/** * Low-level modular bignum functions * * This interface should only be used by the higher-level modular bignum * module (bignum_mod.c) and the ECP module (ecp.c, ecp_curves.c). All other * modules should use the high-level modular bignum interface (bignum_mod.h) * or the legacy bignum interface (bignum.h). * * This is a low-level interface to operations on integers modulo which * has no protection against passing invalid arguments such as arrays of * the wrong size. The functions in bignum_mod.h provide a higher-level * interface that includes protections against accidental misuse, at the * expense of code size and sometimes more cumbersome memory management. * * The functions in this module obey the following conventions unless * explicitly indicated otherwise: * - **Modulus parameters**: the modulus is passed as a pointer to a structure * of type #mbedtls_mpi_mod_modulus. The structure must be set up with an * array of limbs storing the bignum value of the modulus. The modulus must * be odd and is assumed to have no leading zeroes. The modulus is usually * named \c N and is usually input-only. * - **Bignum parameters**: Bignums are passed as pointers to an array of * limbs. A limb has the type #mbedtls_mpi_uint. Unless otherwise specified: * - Bignum parameters called \c A, \c B, ... are inputs, and are not * modified by the function. * - Bignum parameters called \c X, \c Y are outputs or input-output. * The initial content of output-only parameters is ignored. * - \c T is a temporary storage area. The initial content of such a * parameter is ignored and the final content is unspecified. * - **Bignum sizes**: bignum sizes are usually expressed by the \c limbs * member of the modulus argument. All bignum parameters must have the same * number of limbs as the modulus. All bignum sizes must be at least 1 and * must be significantly less than #SIZE_MAX. The behavior if a size is 0 is * undefined. * - **Bignum representation**: the representation of inputs and outputs is * specified by the \c int_rep field of the modulus for arithmetic * functions. Utility functions may allow for different representation. * - **Parameter ordering**: for bignum parameters, outputs come before inputs. * The modulus is passed after other bignum input parameters. Temporaries * come last. * - **Aliasing**: in general, output bignums may be aliased to one or more * inputs. Modulus values may not be aliased to any other parameter. Outputs * may not be aliased to one another. Temporaries may not be aliased to any * other parameter. * - **Overlap**: apart from aliasing of limb array pointers (where two * arguments are equal pointers), overlap is not supported and may result * in undefined behavior. * - **Error handling**: This is a low-level module. Functions generally do not * try to protect against invalid arguments such as nonsensical sizes or * null pointers. Note that passing bignums with a different size than the * modulus may lead to buffer overflows. Some functions which allocate * memory or handle reading/writing of bignums will return an error if * memory allocation fails or if buffer sizes are invalid. * - **Modular representatives**: all functions expect inputs to be in the * range [0, \c N - 1] and guarantee outputs in the range [0, \c N - 1]. If * an input is out of range, outputs are fully unspecified, though bignum * values out of range should not cause buffer overflows (beware that this is * not extensively tested). */ /* * 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_RAW_H #define MBEDTLS_BIGNUM_MOD_RAW_H #include "common.h" #if defined(MBEDTLS_BIGNUM_C) #include "mbedtls/bignum.h" #endif #include "bignum_mod.h" /** * \brief Perform a safe conditional copy of an MPI which doesn't reveal * whether the assignment was done or not. * * The size to copy is determined by \p N. * * \param[out] X The address of the destination MPI. * This must be initialized. Must have enough limbs to * store the full value of \p A. * \param[in] A The address of the source MPI. This must be initialized. * \param[in] N The address of the modulus related to \p X and \p A. * \param assign The condition deciding whether to perform the * assignment or not. Must be either 0 or 1: * * \c 1: Perform the assignment `X = A`. * * \c 0: Keep the original value of \p X. * * \note This function avoids leaking any information about whether * the assignment was done or not. * * \warning If \p assign is neither 0 nor 1, the result of this function * is indeterminate, and the resulting value in \p X might be * neither its original value nor the value in \p A. */ void mbedtls_mpi_mod_raw_cond_assign(mbedtls_mpi_uint *X, const mbedtls_mpi_uint *A, const mbedtls_mpi_mod_modulus *N, unsigned char assign); /** * \brief Perform a safe conditional swap of two MPIs which doesn't reveal * whether the swap was done or not. * * The size to swap is determined by \p N. * * \param[in,out] X The address of the first MPI. This must be initialized. * \param[in,out] Y The address of the second MPI. This must be initialized. * \param[in] N The address of the modulus related to \p X and \p Y. * \param swap The condition deciding whether