Hannes Tschofenig
/
aes-gcm-test-program
Example program to test AES-GCM functionality. Used for a workshop
Diff: SSL/include/polarssl/ecp.h
- Revision:
- 0:796d0f61a05b
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/SSL/include/polarssl/ecp.h Thu Sep 27 06:34:22 2018 +0000 @@ -0,0 +1,653 @@ +/** + * \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 "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 -0x4F00 /**< The buffer is too small to write to. */ +#define POLARSSL_ERR_ECP_FEATURE_UNAVAILABLE -0x4E80 /**< Requested curve not available. */ +#define POLARSSL_ERR_ECP_VERIFY_FAILED -0x4E00 /**< The signature is not valid. */ +#define POLARSSL_ERR_ECP_MALLOC_FAILED -0x4D80 /**< Memory allocation failed. */ +#define POLARSSL_ERR_ECP_RANDOM_FAILED -0x4D00 /**< Generation of random value, such as (ephemeral) key, failed. */ +#define POLARSSL_ERR_ECP_INVALID_KEY -0x4C80 /**< Invalid private or public key. */ +#define POLARSSL_ERR_ECP_SIG_LEN_MISMATCH -0x4C00 /**< Signature is valid but shorter than the user-supplied length. */ + +#ifdef __cplusplus +extern "C" { +#endif + +/** + * Domain parameters (curve, subgroup and generator) identifiers. + * + * Only curves over prime fields are supported. + * + * \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(). + */ +typedef enum +{ + POLARSSL_ECP_DP_NONE = 0, + POLARSSL_ECP_DP_SECP192R1, /*!< 192-bits NIST curve */ + POLARSSL_ECP_DP_SECP224R1, /*!< 224-bits NIST curve */ + POLARSSL_ECP_DP_SECP256R1, /*!< 256-bits NIST curve */ + POLARSSL_ECP_DP_SECP384R1, /*!< 384-bits NIST curve */ + POLARSSL_ECP_DP_SECP521R1, /*!< 521-bits NIST curve */ + POLARSSL_ECP_DP_BP256R1, /*!< 256-bits Brainpool curve */ + POLARSSL_ECP_DP_BP384R1, /*!< 384-bits Brainpool curve */ + POLARSSL_ECP_DP_BP512R1, /*!< 512-bits Brainpool curve */ + POLARSSL_ECP_DP_M221, /*!< (not implemented yet) */ + POLARSSL_ECP_DP_M255, /*!< Curve25519 */ + POLARSSL_ECP_DP_M383, /*!< (not implemented yet) */ + POLARSSL_ECP_DP_M511, /*!< (not implemented yet) */ + POLARSSL_ECP_DP_SECP192K1, /*!< 192-bits "Koblitz" curve */ + POLARSSL_ECP_DP_SECP224K1, /*!< 224-bits "Koblitz" curve */ + POLARSSL_ECP_DP_SECP256K1, /*!< 256-bits "Koblitz" curve */ +} ecp_group_id; + +/** + * Number of supported curves (plus one for NONE). + * + * (Montgomery curves excluded for now.) + */ +#define POLARSSL_ECP_DP_MAX 12 + +/** + * Curve information for use by other modules + */ +typedef struct +{ + ecp_group_id grp_id; /*!< Internal identifier */ + uint16_t tls_id; /*!< TLS NamedCurve identifier */ + uint16_t size; /*!< Curve size in bits */ + const char *name; /*!< Human-friendly name */ +} ecp_curve_info; + +/** + * \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; + +/** + * \brief ECP group structure + * + * We consider two types of curves equations: + * 1. Short Weierstrass y^2 = x^3 + A x + B mod P (SEC1 + RFC 4492) + * 2. Montgomery, y^2 = x^3 + A x^2 + x mod P (M255 + draft) + * In both cases, a generator G for a prime-order subgroup is fixed. In the + * short weierstrass, this subgroup is actually the whole curve, and its + * cardinal is denoted by N. + * + * In the case of Short Weierstrass curves, our code requires that N is an odd + * prime. (Use odd in ecp_mul() and prime in ecdsa_sign() for blinding.) + * + * In the case of Montgomery curves, we don't store A but (A + 2) / 4 which is + * the quantity actually used in the formulas. Also, nbits is not the size of N + * but the required size for private keys. + * + * 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)-1 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-1 + * range by a few additions or substractions. It must return 0 on success and + * non-zero on failure. + */ +typedef struct +{ + ecp_group_id id; /*!< internal group identifier */ + mpi P; /*!< prime modulus of the base field */ + mpi A; /*!< 1. A in the equation, or 2. (A + 2) / 4 */ + mpi B; /*!< 1. B in the equation, or 2. unused */ + ecp_point G; /*!< generator of the (sub)group used */ + mpi N; /*!< 1. the order of G, or 2. unused */ + size_t pbits; /*!< number of bits in P */ + size_t nbits; /*!< number of bits in 1. P, or 2. private keys */ + unsigned int h; /*!< internal: 1 if the constants are static */ + int (*modp)(mpi *); /*!