/**
* \file ecp_internal.h
*
* \brief Function declarations for alternative implementation of elliptic curve
* point arithmetic.
*/
/*
* Copyright (C) 2016, ARM Limited, All Rights Reserved
* 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.
*
* This file is part of mbed TLS (https://tls.mbed.org)
*/
/*
* 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(ECP_SHORTWEIERSTRASS)
#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 /* ECP_SHORTWEIERSTRASS */
#if defined(ECP_MONTGOMERY)
#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 /* ECP_MONTGOMERY */
#endif /* MBEDTLS_ECP_INTERNAL_ALT */
#endif /* ecp_internal.h */