to perform * the swap or not. Must be either 0 or 1: * * \c 1: Swap the values of \p X and \p Y. * * \c 0: Keep the original values of \p X and \p Y. * * \note This function avoids leaking any information about whether * the swap was done or not. * * \warning If \p swap is neither 0 nor 1, the result of this function * is indeterminate, and both \p X and \p Y might end up with * values different to either of the original ones. */ void mbedtls_mpi_mod_raw_cond_swap(mbedtls_mpi_uint *X, mbedtls_mpi_uint *Y, const mbedtls_mpi_mod_modulus *N, unsigned char swap); /** Import X from unsigned binary data. * * The MPI needs to have enough limbs to store the full value (including any * most significant zero bytes in the input). * * \param[out] X The address of the MPI. The size is determined by \p N. * (In particular, it must have at least as many limbs as * the modulus \p N.) * \param[in] N The address of the modulus related to \p X. * \param[in] input The input buffer to import from. * \param input_length The length in bytes of \p input. * \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 X isn't * large enough to hold the value in \p input. * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if the external representation * of \p N is invalid or \p X is not less than \p N. */ int mbedtls_mpi_mod_raw_read(mbedtls_mpi_uint *X, const mbedtls_mpi_mod_modulus *N, const unsigned char *input, size_t input_length, mbedtls_mpi_mod_ext_rep ext_rep); /** Export A into unsigned binary data. * * \param[in] A The address of the MPI. The size is determined by \p N. * (In particular, it must have at least as many limbs as * the modulus \p N.) * \param[in] N The address of the modulus related to \p A. * \param[out] output The output buffer to export to. * \param output_length The length in bytes of \p output. * \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 output isn't * large enough to hold the value of \p A. * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if the external representation * of \p N is invalid. */ int mbedtls_mpi_mod_raw_write(const mbedtls_mpi_uint *A, const mbedtls_mpi_mod_modulus *N, unsigned char *output, size_t output_length, mbedtls_mpi_mod_ext_rep ext_rep); /** \brief Subtract two MPIs, returning the residue modulo the specified * modulus. * * The size of the operation is determined by \p N. \p A and \p B must 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. * * \param[out] X The address of the result MPI. * This must be initialized. Must have enough limbs to * store the full value of the result. * \param[in] A The address of the first MPI. This must be initialized. * \param[in] B The address of the second MPI. This must be initialized. * \param[in] N The address of the modulus. Used to perform a modulo * operation on the result of the subtraction. */ void mbedtls_mpi_mod_raw_sub(mbedtls_mpi_uint *X, const mbedtls_mpi_uint *A, const mbedtls_mpi_uint *B, const mbedtls_mpi_mod_modulus *N); /** \brief Multiply two MPIs, returning the residue modulo the specified * modulus. * * \note Currently handles the case when `N->int_rep` is * MBEDTLS_MPI_MOD_REP_MONTGOMERY. * * The size of the operation is determined by \p N. \p A, \p B and \p X must * all be associated with the modulus \p N and 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. They may not alias \p N (since they must be in canonical * form, they cannot == \p N). * * \param[out] X The address of the result MPI. Must have the same * number of limbs as \p N. * On successful completion, \p X contains the result of * the multiplication `A * B * R^-1` mod N where * `R = 2^(biL * N->limbs)`. * \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 multiplication. * \param[in,out] T Temporary storage of size at least 2 * N->limbs + 1 * limbs. Its initial content is unused and * its final content is indeterminate. * It must not alias or otherwise overlap any of the * other parameters. */ void mbedtls_mpi_mod_raw_mul(mbedtls_mpi_uint *X, const mbedtls_mpi_uint *A, const mbedtls_mpi_uint *B, const mbedtls_mpi_mod_modulus *N, mbedtls_mpi_uint *T); /** * \brief Returns the number of limbs of working memory required for * a call to `mbedtls_mpi_mod_raw_inv_prime()`. * * \note This will always be at least * `mbedtls_mpi_core_montmul_working_limbs(AN_limbs)`, * i.e. sufficient for a call to `mbedtls_mpi_core_montmul()`. * * \param AN_limbs The number of limbs in the input `A` and the modulus `N` * (they must be the same size) that will be given to * `mbedtls_mpi_mod_raw_inv_prime()`. * * \return The number of limbs of working memory required by * `mbedtls_mpi_mod_raw_inv_prime()`. */ size_t mbedtls_mpi_mod_raw_inv_prime_working_limbs(size_t AN_limbs); /** * \brief Perform fixed-width modular inversion of a Montgomery-form MPI with * respect to a modulus \p N that must be prime. * * \p X may be aliased to \p A, but not to \p N or \p RR. * * \param[out] X The modular inverse of \p A with respect to \p N. * Will be in Montgomery form. * \param[in] A The number to calculate the modular inverse of. * Must be in Montgomery form. Must not be 0. * \param[in] N The modulus, as a little-endian array of length \p