| /** |
| * \file ecp.h |
| * |
| * \brief Elliptic curves over GF(p) |
| * |
| * Copyright (C) 2006-2013, Brainspark B.V. |
| * |
| * This file is part of PolarSSL (http://www.polarssl.org) |
| * Lead Maintainer: Paul Bakker <polarssl_maintainer at polarssl.org> |
| * |
| * All rights reserved. |
| * |
| * This program is free software; you can redistribute it and/or modify |
| * it under the terms of the GNU General Public License as published by |
| * the Free Software Foundation; either version 2 of the License, or |
| * (at your option) any later version. |
| * |
| * This program is distributed in the hope that it will be useful, |
| * but WITHOUT ANY WARRANTY; without even the implied warranty of |
| * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
| * GNU General Public License for more details. |
| * |
| * You should have received a copy of the GNU General Public License along |
| * with this program; if not, write to the Free Software Foundation, Inc., |
| * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. |
| */ |
| #ifndef POLARSSL_ECP_H |
| #define POLARSSL_ECP_H |
| |
| #include "polarssl/bignum.h" |
| |
| /* |
| * ECP error codes |
| */ |
| #define POLARSSL_ERR_ECP_BAD_INPUT_DATA -0x4F80 /**< Bad input parameters to function. */ |
| #define POLARSSL_ERR_ECP_BUFFER_TOO_SMALL -0x4F80 /**< The buffer is too small to write to. */ |
| #define POLARSSL_ERR_ECP_GENERIC -0x4F00 /**< Generic ECP error */ |
| |
| /** |
| * \brief ECP point structure (jacobian coordinates) |
| * |
| * \note All functions expect and return points satisfying |
| * the following condition: Z == 0 or Z == 1. (Other |
| * values of Z are used by internal functions only.) |
| * The point is zero, or "at infinity", if Z == 0. |
| * Otherwise, X and Y are its standard (affine) coordinates. |
| */ |
| typedef struct |
| { |
| mpi X; /*!< the point's X coordinate */ |
| mpi Y; /*!< the point's Y coordinate */ |
| mpi Z; /*!< the point's Z coordinate */ |
| } |
| ecp_point; |
| |
| /* |
| * RFC 4492 defines an enum NamedCurve with two-bytes values |
| */ |
| typedef uint16_t ecp_group_id; |
| |
| /** |
| * \brief ECP group structure |
| * |
| * The curves we consider are defined by y^2 = x^3 - 3x + B mod P, |
| * and a generator for a large subgroup of order N is fixed. |
| * |
| * pbits and nbits must be the size of P and N in bits. |
| * |
| * If modp is NULL, reduction modulo P is done using a generic |
| * algorithm. Otherwise, it must point to a function that takes an mpi |
| * in the range 0..2^(2*pbits) and transforms it in-place in an integer |
| * of little more than pbits, so that the integer may be efficiently |
| * brought in the 0..P range by a few additions or substractions. It |
| * must return 0 on success and a POLARSSL_ERR_ECP_XXX error on failure. |
| */ |
| typedef struct |
| { |
| ecp_group_id id; /*!< RFC 4492 group ID */ |
| mpi P; /*!< prime modulus of the base field */ |
| mpi B; /*!< constant term in the equation */ |
| ecp_point G; /*!< generator of the subgroup used */ |
| mpi N; /*!< the order of G */ |
| size_t pbits; /*!< number of bits in P */ |
| size_t nbits; /*!< number of bits in N */ |
| int (*modp)(mpi *); /*!< function for fast reduction mod P */ |
| } |
| ecp_group; |
| |
| /** |
| * RFC 5114 defines a number of standardized ECP groups for use with TLS. |
| * |
| * These also are the NIST-recommended ECP groups, are the random ECP groups |