< function for fast reduction mod P */ + int (*t_pre)(ecp_point *, void *); /*!< unused */ + int (*t_post)(ecp_point *, void *); /*!< unused */ + void *t_data; /*!< unused */ + ecp_point *T; /*!< pre-computed points for ecp_mul_comb() */ + size_t T_size; /*!< number for pre-computed points */ +} +ecp_group; + +/** + * \brief ECP key pair structure + * + * A generic key pair that could be used for ECDSA, fixed ECDH, etc. + * + * \note Members purposefully in the same order as struc ecdsa_context. + */ +typedef struct +{ + ecp_group grp; /*!< Elliptic curve and base point */ + mpi d; /*!< our secret value */ + ecp_point Q; /*!< our public value */ +} +ecp_keypair; + +/** + * \name SECTION: Module settings + * + * The configuration options you can set for this module are in this section. + * Either change them in config.h or define them on the compiler command line. + * \{ + */ + +#if !defined(POLARSSL_ECP_MAX_BITS) +/** + * Maximum size of the groups (that is, of N and P) + */ +#define POLARSSL_ECP_MAX_BITS 521 /**< Maximum bit size of groups */ +#endif + +#define POLARSSL_ECP_MAX_BYTES ( ( POLARSSL_ECP_MAX_BITS + 7 ) / 8 ) +#define POLARSSL_ECP_MAX_PT_LEN ( 2 * POLARSSL_ECP_MAX_BYTES + 1 ) + +#if !defined(POLARSSL_ECP_WINDOW_SIZE) +/* + * Maximum "window" size used for point multiplication. + * Default: 6. + * Minimum value: 2. Maximum value: 7. + * + * Result is an array of at most ( 1 << ( POLARSSL_ECP_WINDOW_SIZE - 1 ) ) + * points used for point multiplication. This value is directly tied to EC + * peak memory usage, so decreasing it by one should roughly cut memory usage + * by two (if large curves are in use). + * + * Reduction in size may reduce speed, but larger curves are impacted first. + * Sample performances (in ECDHE handshakes/s, with FIXED_POINT_OPTIM = 1): + * w-size: 6 5 4 3 2 + * 521 145 141 135 120 97 + * 384 214 209 198 177 146 + * 256 320 320 303 262 226 + + * 224 475 475 453 398 342 + * 192 640 640 633 587 476 + */ +#define POLARSSL_ECP_WINDOW_SIZE 6 /**< Maximum window size used */ +#endif + +#if !defined(POLARSSL_ECP_FIXED_POINT_OPTIM) +/* + * Trade memory for speed on fixed-point multiplication. + * + * This speeds up repeated multiplication of the generator (that is, the + * multiplication in ECDSA signatures, and half of the multiplications in + * ECDSA verification and ECDHE) by a factor roughly 3 to 4. + * + * The cost is increasing EC peak memory usage by a factor roughly 2. + * + * Change this value to 0 to reduce peak memory usage. + */ +#define POLARSSL_ECP_FIXED_POINT_OPTIM 1 /**< Enable fixed-point speed-up */ +#endif + +/* \} name SECTION: Module settings */ + +/* + * 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 */ + +/** + * \brief Get the list of supported curves in order of preferrence + * (full information) + * + * \return A statically allocated array, the last entry is 0. + */ +const ecp_curve_info *ecp_curve_list( void ); + +/** + * \brief Get the list of supported curves in order of preferrence + * (grp_id only) + * + * \return A statically allocated array, + * terminated with POLARSSL_ECP_DP_NONE. + */ +const ecp_group_id *ecp_grp_id_list( void ); + +/** + * \brief Get curve information from an internal group identifier + * + * \param grp_id A POLARSSL_ECP_DP_XXX value + * + * \return The associated curve information or NULL + */ +const ecp_curve_info *ecp_curve_info_from_grp_id( ecp_group_id grp_id ); + +/** + * \brief Get curve information from a TLS NamedCurve value + * + * \param tls_id A POLARSSL_ECP_DP_XXX value + * + * \return The associated curve information or NULL + */ +const ecp_curve_info *ecp_curve_info_from_tls_id( uint16_t tls_id ); + +/** + * \brief Get curve information from a human-readable name + * + * \param name The name + * + * \return The associated curve information or NULL + */ +const ecp_curve_info *ecp_curve_info_from_name( const char *name ); + +/** + * \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 Initialize a key pair (as an invalid one) + */ +void ecp_keypair_init( ecp_keypair *key ); + +/** + * \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 Free the components of a key pair + */ +void ecp_keypair_free( ecp_keypair *key ); + +/** + * \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 Copy