/** * Core bignum functions * * This interface should only be used by the legacy bignum module (bignum.h) * and the modular bignum modules (bignum_mod.c, bignum_mod_raw.c). All other * modules should use the high-level modular bignum interface (bignum_mod.h) * or the legacy bignum interface (bignum.h). * * This module is about processing non-negative integers with a fixed upper * bound that's of the form 2^n-1 where n is a multiple of #biL. * These can be thought of integers written in base 2^#biL with a fixed * number of digits. Digits in this base are called *limbs*. * Many operations treat these numbers as the principal representation of * a number modulo 2^n or a smaller bound. * * The functions in this module obey the following conventions unless * explicitly indicated otherwise: * * - **Overflow**: some functions indicate overflow from the range * [0, 2^n-1] by returning carry parameters, while others operate * modulo and so cannot overflow. This should be clear from the function * documentation. * - **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 \p A, \p B, ... are inputs, and are * not modified by the function. * - For operations modulo some number, the modulus is called \p N * and is input-only. * - Bignum parameters called \p X, \p Y are outputs or input-output. * The initial content of output-only parameters is ignored. * - Some functions use different names that reflect traditional * naming of operands of certain operations (e.g. * divisor/dividend/quotient/remainder). * - \p T is a temporary storage area. The initial content of such * parameter is ignored and the final content is unspecified. * - **Bignum sizes**: bignum sizes are always expressed in limbs. * Most functions work on bignums of a given size and take a single * \p limbs parameter that applies to all parameters that are limb arrays. * 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. The behavior if the * total size of all parameters overflows #SIZE_MAX is undefined. * - **Parameter ordering**: for bignum parameters, outputs come before inputs. * Temporaries come last. * - **Aliasing**: in general, output bignums may be aliased to one or more * inputs. As an exception, parameters that are documented as a modulus value * may not be aliased to an output. 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 some functions that operate on bignums of * different sizes have constraints about their size, and violating those * constraints may lead to buffer overflows. * - **Modular representatives**: functions that operate modulo \p N expect * all modular inputs to be in the range [0, \p N - 1] and guarantee outputs * in the range [0, \p 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 OR GPL-2.0-or-later */ #ifndef MBEDTLS_BIGNUM_CORE_H #define MBEDTLS_BIGNUM_CORE_H #include "common.h" #if defined(MBEDTLS_BIGNUM_C) #include "mbedtls/bignum.h" #endif #include "constant_time_internal.h" #define ciL … #define biL … #define biH … /* * Convert between bits/chars and number of limbs * Divide first in order to avoid potential overflows */ #define BITS_TO_LIMBS(i) … #define CHARS_TO_LIMBS(i) … /* Get a specific byte, without range checks. */ #define GET_BYTE(X, i) … /* Constants to identify whether a value is public or secret. If a parameter is marked as secret by * this constant, the function must be constant time with respect to the parameter. * * This is only needed for functions with the _optionally_safe postfix. All other functions have * fixed behavior that can't be changed at runtime and are constant time with respect to their * parameters as prescribed by their documentation or by conventions in their module's documentation. * * Parameters should be named X_public where X is the name of the * corresponding input parameter. * * Implementation should always check using * if (X_public == MBEDTLS_MPI_IS_PUBLIC) { * // unsafe path * } else { * // safe path * } * not the other way round, in order to prevent misuse. (This is, if a value * other than the two below is passed, default to the safe path.) */ #define MBEDTLS_MPI_IS_PUBLIC … #define MBEDTLS_MPI_IS_SECRET … /** Count leading zero bits in a given integer. * * \warning The result is undefined if \p a == 0 * * \param a Integer to count leading zero bits. * * \return The number of leading zero bits in \p a, if \p a != 0. * If \p a == 0, the result is undefined. */ size_t mbedtls_mpi_core_clz(mbedtls_mpi_uint