library/ecp_alt.h - third_party/github/ARMmbed/mbedtls - Git at Google

 /**
  * \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 */
	/**
	* \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 */