| /** |
| * \file ecp_internal_alt.h |
| * |
| * \brief Function declarations for alternative implementation of elliptic curve |
| * point arithmetic. |
| */ |
| /* |
| * Copyright The Mbed TLS Contributors |
| * SPDX-License-Identifier: Apache-2.0 |
| * |
| * Licensed under the Apache License, Version 2.0 (the "License"); you may |
| * not use this file except in compliance with the License. |
| * You may obtain a copy of the License at |
| * |
| * http://www.apache.org/licenses/LICENSE-2.0 |
| * |
| * Unless required by applicable law or agreed to in writing, software |
| * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT |
| * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| * See the License for the specific language governing permissions and |
| * limitations under the License. |
| */ |
| |
| /* |
| * References: |
| * |
| * [1] BERNSTEIN, Daniel J. Curve25519: new Diffie-Hellman speed records. |
| * <http://cr.yp.to/ecdh/curve25519-20060209.pdf> |
| * |
| * [2] CORON, Jean-S'ebastien. Resistance against differential power analysis |
| * for elliptic curve cryptosystems. In : Cryptographic Hardware and |
| * Embedded Systems. Springer Berlin Heidelberg, 1999. p. 292-302. |
| * <http://link.springer.com/chapter/10.1007/3-540-48059-5_25> |
| * |
| * [3] HEDABOU, Mustapha, PINEL, Pierre, et B'EN'ETEAU, Lucien. A comb method to |
| * render ECC resistant against Side Channel Attacks. IACR Cryptology |
| * ePrint Archive, 2004, vol. 2004, p. 342. |
| * <http://eprint.iacr.org/2004/342.pdf> |
| * |
| * [4] Certicom Research. SEC 2: Recommended Elliptic Curve Domain Parameters. |
| * <http://www.secg.org/sec2-v2.pdf> |
| * |
| * [5] HANKERSON, Darrel, MENEZES, Alfred J., VANSTONE, Scott. Guide to Elliptic |
| * Curve Cryptography. |
| * |
| * [6] Digital Signature Standard (DSS), FIPS 186-4. |
| * <http://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.186-4.pdf> |
| * |
| * [7] Elliptic Curve Cryptography (ECC) Cipher Suites for Transport Layer |
| * Security (TLS), RFC 4492. |
| * <https://tools.ietf.org/search/rfc4492> |
| * |
| * [8] <http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html> |
| * |
| * [9] COHEN, Henri. A Course in Computational Algebraic Number Theory. |
| * Springer Science & Business Media, 1 Aug 2000 |
| */ |
| |
| #ifndef MBEDTLS_ECP_INTERNAL_H |
| #define MBEDTLS_ECP_INTERNAL_H |
| |
| #if !defined(MBEDTLS_CONFIG_FILE) |
| #include "mbedtls/config.h" |
| #else |
| #include MBEDTLS_CONFIG_FILE |
| #endif |
| |
| #if defined(MBEDTLS_ECP_INTERNAL_ALT) |
| |
| /** |
| * \brief Indicate if the Elliptic Curve Point module extension can |
| * handle the group. |
| * |
| * \param grp The pointer to the elliptic curve group that will be the |
| * basis of the cryptographic computations. |
| * |
| * \return Non-zero if successful. |
| */ |
| unsigned char mbedtls_internal_ecp_grp_capable( const mbedtls_ecp_group *grp ); |
| |
| /** |
| * \brief Initialise the Elliptic Curve Point module extension. |
| * |
| * If mbedtls_internal_ecp_grp_capable returns true for a |
| * group, this function has to be able to initialise the |
| * module for it. |
| * |
| * This module can be a driver to a crypto hardware |
| * accelerator, for which this could be an initialise function. |
| * |
| * \param grp The pointer to the group the module needs to be |
| * initialised for. |
| * |