a); /** Return the minimum number of bits required to represent the value held * in the MPI. * * \note This function returns 0 if all the limbs of \p A are 0. * * \param[in] A The address of the MPI. * \param A_limbs The number of limbs of \p A. * * \return The number of bits in \p A. */ size_t mbedtls_mpi_core_bitlen(const mbedtls_mpi_uint *A, size_t A_limbs); /** Convert a big-endian byte array aligned to the size of mbedtls_mpi_uint * into the storage form used by mbedtls_mpi. * * \param[in,out] A The address of the MPI. * \param A_limbs The number of limbs of \p A. */ void mbedtls_mpi_core_bigendian_to_host(mbedtls_mpi_uint *A, size_t A_limbs); /** \brief Compare a machine integer with an MPI. * * This function operates in constant time with respect * to the values of \p min and \p A. * * \param min A machine integer. * \param[in] A An MPI. * \param A_limbs The number of limbs of \p A. * This must be at least 1. * * \return MBEDTLS_CT_TRUE if \p min is less than or equal to \p A, otherwise MBEDTLS_CT_FALSE. */ mbedtls_ct_condition_t mbedtls_mpi_core_uint_le_mpi(mbedtls_mpi_uint min, const mbedtls_mpi_uint *A, size_t A_limbs); /** * \brief Check if one unsigned MPI is less than another in constant * time. * * \param A The left-hand MPI. This must point to an array of limbs * with the same allocated length as \p B. * \param B The right-hand MPI. This must point to an array of limbs * with the same allocated length as \p A. * \param limbs The number of limbs in \p A and \p B. * This must not be 0. * * \return MBEDTLS_CT_TRUE if \p A is less than \p B. * MBEDTLS_CT_FALSE if \p A is greater than or equal to \p B. */ mbedtls_ct_condition_t mbedtls_mpi_core_lt_ct(const mbedtls_mpi_uint *A, const mbedtls_mpi_uint *B, size_t limbs); /** * \brief Perform a safe conditional copy of an MPI which doesn't reveal * whether assignment was done or not. * * \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 limbs The number of limbs of \p A. * \param assign The condition deciding whether to perform the * assignment or not. Callers will need to use * the constant time interface (e.g. `mbedtls_ct_bool()`) * to construct this argument. * * \note This function avoids leaking any information about whether * the assignment was done or not. */ void mbedtls_mpi_core_cond_assign(mbedtls_mpi_uint *X, const mbedtls_mpi_uint *A, size_t limbs, mbedtls_ct_condition_t assign); /** * \brief Perform a safe conditional swap of two MPIs which doesn't reveal * whether the swap was done or not. * * \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 limbs The number of limbs of \p X and \p Y. * \param swap The condition deciding whether to perform * the swap or not. * * \note This function avoids leaking any information about whether * the swap was done or not. */ void mbedtls_mpi_core_cond_swap(mbedtls_mpi_uint *X, mbedtls_mpi_uint *Y, size_t limbs, mbedtls_ct_condition_t swap); /** Import X from unsigned binary data, little-endian. * * 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. * \param X_limbs The number of limbs of \p X. * \param[in] input The input buffer to import from. * \param input_length The length bytes of \p input. * * \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. */ int mbedtls_mpi_core_read_le(mbedtls_mpi_uint *X, size_t X_limbs, const unsigned char *input, size_t input_length); /** Import X from unsigned binary data, big-endian. * * 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. * May only be #NULL if \p X_limbs is 0 and \p input_length * is 0. * \param X_limbs The number of limbs of \p X. * \param[in] input The input buffer to import from. * May only be #NULL if \p input_length is 0. * \param input_length The length in bytes of \p input. * * \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. */ int mbedtls_mpi_core_read_be(mbedtls_mpi_uint *X, size_t X_limbs, const unsigned char *input, size_t input_length); /** Export A into unsigned binary data, little-endian. * * \note If \p output is shorter than \p A the export is still successful if the * value held in \p A fits in the buffer (that is, if enough of the most * significant bytes of \p A are 0). * * \param[in] A The address of the MPI. * \param A_limbs The number of limbs of \p A. * \param[out] output The output buffer to export to. * \param output_length The length in bytes of \p output. * * \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. */ int mbedtls_mpi_core_write_le(const mbedtls_mpi_uint *A, size_t A_limbs, unsigned char *output, size_t output_length); /** Export A into unsigned binary data, big-endian. * * \note If \p output is shorter than \p A the export is still successful if the * value held in \p A fits in the buffer (that is, if enough of the most * significant bytes of \p A are 0). * * \param[in] A The address of the MPI. * \param A_limbs The number of limbs of \p A. * \param[out] output The output buffer to export to. * \param output_length The length in bytes of \p output. * * \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. */ int mbedtls_mpi_core_write_be(const mbedtls_mpi_uint *A, size_t A_limbs, unsigned char *output, size_t output_length); /** \brief Shift an MPI in-place right by a number of bits. * * Shifting by more bits than there are bit positions * in \p X is valid and results in setting \p X to 0. * * This function's execution time depends on the value * of \p count (and of course \p limbs). * * \param[in,out] X The number to shift. * \param limbs The number of limbs of \p X. This must be at least 1. * \param count The number of bits to shift by. */ void mbedtls_mpi_core_shift_r(mbedtls_mpi_uint *X, size_t limbs, size_t count); /** * \brief Shift an MPI in-place left by a number of bits. * * Shifting by more bits than there are bit positions * in \p X will produce an unspecified result. * * This function's execution time depends on the value * of \p count (and of course \p limbs). * \param[in,out] X The number to shift. * \param limbs The number of limbs of \p X. This must be at least 1. * \param count The number of bits to shift by. */ void mbedtls_mpi_core_shift_l(mbedtls_mpi_uint *X, size_t limbs, size_t count); /** * \brief Add two fixed-size large unsigned integers, returning the carry. * * Calculates `A + B` where `A` and `B` have the same size. * * This function operates modulo `2^(biL*limbs)` and returns the carry * (1 if there was a wraparound, and 0 otherwise). * * \p X may be aliased to \p A or \p B. * * \param[out] X The result of the addition. * \param[in] A Little-endian presentation of the left operand. * \param[in] B Little-endian presentation of the right operand. * \param limbs Number of limbs of \p X, \p A and \p B. * * \return 1 if `A + B >= 2^(biL*limbs)`, 0 otherwise. */ mbedtls_mpi_uint mbedtls_mpi_core_add(mbedtls_mpi_uint *X, const mbedtls_mpi_uint *A, const mbedtls_mpi_uint *B, size_t limbs); /** * \brief Conditional addition of two fixed-size large unsigned integers, * returning the carry. * * Functionally equivalent to * * ``` * if( cond ) * X += A; * return carry; * ``` * * This function operates modulo `2^(biL*limbs)`. * * \param[in,out] X The pointer to the (little-endian) array * representing the bignum to accumulate onto. * \param[in] A The pointer to the (little-endian) array * representing the bignum to conditionally add * to \p X. This may be aliased to \p X but may not * overlap otherwise. * \param limbs Number of limbs of \p X and \p A. * \param cond Condition bit dictating whether addition should * happen or not. This must be \c 0 or \c 1. * * \warning If \p cond is neither 0 nor 1, the result of this function * is unspecified, and the resulting value in \p X might be * neither its original value nor \p X + \p A. * * \return 1 if `X + cond * A >= 2^(biL*limbs)`, 0 otherwise. */ mbedtls_mpi_uint mbedtls_mpi_core_add_if(mbedtls_mpi_uint *X, const mbedtls_mpi_uint *A, size_t limbs, unsigned cond); /** * \brief Subtract two fixed-size large unsigned integers, returning the borrow. * * Calculate `A - B` where \p A and \p B have the same size. * This function operates modulo `2^(biL*limbs)` and returns the carry * (1 if there was a wraparound, i.e. if `A < B`, and 0 otherwise). * * \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 subtraction. * \param[in] A Little-endian presentation of left operand. * \param[in] B Little-endian presentation of right operand. * \param limbs Number of limbs of \p X, \p A and \p B. * * \return 1 if `A < B`. * 0 if `A >= B`. */ mbedtls_mpi_uint mbedtls_mpi_core_sub(mbedtls_mpi_uint *X, const mbedtls_mpi_uint *A, const mbedtls_mpi_uint *B, size_t limbs); /** * \brief Perform a fixed-size multiply accumulate operation: X += b * A * * \p X may be aliased to \p A (when \p X_limbs == \p A_limbs), but may not * otherwise overlap. * * This function operates modulo `2^(biL*X_limbs)`. * * \param[in,out] X The pointer to the (little-endian) array * representing the bignum to accumulate onto. * \param X_limbs The number of limbs of \p X. This must be * at least \p A_limbs. * \param[in] A The pointer to the (little-endian) array * representing the bignum to multiply with. * This may be aliased to \p X but may not overlap * otherwise. * \param A_limbs The number of limbs of \p A. * \param b X scalar to multiply with. * * \return The carry at the end of the operation. */ mbedtls_mpi_uint mbedtls_mpi_core_mla(mbedtls_mpi_uint *X, size_t X_limbs, const mbedtls_mpi_uint *A, size_t A_limbs, mbedtls_mpi_uint b); /** * \brief Perform a known-size multiplication * * \p X may not be aliased to any of the inputs for this function. * \p A may be aliased to \p B. * * \param[out] X The pointer to the (little-endian) array to receive * the product of \p A_limbs and \p B_limbs. * This must be of length \p A_limbs + \p B_limbs. * \param[in] A The pointer to the (little-endian) array * representing the first factor. * \param A_limbs The number of limbs in \p A. * \param[in] B The pointer to the (little-endian) array * representing the second factor. * \param B_limbs The number of limbs in \p B. */ void mbedtls_mpi_core_mul(mbedtls_mpi_uint *X, const mbedtls_mpi_uint *A, size_t A_limbs, const mbedtls_mpi_uint *B, size_t B_limbs); /** * \brief Calculate initialisation value for fast Montgomery modular * multiplication * * \param[in] N Little-endian presentation of the modulus. This must have * at least one limb. * * \return The initialisation value for fast Montgomery modular multiplication */ mbedtls_mpi_uint mbedtls_mpi_core_montmul_init(const mbedtls_mpi_uint *N); /** * \brief Montgomery multiplication: X = A * B * R^-1 mod N (HAC 14.36) * * \p A and \p B must be in canonical form. That is, < \p N. * * \p X may be aliased to \p A or \p N, or even \p B (if \p AN_limbs == * \p B_limbs) but may not overlap any parameters otherwise. * * \p A and \p B may alias each other, if \p AN_limbs == \p B_limbs. They may * not alias \p N (since they must be in canonical form, they cannot == \p N). * * \param[out] X The destination MPI, as a little-endian array of * length \p AN_limbs. * On successful completion, X contains the result of * the multiplication `A * B * R^-1` mod N where * `R = 2^(biL*AN_limbs)`. * \param[in] A Little-endian presentation of first operand. * Must have the same number of limbs as \p N. * \param[in] B Little-endian presentation of second operand. * \param[in] B_limbs The number of limbs in \p B. * Must be <= \p AN_limbs. * \param[in] N Little-endian presentation of the modulus. * This must be odd, and have exactly the same number * of limbs as \p A. * It may alias \p X, but must not alias or otherwise * overlap any of the other parameters. * \param[in] AN_limbs The number of limbs in \p X, \p A and \p N. * \param mm The Montgomery constant for \p N: -N^-1 mod 2^biL. * This can be calculated by `mbedtls_mpi_core_montmul_init()`. * \param[in,out] T Temporary storage of size at least 2*AN_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_core_montmul(mbedtls_mpi_uint *X, const mbedtls_mpi_uint *A, const mbedtls_mpi_uint *B, size_t B_limbs, const mbedtls_mpi_uint *N, size_t AN_limbs, mbedtls_mpi_uint mm, mbedtls_mpi_uint *T); /** * \brief Calculate the square of the Montgomery constant. (Needed * for conversion and operations in Montgomery form.) * * \param[out] X A pointer to the result of the calculation of * the square of the Montgomery constant: * 2^{2*n*biL} mod N. * \param[in] N Little-endian presentation of the modulus, which must be odd. * * \return 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if there is not enough space * to store the value of Montgomery constant squared. * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p N modulus is zero. * \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p N modulus is negative. */ int mbedtls_mpi_core_get_mont_r2_unsafe(mbedtls_mpi *X, const mbedtls_mpi *N); #if defined(MBEDTLS_TEST_HOOKS) /** * Copy an MPI from a table without leaking the index. * * \param dest The destination buffer. This must point to a writable * buffer of at least \p limbs limbs. * \param table The address of the table. This must point to a readable * array of \p count elements of \p limbs limbs each. * \param limbs The number of limbs in each table entry. * \param count The number of entries in \p table. * \param index The (secret) table index to look up. This must be in the * range `0 .. count-1`. */ void mbedtls_mpi_core_ct_uint_table_lookup(mbedtls_mpi_uint *dest, const mbedtls_mpi_uint *table, size_t limbs, size_t count, size_t index); #endif /* MBEDTLS_TEST_HOOKS */ /** * \brief Fill an integer with a number of random bytes. * * \param X The destination MPI. * \param X_limbs The number of limbs of \p X. * \param bytes The number of random bytes to generate. * \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. This may be * \c NULL if \p f_rng doesn't need a context argument. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \p X does not have * enough room for \p bytes bytes. * \return A negative error code on RNG failure. * * \note The bytes obtained from the RNG are interpreted * as a big-endian representation of an MPI; this can * be relevant in applications like deterministic ECDSA. */ int mbedtls_mpi_core_fill_random(mbedtls_mpi_uint *X, size_t X_limbs, size_t bytes, int (*f_rng)(void *, unsigned char *, size_t), void *p_rng); /** 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 §3.3 (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, with \p limbs limbs. * It must not be aliased with \p N or otherwise overlap it. * \param min The minimum value to return. * \param N The upper bound of the range, exclusive, with \p limbs limbs. * In other words, this is one plus the maximum value to return. * \p N must be strictly larger than \p min. * \param limbs The number of limbs of \p N and \p X. * This must not be 0. * \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_core_random(mbedtls_mpi_uint *X, mbedtls_mpi_uint min, const mbedtls_mpi_uint *N, size_t limbs, int (*f_rng)(void *, unsigned char *, size_t), void *p_rng); /** * \brief Returns the number of limbs of working memory required for * a call to `mbedtls_mpi_core_exp_mod()`. * * \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_core_exp_mod()`. * \param E_limbs The number of limbs in the exponent `E` that will be given * to `mbedtls_mpi_core_exp_mod()`. * * \return The number of limbs of working memory required by * `mbedtls_mpi_core_exp_mod()`. */ size_t mbedtls_mpi_core_exp_mod_working_limbs(size_t AN_limbs, size_t E_limbs); /** * \brief Perform a modular exponentiation with public or secret exponent: * X = A^E mod N, where \p A is already in Montgomery form. * * \warning This function is not constant time with respect to \p E (the exponent). * * \p X may be aliased to \p A, but not to \p RR or \p E, even if \p E_limbs == * \p AN_limbs. * * \param[out] X The destination MPI, as a little endian array of length * \p AN_limbs. * \param[in] A The base MPI, as a little endian array of length \p AN_limbs. * Must be in Montgomery form. * \param[in] N The modulus, as a little endian array of length \p AN_limbs. * \param AN_limbs The number of limbs in \p X, \p A, \p N, \p RR. * \param[in] E The exponent, as a little endian array of length \p E_limbs. * \param E_limbs The number of limbs in \p E. * \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_core_exp_mod_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_core_exp_mod_unsafe(mbedtls_mpi_uint *X, const mbedtls_mpi_uint *A, const mbedtls_mpi_uint *N, size_t AN_limbs, const mbedtls_mpi_uint *E, size_t E_limbs, const mbedtls_mpi_uint *RR, mbedtls_mpi_uint *T); /** * \brief Perform a modular exponentiation with secret exponent: * X = A^E mod N, where \p A is already in Montgomery form. * * \p X may be aliased to \p A, but not to \p RR or \p E, even if \p E_limbs == * \p AN_limbs. * * \param[out] X The destination MPI, as a little endian array of length * \p AN_limbs. * \param[in] A The base MPI, as a little endian array of length \p AN_limbs. * Must be in Montgomery form. * \param[in] N The modulus, as a little endian array of length \p AN_limbs. * \param AN_limbs The number of limbs in \p X, \p A, \p N, \p RR. * \param[in] E The exponent, as a little endian array of length \p E_limbs. * \param E_limbs The number of limbs in \p E. * \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_core_exp_mod_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_core_exp_mod(mbedtls_mpi_uint *X, const mbedtls_mpi_uint *A, const mbedtls_mpi_uint *N, size_t AN_limbs, const mbedtls_mpi_uint *E, size_t E_limbs, const mbedtls_mpi_uint *RR, mbedtls_mpi_uint *T); /** * \brief