AN_limbs. * Must be prime. * \param AN_limbs The number of limbs in \p A, \p N and \p RR. * \param[in] RR The precomputed residue of 2^{2*biL} modulo N, as a little- * endian array of length \p AN_limbs. * \param[in,out] T Temporary storage of at least the number of limbs returned * by `mbedtls_mpi_mod_raw_inv_prime_working_limbs()`. * Its initial content is unused and its final content is * indeterminate. * It must not alias or otherwise overlap any of the other * parameters. * It is up to the caller to zeroize \p T when it is no * longer needed, and before freeing it if it was dynamically * allocated. */ void mbedtls_mpi_mod_raw_inv_prime(mbedtls_mpi_uint *X, const mbedtls_mpi_uint *A, const mbedtls_mpi_uint *N, size_t AN_limbs, const mbedtls_mpi_uint *RR, mbedtls_mpi_uint *T); /** * \brief Perform a known-size modular addition. * * Calculate `A + B modulo N`. * * The number of limbs in each operand, and the result, is given by the * modulus \p N. * * \p X may be aliased to \p A or \p B, or even both, but may not overlap * either otherwise. * * \param[out] X The result of the modular addition. * \param[in] A Little-endian presentation of the left operand. This * must be smaller than \p N. * \param[in] B Little-endian presentation of the right operand. This * must be smaller than \p N. * \param[in] N The address of the modulus. */ void mbedtls_mpi_mod_raw_add(mbedtls_mpi_uint *X, const mbedtls_mpi_uint *A, const mbedtls_mpi_uint *B, const mbedtls_mpi_mod_modulus *N); /** Convert an MPI from canonical representation (little-endian limb array) * to the representation associated with the modulus. * * \param[in,out] X The limb array to convert. * It must have as many limbs as \p N. * It is converted in place. * If this function returns an error, the content of \p X * is unspecified. * \param[in] N The modulus structure. * * \return \c 0 if successful. * Otherwise an \c MBEDTLS_ERR_MPI_xxx error code. */ int mbedtls_mpi_mod_raw_canonical_to_modulus_rep( mbedtls_mpi_uint *X, const mbedtls_mpi_mod_modulus *N); /** Convert an MPI from the representation associated with the modulus * to canonical representation (little-endian limb array). * * \param[in,out] X The limb array to convert. * It must have as many limbs as \p N. * It is converted in place. * If this function returns an error, the content of \p X * is unspecified. * \param[in] N The modulus structure. * * \return \c 0 if successful. * Otherwise an \c MBEDTLS_ERR_MPI_xxx error code. */ int mbedtls_mpi_mod_raw_modulus_to_canonical_rep( mbedtls_mpi_uint *X, const mbedtls_mpi_mod_modulus *N); /** Generate a random number uniformly in a range. * * This function generates a random number between \p min inclusive and * \p N exclusive. * * The procedure complies with RFC 6979 ยง3.3 (deterministic ECDSA) * when the RNG is a suitably parametrized instance of HMAC_DRBG * and \p min is \c 1. * * \note There are `N - min` possible outputs. The lower bound * \p min can be reached, but the upper bound \p N cannot. * * \param X The destination MPI, in canonical representation modulo \p N. * It must not be aliased with \p N or otherwise overlap it. * \param min The minimum value to return. It must be strictly smaller * than \b N. * \param N The modulus. * This is the upper bound of the output range, exclusive. * \param f_rng The RNG function to use. This must not be \c NULL. * \param p_rng The RNG parameter to be passed to \p f_rng. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if the implementation was * unable to find a suitable value within a limited number * of attempts. This has a negligible probability if \p N * is significantly larger than \p min, which is the case * for all usual cryptographic applications. */ int mbedtls_mpi_mod_raw_random(mbedtls_mpi_uint *X, mbedtls_mpi_uint min, const mbedtls_mpi_mod_modulus *N, int (*f_rng)(void *, unsigned char *, size_t), void *p_rng); /** Convert an MPI into Montgomery form. * * \param X The address of the MPI. * Must have the same number of limbs as \p N. * \param N The address of the modulus, which gives the size of * the base `R` = 2^(biL*N->limbs). * * \return \c 0 if successful. */ int mbedtls_mpi_mod_raw_to_mont_rep(mbedtls_mpi_uint *X, const mbedtls_mpi_mod_modulus *N); /** Convert an MPI back from Montgomery representation. * * \param X The address of the MPI. * Must have the same number of limbs as \p N. * \param N The address of the modulus, which gives the size of * the base `R`= 2^(biL*N->limbs). * * \return \c 0 if successful. */ int mbedtls_mpi_mod_raw_from_mont_rep(mbedtls_mpi_uint *X, const mbedtls_mpi_mod_modulus *N); /** \brief Perform fixed width modular negation. * * The size of the operation is determined by \p N. \p A must have * the same number of limbs as \p N. * * \p X may be aliased to \p A. * * \param[out] X The result of the modular negation. * This must be initialized. * \param[in] A Little-endian presentation of the input operand. This * must be less than or equal to \p N. * \param[in] N The modulus to use. */ void mbedtls_mpi_mod_raw_neg(mbedtls_mpi_uint *X, const mbedtls_mpi_uint *A, const mbedtls_mpi_mod_modulus *N); #endif /* MBEDTLS_BIGNUM_MOD_RAW_H */