include/mbedtls/ecp_internal.h

/**
 * \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:
 *
 * SEC1 http://www.secg.org/index.php?action=secg,docs_secg
 * GECC = Guide to Elliptic Curve Cryptography - Hankerson, Menezes, Vanstone
 * FIPS 186-3 http://csrc.nist.gov/publications/fips/fips186-3/fips_186-3.pdf
 * RFC 4492 for the related TLS structures and constants
 *
 * [Curve25519] 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>
 */

#ifndef MBEDTLS_ECP_INTERNAL_H
#define MBEDTLS_ECP_INTERNAL_H

#if defined(MBEDTLS_ECP_INTERNAL_ALT)

/**
 * \brief           Tell if the cryptographic hardware can handle the group.
 *
 * \param grp       The pointer to the group.
 *
 * \return          Non-zero if successful.
 */
unsigned char mbedtls_internal_ecp_grp_capable( const mbedtls_ecp_group *grp );

/**
 * \brief           Initialise the crypto hardware accelerator.
 *
 *                  If mbedtls_internal_ecp_grp_capable returns true for a
 *                  group, this function has to be able to initialise the
 *                  hardware for it.
 *
 * \param grp       The pointer to the group the hardware needs to be
 *                  initialised for.
 *
 * \return          0 if successful.
 */
int mbedtls_internal_ecp_init( const mbedtls_ecp_group *grp );

/**
 * \brief           Reset the crypto hardware accelerator to an uninitialised
 *                  state.
 *
 * \param grp       The pointer to the group the hardware 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.
 *
 *                  This is sort of the reverse operation of
 *                  ecp_normalize_jac().
 *
 * \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.
 *
 *                  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 GECC 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 
 *                  http://www.hyperelliptic.org/EFD/g1p/
 *                      auto-shortw-jacobian.html#doubling-dbl-1998-cmo-2
 *                  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 Cohen's "A Course in Computational
 *                  Algebraic Number Theory", Algorithm 10.3.4.)
 *
 *                  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 GECC 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
 *                  This is sort of the reverse operation of ecp_normalize_mxz().
 *
 * \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 */