT *b); |
| void ec_GFp_simple_dbl(const EC_GROUP *, EC_RAW_POINT *r, |
| const EC_RAW_POINT *a); |
| void ec_GFp_simple_invert(const EC_GROUP *, EC_RAW_POINT *); |
| int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_RAW_POINT *); |
| int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_RAW_POINT *); |
| int ec_GFp_simple_cmp(const EC_GROUP *, const EC_RAW_POINT *a, |
| const EC_RAW_POINT *b); |
| void ec_simple_scalar_inv_montgomery(const EC_GROUP *group, EC_SCALAR *r, |
| const EC_SCALAR *a); |
| |
| // method functions in montgomery.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_felem_mul(const EC_GROUP *, EC_FELEM *r, const EC_FELEM *a, |
| const EC_FELEM *b); |
| void ec_GFp_mont_felem_sqr(const EC_GROUP *, EC_FELEM *r, const EC_FELEM *a); |
| |
| int ec_GFp_mont_bignum_to_felem(const EC_GROUP *group, EC_FELEM *out, |
| const BIGNUM *in); |
| int ec_GFp_mont_felem_to_bignum(const EC_GROUP *group, BIGNUM *out, |
| const EC_FELEM *in); |
| |
| void ec_GFp_nistp_recode_scalar_bits(uint8_t *sign, uint8_t *digit, uint8_t in); |
| |
| const EC_METHOD *EC_GFp_nistp224_method(void); |
| const EC_METHOD *EC_GFp_nistp256_method(void); |
| |
| // EC_GFp_nistz256_method is a GFp method using montgomery multiplication, with |
| // x86-64 optimized P256. See http://eprint.iacr.org/2013/816. |
| const EC_METHOD *EC_GFp_nistz256_method(void); |
| |
| // An EC_WRAPPED_SCALAR is an |EC_SCALAR| with a parallel |BIGNUM| |
| // representation. It exists to support the |EC_KEY_get0_private_key| API. |
| typedef struct { |
| BIGNUM bignum; |
| EC_SCALAR scalar; |
| } EC_WRAPPED_SCALAR; |
| |
| struct ec_key_st { |
| EC_GROUP *group; |
| |
| EC_POINT *pub_key; |
| EC_WRAPPED_SCALAR *priv_key; |
| |
| // fixed_k may contain a specific value of 'k', to be used in ECDSA signing. |
| // This is only for the FIPS power-on tests. |
| BIGNUM *fixed_k; |
| |
| unsigned int enc_flag; |
| point_conversion_form_t conv_form; |
| |
| CRYPTO_refcount_t references; |
| |
| ECDSA_METHOD *ecdsa_meth; |
| |
| CRYPTO_EX_DATA ex_data; |
| } /* EC_KEY */; |
| |
| struct built_in_curve { |
| int nid; |
| const uint8_t *oid; |
| uint8_t oid_len; |
| // comment is a human-readable string describing the curve. |
| const char *comment; |
| // param_len is the number of bytes needed to store a field element. |
| uint8_t param_len; |
| // params points to an array of 6*|param_len| bytes which hold the field |
| // elements of the following (in big-endian order): prime, a, b, generator x, |
| // generator y, order. |
| const uint8_t *params; |
| const EC_METHOD *method; |
| }; |
| |
| #define OPENSSL_NUM_BUILT_IN_CURVES 4 |
| |
| struct built_in_curves { |
| struct built_in_curve curves[OPENSSL_NUM_BUILT_IN_CURVES]; |
| }; |
| |
| // OPENSSL_built_in_curves returns a pointer to static information about |
| // standard curves. The array is terminated with an entry where |nid| is |
| // |NID_undef|. |
| const struct built_in_curves *OPENSSL_built_in_curves(void); |
| |
| #if defined(__cplusplus) |
| } // extern C |
| #endif |
| |
| #endif // OPENSSL_HEADER_EC_INTERNAL_H |