| * recommended by SECG, and include the two groups used by NSA Suite B. |
| * There are known as secpLLLr1 with LLL = 192, 224, 256, 384, 521. |
| * |
| * \warning This library does not support validation of arbitrary domain |
| * parameters. Therefore, only well-known domain parameters from trusted |
| * sources should be used. See ecp_use_known_dp(). |
| * |
| * \note The values are taken from RFC 4492's enum NamedCurve. |
| */ |
| #define POLARSSL_ECP_DP_SECP192R1 19 |
| #define POLARSSL_ECP_DP_SECP224R1 21 |
| #define POLARSSL_ECP_DP_SECP256R1 23 |
| #define POLARSSL_ECP_DP_SECP384R1 24 |
| #define POLARSSL_ECP_DP_SECP521R1 25 |
| |
| /** |
| * Maximum bit size of the groups (that is, of N) |
| */ |
| #define POLARSSL_ECP_MAX_N_BITS 521 |
| |
| /* |
| * Maximum window size (actually, NAF width) used for point multipliation. |
| * Default: 7. |
| * Minimum value: 2. Maximum value: 8. |
| * |
| * Result is an array of at most ( 1 << ( POLARSSL_ECP_WINDOW_SIZE - 1 ) ) |
| * points used for point multiplication, so at most 64 by default. |
| * In practice, most curves will use less precomputed points. |
| * |
| * Reduction in size may reduce speed for big curves. |
| */ |
| #define POLARSSL_ECP_WINDOW_SIZE 7 /**< Maximum NAF width used. */ |
| |
| /* |
| * Point formats, from RFC 4492's enum ECPointFormat |
| */ |
| #define POLARSSL_ECP_PF_UNCOMPRESSED 0 /**< Uncompressed point format */ |
| #define POLARSSL_ECP_PF_COMPRESSED 1 /**< Compressed point format */ |
| |
| /* |
| * Some other constants from RFC 4492 |
| */ |
| #define POLARSSL_ECP_TLS_NAMED_CURVE 3 /**< ECCurveType's named_curve */ |
| |
| |
| #ifdef __cplusplus |
| extern "C" { |
| #endif |
| |
| /** |
| * \brief Initialize a point (as zero) |
| */ |
| void ecp_point_init( ecp_point *pt ); |
| |
| /** |
| * \brief Initialize a group (to something meaningless) |
| */ |
| void ecp_group_init( ecp_group *grp ); |
| |
| /** |
| * \brief Free the components of a point |
| */ |
| void ecp_point_free( ecp_point *pt ); |
| |
| /** |
| * \brief Free the components of an ECP group |
| */ |
| void ecp_group_free( ecp_group *grp ); |
| |
| /** |
| * \brief Set a point to zero |
| * |
| * \param pt Destination point |
| * |
| * \return 0 if successful, |
| * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed |
| */ |
| int ecp_set_zero( ecp_point *pt ); |
| |
| /** |
| * \brief Tell if a point is zero |
| * |
| * \param pt Point to test |
| * |
| * \return 1 if point is zero, 0 otherwise |
| */ |
| int ecp_is_zero( ecp_point *pt ); |
| |
| /** |
| * \brief Copy the contents of point Q into P |
| * |
| * \param P Destination point |
| * \param Q Source point |
| * |
| * \return 0 if successful, |
| * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed |
| */ |
| int ecp_copy( ecp_point *P, const ecp_point *Q ); |
| |
| /** |
| * \brief Check that a point is a valid public key on this curve |
| * |
| * \param grp Curve/group the point should belong to |
| * \param pt Point to check |
| * |
| * \return 0 if point is a valid public key, |
| * POLARSSL_ERR_ECP_GENERIC otherwise. |
| * |
| * \note This function only checks the point is non-zero, has valid |
| * coordinates and lies on the curve, but not that it is |
| * indeed a multiple of G. This is additional check is more |
| * expensive, isn't required by standards, and shouldn't be |
| * necessary if the group used has a small cofactor. In |
| * particular, it is useless for the NIST groups which all |
