src/crypto/fipsmodule/ec/internal.h

/* 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"
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 *    permission of the OpenSSL Project.
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 * 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
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 * ====================================================================
 *
 * 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;

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_POINT *,
                                      BIGNUM *x, BIGNUM *y, BN_CTX *);

  // 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.
  int (*mul)(const EC_GROUP *group, EC_POINT *r, const EC_SCALAR *g_scalar,
             const EC_POINT *p, const EC_SCALAR *p_scalar, BN_CTX *ctx);
  // 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.
  int (*mul_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);

  // '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_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
  int (*field_decode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
                      BN_CTX *);  // e.g. from Montgomery
} /* 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.

  BIGNUM 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.

  BIGNUM 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;

  BIGNUM X;
  BIGNUM Y;
  BIGNUM Z;  // Jacobian projective coordinates:
             // (X, Y, Z)  represents  (X/Z^2, Y/Z^3)  if  Z != 0
} /* EC_POINT */;

EC_GROUP *ec_group_new(const EC_METHOD *meth);

// 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_bignum_to_scalar_unchecked behaves like |ec_bignum_to_scalar| but does not
// check |in| is fully reduced.
int ec_bignum_to_scalar_unchecked(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_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);

// ec_compute_wNAF writes the modified width-(w+1) Non-Adjacent Form (wNAF) of
// |scalar| to |out| and returns one on success or zero on internal error. |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.
int ec_compute_wNAF(const EC_GROUP *group, int8_t *out, const EC_SCALAR *scalar,
                    size_t bits, int w);

int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const EC_SCALAR *g_scalar,
                const EC_POINT *p, const EC_SCALAR *p_scalar, BN_CTX *ctx);

// 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, BN_CTX *);
unsigned ec_GFp_simple_group_get_degree(const EC_GROUP *);
int ec_GFp_simple_point_init(EC_POINT *);
void ec_GFp_simple_point_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_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
                                               const BIGNUM *x, const BIGNUM *y,
                                               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 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 *);
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 *);

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