Subtract unsigned integer from known-size large unsigned integers. * Return the borrow. * * \param[out] X The result of the subtraction. * \param[in] A The left operand. * \param b The unsigned scalar to subtract. * \param limbs Number of limbs of \p X and \p A. * * \return 1 if `A < b`. * 0 if `A >= b`. */ mbedtls_mpi_uint mbedtls_mpi_core_sub_int(mbedtls_mpi_uint *X, const mbedtls_mpi_uint *A, mbedtls_mpi_uint b, size_t limbs); /** * \brief Determine if a given MPI has the value \c 0 in constant time with * respect to the value (but not with respect to the number of limbs). * * \param[in] A The MPI to test. * \param limbs Number of limbs in \p A. * * \return MBEDTLS_CT_FALSE if `A == 0` * MBEDTLS_CT_TRUE if `A != 0`. */ mbedtls_ct_condition_t mbedtls_mpi_core_check_zero_ct(const mbedtls_mpi_uint *A, size_t limbs); /** * \brief Returns the number of limbs of working memory required 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_core_montmul()` or one of the other functions * that specifies this as the amount of working memory needed. * * \return The number of limbs of working memory required by * `mbedtls_mpi_core_montmul()` (or other similar function). */ static inline size_t mbedtls_mpi_core_montmul_working_limbs(size_t AN_limbs) { … } /** Convert an MPI into Montgomery form. * * \p X may be aliased to \p A, but may not otherwise overlap it. * * \p X may not alias \p N (it is in canonical form, so must be strictly less * than \p N). Nor may it alias or overlap \p rr (this is unlikely to be * required in practice.) * * This function is a thin wrapper around `mbedtls_mpi_core_montmul()` that is * an alternative to calling `mbedtls_mpi_mod_raw_to_mont_rep()` when we * don't want to allocate memory. * * \param[out] X The result of the conversion. * Must have the same number of limbs as \p A. * \param[in] A The MPI to convert into Montgomery form. * Must have the same number of limbs as the modulus. * \param[in] N The address of the modulus, which gives the size of * the base `R` = 2^(biL*N->limbs). * \param[in] AN_limbs The number of limbs in \p X, \p A, \p N and \p rr. * \param mm The Montgomery constant for \p N: -N^-1 mod 2^biL. * This can be determined by calling * `mbedtls_mpi_core_montmul_init()`. * \param[in] rr The residue for `2^{2*n*biL} mod N`. * \param[in,out] T Temporary storage of size at least * `mbedtls_mpi_core_montmul_working_limbs(AN_limbs)` * 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_core_to_mont_rep(mbedtls_mpi_uint *X, const mbedtls_mpi_uint *A, const mbedtls_mpi_uint *N, size_t AN_limbs, mbedtls_mpi_uint mm, const mbedtls_mpi_uint *rr, mbedtls_mpi_uint *T); /** Convert an MPI from Montgomery form. * * \p X may be aliased to \p A, but may not otherwise overlap it. * * \p X may not alias \p N (it is in canonical form, so must be strictly less * than \p N). * * This function is a thin wrapper around `mbedtls_mpi_core_montmul()` that is * an alternative to calling `mbedtls_mpi_mod_raw_from_mont_rep()` when we * don't want to allocate memory. * * \param[out] X The result of the conversion. * Must have the same number of limbs as \p A. * \param[in] A The MPI to convert from Montgomery form. * Must have the same number of limbs as the modulus. * \param[in] N The address of the modulus, which gives the size of * the base `R` = 2^(biL*N->limbs). * \param[in] AN_limbs The number of limbs in \p X, \p A and \p N. * \param mm The Montgomery constant for \p N: -N^-1 mod 2^biL. * This can be determined by calling * `mbedtls_mpi_core_montmul_init()`. * \param[in,out] T Temporary storage of size at least * `mbedtls_mpi_core_montmul_working_limbs(AN_limbs)` * 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_core_from_mont_rep(mbedtls_mpi_uint *X, const mbedtls_mpi_uint *A, const mbedtls_mpi_uint *N, size_t AN_limbs, mbedtls_mpi_uint mm, mbedtls_mpi_uint *T); /* * Can't define thread local variables with our abstraction layer: do nothing if threading is on. */ #if defined(MBEDTLS_TEST_HOOKS) && !defined(MBEDTLS_THREADING_C) extern int mbedtls_mpi_optionally_safe_codepath; static inline void mbedtls_mpi_optionally_safe_codepath_reset(void) { // Set to a default that is neither MBEDTLS_MPI_IS_PUBLIC nor MBEDTLS_MPI_IS_SECRET mbedtls_mpi_optionally_safe_codepath = MBEDTLS_MPI_IS_PUBLIC + MBEDTLS_MPI_IS_SECRET + 1; } #endif #endif /* MBEDTLS_BIGNUM_CORE_H */
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