| * have a cofactor of 1. |
| */ |
| int ecp_check_pubkey( const ecp_group *grp, const ecp_point *pt ); |
| |
| /** |
| * \brief Import a non-zero point from two ASCII strings |
| * |
| * \param P Destination point |
| * \param radix Input numeric base |
| * \param x First affine coordinate as a null-terminated string |
| * \param y Second affine coordinate as a null-terminated string |
| * |
| * \return 0 if successful, or a POLARSSL_ERR_MPI_XXX error code |
| */ |
| int ecp_point_read_string( ecp_point *P, int radix, |
| const char *x, const char *y ); |
| |
| /** |
| * \brief Import an ECP group from null-terminated ASCII strings |
| * |
| * \param grp Destination group |
| * \param radix Input numeric base |
| * \param p Prime modulus of the base field |
| * \param b Constant term in the equation |
| * \param gx The generator's X coordinate |
| * \param gy The generator's Y coordinate |
| * \param n The generator's order |
| * |
| * \return 0 if successful, or a POLARSSL_ERR_MPI_XXX error code |
| * |
| * \note Sets all fields except modp. |
| */ |
| int ecp_group_read_string( ecp_group *grp, int radix, |
| const char *p, const char *b, |
| const char *gx, const char *gy, const char *n); |
| |
| /** |
| * \brief Export a point into unsigned binary data |
| * |
| * \param grp Group to which the point should belong |
| * \param P Point to export |
| * \param format Point format, should be a POLARSSL_ECP_PF_XXX macro |
| * \param olen Length of the actual output |
| * \param buf Output buffer |
| * \param buflen Length of the output buffer |
| * |
| * \return 0 if successful, |
| * or POLARSSL_ERR_ECP_BAD_INPUT_DATA |
| * or POLARSSL_ERR_ECP_BUFFER_TOO_SMALL |
| */ |
| int ecp_point_write_binary( const ecp_group *grp, const ecp_point *P, |
| int format, size_t *olen, |
| unsigned char *buf, size_t buflen ); |
| |
| /** |
| * \brief Import a point from unsigned binary data |
| * |
| * \param grp Group to which the point should belong |
| * \param P Point to import |
| * \param buf Input buffer |
| * \param ilen Actual length of input |
| * |
| * \return 0 if successful, |
| * POLARSSL_ERR_ECP_GENERIC if input is invalid |
| * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed |
| * |
| * \note This function does NOT check that the point actually |
| * belongs to the given group, see ecp_check_pubkey() for |
| * that. |
| */ |
| int ecp_point_read_binary( const ecp_group *grp, ecp_point *P, |
| const unsigned char *buf, size_t ilen ); |
| |
| /** |
| * \brief Set a group using well-known domain parameters |
| * |
| * \param grp Destination group |
| * \param index Index in the list of well-known domain parameters |
| * |
| * \return O if successful, |
| * POLARSSL_ERR_MPI_XXX if initialization failed |
| * POLARSSL_ERR_ECP_GENERIC if index is out of range |
| * |
| * \note Index should be a value of RFC 4492's enum NamdeCurve, |
| * possibly in the form of a POLARSSL_ECP_DP_XXX macro. |
| */ |
| int ecp_use_known_dp( ecp_group *grp, ecp_group_id id ); |
| |
| /** |
| * \brief Set a group from a TLS ECParameters record |
| * |
| * \param grp Destination group |
| * \param buf &(Start of input buffer) |
| * \param len Buffer length |
| * |
| * \return O if successful, |
| * POLARSSL_ERR_MPI_XXX if initialization failed |
| * POLARSSL_ERR_ECP_BAD_INPUT_DATA if input is invalid |
| */ |
| int ecp_tls_read_group( ecp_group *grp, const unsigned char **buf, size_t len ); |
| |
| /** |
