/** * Modular bignum functions * * This module implements operations on integers modulo some fixed modulus. */ /* * 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. */ #ifndef MBEDTLS_BIGNUM_MOD_H #define MBEDTLS_BIGNUM_MOD_H #include "common.h" #if defined(MBEDTLS_BIGNUM_C) #include "mbedtls/bignum.h" #endif /* Skip 1 as it is slightly easier to accidentally pass to functions. */ typedef enum { MBEDTLS_MPI_MOD_REP_INVALID = 0, MBEDTLS_MPI_MOD_REP_MONTGOMERY = 2, MBEDTLS_MPI_MOD_REP_OPT_RED } mbedtls_mpi_mod_rep_selector; /* Make mbedtls_mpi_mod_rep_selector and mbedtls_mpi_mod_ext_rep disjoint to * make it easier to catch when they are accidentally swapped. */ typedef enum { MBEDTLS_MPI_MOD_EXT_REP_INVALID = 0, MBEDTLS_MPI_MOD_EXT_REP_LE = 8, MBEDTLS_MPI_MOD_EXT_REP_BE } mbedtls_mpi_mod_ext_rep; typedef struct { mbedtls_mpi_uint *p; size_t limbs; } mbedtls_mpi_mod_residue; typedef struct { mbedtls_mpi_uint const *rr; /* The residue for 2^{2*n*biL} mod N */ mbedtls_mpi_uint mm; /* Montgomery const for -N^{-1} mod 2^{ciL} */ } mbedtls_mpi_mont_struct; typedef void *mbedtls_mpi_opt_red_struct; typedef struct { const mbedtls_mpi_uint *p; size_t limbs; // number of limbs size_t bits; // bitlen of p mbedtls_mpi_mod_rep_selector int_rep; // selector to signal the active member of the union union rep { mbedtls_mpi_mont_struct mont; mbedtls_mpi_opt_red_struct ored; } rep; } mbedtls_mpi_mod_modulus; /** Setup a residue structure. * * The residue will be set up with the buffer \p p and modulus \p m. * * The memory pointed to by \p p will be used by the resulting residue structure. * The value at the pointed-to memory will be the initial value of \p r and must * hold a value that is less than the modulus. This value will be used as-is * and interpreted according to the value of the `m->int_rep` field. * * The modulus \p m will be the modulus associated with \p r. The residue \p r * should only be used in operations where the modulus is \p m. * * \param[out] r The address of the residue to setup. * \param[in] m The address of the modulus related to \p r. * \param[in] p The address of the limb array containing the value of \p r. * The memory pointed to by \p p will be used by \p r and must * not be modified in any way until after * mbedtls_mpi_mod_residue_release() is called. The data * pointed to by \p p must be less than the modulus (the value * pointed to by `m->p`) and already in the representation * indicated by `m->int_rep`. * \param p_limbs The number of limbs of \p p. Must be the same as the number * of limbs in the modulus \p m. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \p p_limbs is less than the * limbs in \p m or if \p p is not less than \p m. */ int mbedtls_mpi_mod_residue_setup( mbedtls_mpi_mod_residue *r, const mbedtls_mpi_mod_modulus *m, mbedtls_mpi_uint *p, size_t p_limbs ); /** Unbind elements of a residue structure. * * This function removes the reference to the limb array that was passed to * mbedtls_mpi_mod_residue_setup() to make it safe to free or use again. * * This function invalidates \p r and it must not be used until after * mbedtls_mpi_mod_residue_setup() is called on it again. * * \param[out] r The address of residue to release. */ void mbedtls_mpi_mod_residue_release( mbedtls_mpi_mod_residue *r ); /** Initialize a modulus structure. * * \param[out] m The address of the modulus structure to initialize. */ void mbedtls_mpi_mod_modulus_init( mbedtls_mpi_mod_modulus *m ); /** Setup a modulus structure. * * \param[out] m The address of the modulus structure to populate. * \param[in] p The address of the limb array storing the value of \p m. * The memory pointed to by \p p will be used by \p m and must * not be modified in any way until after * mbedtls_mpi_mod_modulus_free() is called. * \param p_limbs The number of limbs of \p p. * \param int_rep The internal representation to be used for residues * associated with \p m (see #mbedtls_mpi_mod_rep_selector). * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \p int_rep is invalid. */ int mbedtls_mpi_mod_modulus_setup( mbedtls_mpi_mod_modulus *m, const mbedtls_mpi_uint *p, size_t p_limbs, mbedtls_mpi_mod_rep_selector int_rep ); /** Free elements of a modulus structure. * * This function frees any memory allocated by mbedtls_mpi_mod_modulus_setup(). * * \warning This function does not free the limb array passed to * mbedtls_mpi_mod_modulus_setup() only removes the