the contents of a group object + * + * \param dst Destination group + * \param src Source group + * + * \return 0 if successful, + * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed + */ +int ecp_group_copy( ecp_group *dst, const ecp_group *src ); + +/** + * \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 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 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_BAD_INPUT_DATA if input is invalid, + * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed, + * POLARSSL_ERR_ECP_FEATURE_UNAVAILABLE if the point format + * is not implemented. + * + * \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 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 olen length of data written + * \param buf Buffer to write to + * \param blen 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 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 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_FEATURE_UNAVAILABLE for unkownn groups + * + * \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 index ); + +/** + * \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 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 + * + * \note This function does not support Montgomery curves, such as + * Curve25519. + */ +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 + * + * \note This function does not support Montgomery curves, such as + * Curve25519. + */ +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 + * (Not thread-safe to use same group in multiple threads) + * + * \param grp ECP group + * \param R Destination point + * \param m Integer by which to multiply + * \param P Point to multiply + * \param f_rng RNG function (see notes) + * \param p_rng RNG parameter + * + * \return 0 if successful, + * POLARSSL_ERR_ECP_INVALID_KEY if m is not a valid privkey + * or P is not a valid pubkey, + * POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed + * + * \note In order to prevent timing attacks, this function + * executes the exact same sequence of (base field) + * operations for any valid m. It avoids any if-branch or + * array index depending on the value of m. + * + * \note If f_rng is not NULL, it is used to randomize intermediate + * results in order to prevent potential timing attacks + * targeting these results. It is recommended to always + * provide a non-NULL f_rng (the overhead is negligible). + */ +int ecp_mul( ecp_group *grp, ecp_point *R, + const mpi *m, const ecp_point *P, + int (*f_rng)(void *, unsigned char *, size_t), void *p_rng ); + +/** + * \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_INVALID_KEY 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. + * + * \note Uses bare components rather than an ecp_keypair structure + * in order to ease use with other structures such as + * ecdh_context of ecdsa_context. + */ +int ecp_check_pubkey( const ecp_group *grp, const ecp_point *pt ); + +/** + * \brief Check that an mpi is a valid private key for this curve + * + * \param grp Group used + * \param d Integer to check + * + * \return 0 if point is a valid private key, + * POLARSSL_ERR_ECP_INVALID_KEY otherwise. + * + * \note Uses bare components rather than an ecp_keypair structure + * in order to ease use with other structures such as + * ecdh_context of ecdsa_context. + */ +int ecp_check_privkey( const ecp_group *grp, const mpi *d ); + +/** + * \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 + * + * \note Uses bare components rather than an ecp_keypair structure + * in order to ease use with other structures such as + * ecdh_context of ecdsa_context. + */ +int ecp_gen_keypair( ecp_group *grp, mpi *d, ecp_point *Q, + int (*f_rng)(void *, unsigned char *, size_t), + void *p_rng ); + +/** + * \brief Generate a keypair + * + * \param grp_id ECP group identifier + * \param key Destination keypair + * \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_key( ecp_group_id grp_id, ecp_keypair *key, + int (*f_rng)(void *, unsigned char *, size_t), void *p_rng ); + +#if defined(POLARSSL_SELF_TEST) +/** + * \brief Checkup routine + * + * \return 0 if successful, or 1 if a test failed + */ +int ecp_self_test( int verbose ); +#endif + +#ifdef __cplusplus +} +#endif + +#endif /* ecp.h */ + +