pigweed / third_party / github / ARMmbed / mbedtls / e3c48b4a883e8812214a4c57c319d005f34b7ccc / . / library / ecp_alt.h

/** | |

* \file ecp_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_alt.h */ | |