reference to it, * making it safe to free or to use it again. * * \param[in,out] m The address of the modulus structure to free. */ void mbedtls_mpi_mod_modulus_free( mbedtls_mpi_mod_modulus *m ); /* BEGIN MERGE SLOT 1 */ /* END MERGE SLOT 1 */ /* BEGIN MERGE SLOT 2 */ /* END MERGE SLOT 2 */ /* BEGIN MERGE SLOT 3 */ /** * \brief Perform a fixed-size modular subtraction. * * Calculate `A - B modulo N`. * * \p A, \p B and \p X must all have the same number of limbs as \p N. * * \p X may be aliased to \p A or \p B, or even both, but may not overlap * either otherwise. * * \note This function does not check that \p A or \p B are in canonical * form (that is, are < \p N) - that will have been done by * mbedtls_mpi_mod_residue_setup(). * * \param[out] X The address of the result MPI. Must be initialized. * Must have the same number of limbs as the modulus \p N. * \param[in] A The address of the first MPI. * \param[in] B The address of the second MPI. * \param[in] N The address of the modulus. Used to perform a modulo * operation on the result of the subtraction. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if the given MPIs do not * have the correct number of limbs. */ int mbedtls_mpi_mod_sub( mbedtls_mpi_mod_residue *X, const mbedtls_mpi_mod_residue *A, const mbedtls_mpi_mod_residue *B, const mbedtls_mpi_mod_modulus *N ); /* END MERGE SLOT 3 */ /* BEGIN MERGE SLOT 4 */ /* END MERGE SLOT 4 */ /* BEGIN MERGE SLOT 5 */ /* END MERGE SLOT 5 */ /* BEGIN MERGE SLOT 6 */ /* END MERGE SLOT 6 */ /* BEGIN MERGE SLOT 7 */ /** Read a residue from a byte buffer. * * The residue will be automatically converted to the internal representation * based on the value of the `m->int_rep` field. * * The modulus \p m will be the modulus associated with \p r. The residue \p r * should only be used in operations where the modulus is \p m or a modulus * equivalent to \p m (in the sense that all their fields or memory pointed by * their fields hold the same value). * * \param[out] r The address of the residue. It must have exactly the same * number of limbs as the modulus \p m. * \param[in] m The address of the modulus. * \param[in] buf The input buffer to import from. * \param buflen The length in bytes of \p buf. * \param ext_rep The endianness of the number in the input buffer. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p r isn't * large enough to hold the value in \p buf. * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \p ext_rep * is invalid or the value in the buffer is not less than \p m. */ int mbedtls_mpi_mod_read( mbedtls_mpi_mod_residue *r, const mbedtls_mpi_mod_modulus *m, const unsigned char *buf, size_t buflen, mbedtls_mpi_mod_ext_rep ext_rep ); /** Write a residue into a byte buffer. * * The modulus \p m must be the modulus associated with \p r (see * mbedtls_mpi_mod_residue_setup() and mbedtls_mpi_mod_read()). * * The residue will be automatically converted from the internal representation * based on the value of `m->int_rep` field. * * \warning If the buffer is smaller than `m->bits`, the number of * leading zeroes is leaked through timing. If \p r is * secret, the caller must ensure that \p buflen is at least * (`m->bits`+7)/8. * * \param[in] r The address of the residue. It must have the same number of * limbs as the modulus \p m. (\p r is an input parameter, but * its value will be modified during execution and restored * before the function returns.) * \param[in] m The address of the modulus associated with \r. * \param[out] buf The output buffer to export to. * \param buflen The length in bytes of \p buf. * \param ext_rep The endianness in which the number should be written into * the output buffer. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p buf isn't * large enough to hold the value of \p r (without leading * zeroes). * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \p ext_rep is invalid. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if couldn't allocate enough * memory for conversion. Can occur only for moduli with * MBEDTLS_MPI_MOD_REP_MONTGOMERY. */ int mbedtls_mpi_mod_write( const mbedtls_mpi_mod_residue *r, const mbedtls_mpi_mod_modulus *m, unsigned char *buf, size_t buflen, mbedtls_mpi_mod_ext_rep ext_rep ); /* END MERGE SLOT 7 */ /* BEGIN MERGE SLOT 8 */ /* END MERGE SLOT 8 */ /* BEGIN MERGE SLOT 9 */ /* END MERGE SLOT 9 */ /* BEGIN MERGE SLOT 10 */ /* END MERGE SLOT 10 */ #endif /* MBEDTLS_BIGNUM_MOD_H */