| * \brief Write the TLS ECParameters record for a group |
| * |
| * \param grp ECP group used |
| * \param olen Number of bytes actually written |
| * \param buf Buffer to write to |
| * \param blen Buffer length |
| * |
| * \return 0 if successful, |
| * or POLARSSL_ERR_ECP_BUFFER_TOO_SMALL |
| */ |
| int ecp_tls_write_group( const ecp_group *grp, size_t *olen, |
| unsigned char *buf, size_t blen ); |
| |
| /** |
| * \brief Import a point from a TLS ECPoint record |
| * |
| * \param grp ECP group used |
| * \param pt Destination point |
| * \param buf $(Start of input buffer) |
| * \param len Buffer length |
| * |
| * \return O if successful, |
| * POLARSSL_ERR_MPI_XXX if initialization failed |
| * POLARSSL_ERR_ECP_BAD_INPUT_DATA if input is invalid |
| */ |
| int ecp_tls_read_point( const ecp_group *grp, ecp_point *pt, |
| const unsigned char **buf, size_t len ); |
| |
| /** |
| * \brief Export a point as a TLS ECPoint record |
| * |
| * \param grp ECP group used |
| * \param pt Point to export |
| * \param format Export format |
| * \param buf Buffer to write to |
| * \param len Buffer length |
| * |
| * \return 0 if successful, |
| * or POLARSSL_ERR_ECP_BAD_INPUT_DATA |
| * or POLARSSL_ERR_ECP_BUFFER_TOO_SMALL |
| */ |
| int ecp_tls_write_point( const ecp_group *grp, const ecp_point *pt, |
| int format, size_t *olen, |
| unsigned char *buf, size_t blen ); |
| |
| /** |
| * \brief Addition: R = P + Q |
| * |
| * \param grp ECP group |
| * \param R Destination point |
| * \param P Left-hand point |
| * \param Q Right-hand point |
| * |
| * \return 0 if successful, |
| * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed |
| */ |
| int ecp_add( const ecp_group *grp, ecp_point *R, |
| const ecp_point *P, const ecp_point *Q ); |
| |
| /** |
| * \brief Subtraction: R = P - Q |
| * |
| * \param grp ECP group |
| * \param R Destination point |
| * \param P Left-hand point |
| * \param Q Right-hand point |
| * |
| * \return 0 if successful, |
| * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed |
| */ |
| int ecp_sub( const ecp_group *grp, ecp_point *R, |
| const ecp_point *P, const ecp_point *Q ); |
| |
| /** |
| * \brief Multiplication by an integer: R = m * P |
| * |
| * \param grp ECP group |
| * \param R Destination point |
| * \param m Integer by which to multiply |
| * \param P Point to multiply |
| * |
| * \return 0 if successful, |
| * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed |
| * POLARSSL_ERR_ECP_GENERIC if m < 0 of m has greater bit |
| * length than N, the number of points in the group. |
| * |
| * \note This function executes a constant number of operations |
| * for random m in the allowed range. |
| */ |
| int ecp_mul( const ecp_group *grp, ecp_point *R, |
| const mpi *m, const ecp_point *P ); |
| |
| /** |
| * \brief Generate a keypair |
| * |
| * \param grp ECP group |
| * \param d Destination MPI (secret part) |
| * \param Q Destination point (public part) |
| * \param f_rng RNG function |
| * \param p_rng RNG parameter |
| * |
| * \return 0 if successful, |
| * or a POLARSSL_ERR_ECP_XXX or POLARSSL_MPI_XXX error code |
| */ |
| int ecp_gen_keypair( const ecp_group *grp, mpi *d, ecp_point *Q, |
| int (*f_rng)(void *, unsigned char *, size_t), |
| void *p_rng ); |
| |
| /** |
| * \brief Checkup routine |
| * |
| * \return 0 if successful, or 1 if the test failed |
| */ |
| int ecp_self_test( int verbose ); |
| |
| #ifdef __cplusplus |
| } |
| #endif |
| |
| #endif |