| * \return 0 if successful. |
| */ |
| int mbedtls_internal_ecp_init( const mbedtls_ecp_group *grp ); |
| |
| /** |
| * \brief Frees and deallocates the Elliptic Curve Point module |
| * extension. |
| * |
| * \param grp The pointer to the group the module was initialised for. |
| */ |
| void mbedtls_internal_ecp_free( const mbedtls_ecp_group *grp ); |
| |
| #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) |
| |
| #if defined(MBEDTLS_ECP_RANDOMIZE_JAC_ALT) |
| /** |
| * \brief Randomize jacobian coordinates: |
| * (X, Y, Z) -> (l^2 X, l^3 Y, l Z) for random l. |
| * |
| * \param grp Pointer to the group representing the curve. |
| * |
| * \param pt The point on the curve to be randomised, given with Jacobian |
| * coordinates. |
| * |
| * \param f_rng A function pointer to the random number generator. |
| * |
| * \param p_rng A pointer to the random number generator state. |
| * |
| * \return 0 if successful. |
| */ |
| int mbedtls_internal_ecp_randomize_jac( const mbedtls_ecp_group *grp, |
| mbedtls_ecp_point *pt, int (*f_rng)(void *, unsigned char *, size_t), |
| void *p_rng ); |
| #endif |
| |
| #if defined(MBEDTLS_ECP_ADD_MIXED_ALT) |
| /** |
| * \brief Addition: R = P + Q, mixed affine-Jacobian coordinates. |
| * |
| * The coordinates of Q must be normalized (= affine), |
| * but those of P don't need to. R is not normalized. |
| * |
| * This function is used only as a subrutine of |
| * ecp_mul_comb(). |
| * |
| * Special cases: (1) P or Q is zero, (2) R is zero, |
| * (3) P == Q. |
| * None of these cases can happen as intermediate step in |
| * ecp_mul_comb(): |
| * - at each step, P, Q and R are multiples of the base |
| * point, the factor being less than its order, so none of |
| * them is zero; |
| * - Q is an odd multiple of the base point, P an even |
| * multiple, due to the choice of precomputed points in the |
| * modified comb method. |
| * So branches for these cases do not leak secret information. |
| * |
| * We accept Q->Z being unset (saving memory in tables) as |
| * meaning 1. |
| * |
| * Cost in field operations if done by [5] 3.22: |
| * 1A := 8M + 3S |
| * |
| * \param grp Pointer to the group representing the curve. |
| * |
| * \param R Pointer to a point structure to hold the result. |
| * |
| * \param P Pointer to the first summand, given with Jacobian |
| * coordinates |
| * |
| * \param Q Pointer to the second summand, given with affine |
| * coordinates. |
| * |
| * \return 0 if successful. |
| */ |
| int mbedtls_internal_ecp_add_mixed( const mbedtls_ecp_group *grp, |
| mbedtls_ecp_point *R, const mbedtls_ecp_point *P, |
| const mbedtls_ecp_point *Q ); |
| #endif |
| |
| /** |
| * \brief Point doubling R = 2 P, Jacobian coordinates. |
| * |
| * Cost: 1D := 3M + 4S (A == 0) |
| * 4M + 4S (A == -3) |
| * 3M + 6S + 1a otherwise |
| * when the implementation is based on the "dbl-1998-cmo-2" |
| * doubling formulas in [8] and standard optimizations are |
| * applied when curve parameter A is one of { 0, -3 }. |
| * |
| * \param grp Pointer to the group representing the curve. |
| * |
| * \param R Pointer to a point structure to hold the result. |
| * |
| * \param P Pointer to the point that has to be doubled, given with |
| * Jacobian coordinates. |
| * |
| * \return 0 if successful. |
| */ |
| #if defined(MBEDTLS_ECP_DOUBLE_JAC_ALT) |
| int mbedtls_internal_ecp_double_jac( const mbedtls_ecp_group *grp, |
| mbedtls_ecp_point *R, const mbedtls_ecp_point *P ); |
| #endif |
| |
| /** |
| * \brief Normalize jacobian coordinates of an array of (pointers to) |
| * points. |
| * |
| * Using Montgomery's trick to perform only one inversion mod P |
| * the cost is: |
| * 1N(t) := 1I + (6t - 3)M + 1S |
| * (See for example Algorithm 10.3.4. in [9]) |
| * |
| * This function is used only as a subrutine of |
| * ecp_mul_comb(). |
| * |
| * Warning: fails (returning an error) if one of the points is |
| * zero! |
| * This should never happen, see choice of w in ecp_mul_comb(). |
| * |
| * \param grp Pointer to the group representing the curve. |
| * |
| * \param T Array of pointers to the points to normalise. |
| * |
| * \param t_len Number of elements in the array. |
| * |
| * \return 0 if successful, |
| * an error if one of the points is zero. |
| */ |
| #if defined(MBEDTLS_ECP_NORMALIZE_JAC_MANY_ALT) |
| int mbedtls_internal_ecp_normalize_jac_many( const mbedtls_ecp_group *grp, |
| mbedtls_ecp_point *T[], size_t t_len ); |
| #endif |
| |
| /** |
| * \brief Normalize jacobian coordinates so that Z == 0 || Z == 1. |
| * |
| * Cost in field operations if done by [5] 3.2.1: |
| * 1N := 1I + 3M + 1S |
| * |
| * \param grp Pointer to the group representing the curve. |
| * |
| * \param pt pointer to the point to be normalised. This is an |
| * input/output parameter. |
| * |
| * \return 0 if successful. |
| */ |
| #if defined(MBEDTLS_ECP_NORMALIZE_JAC_ALT) |
| int mbedtls_internal_ecp_normalize_jac( const mbedtls_ecp_group *grp, |
| mbedtls_ecp_point *pt ); |
| #endif |
| |
| #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ |
| |
| #if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED) |
| |
| #if defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT) |
| int mbedtls_internal_ecp_double_add_mxz( const mbedtls_ecp_group *grp, |
| mbedtls_ecp_point *R, mbedtls_ecp_point *S, const mbedtls_ecp_point *P, |
| const mbedtls_ecp_point *Q, const mbedtls_mpi *d ); |
| #endif |
| |
| /** |
| * \brief Randomize projective x/z coordinates: |
| * (X, Z) -> (l X, l Z) for random l |
| * |
| * \param grp pointer to the group representing the curve |
| * |
| * \param P the point on the curve to be randomised given with |
| * projective coordinates. This is an input/output parameter. |
| * |
| * \param f_rng a function pointer to the random number generator |
| * |
| * \param p_rng a pointer to the random number generator state |
| * |
| * \return 0 if successful |
| */ |
| #if defined(MBEDTLS_ECP_RANDOMIZE_MXZ_ALT) |
| int mbedtls_internal_ecp_randomize_mxz( const mbedtls_ecp_group *grp, |
| mbedtls_ecp_point *P, int (*f_rng)(void *, unsigned char *, size_t), |
| void *p_rng ); |
| #endif |
| |
| /** |
| * \brief Normalize Montgomery x/z coordinates: X = X/Z, Z = 1. |
| * |
| * \param grp pointer to the group representing the curve |
| * |
| * \param P pointer to the point to be normalised. This is an |
| * input/output parameter. |
| * |
| * \return 0 if successful |
| */ |
| #if defined(MBEDTLS_ECP_NORMALIZE_MXZ_ALT) |
| int mbedtls_internal_ecp_normalize_mxz( const mbedtls_ecp_group *grp, |
| mbedtls_ecp_point *P ); |
| #endif |
| |
| #endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */ |
| |
| #endif /* MBEDTLS_ECP_INTERNAL_ALT */ |
| |
| #endif /* ecp_internal_alt.h */ |
| |