| /** |
| * Modular bignum functions |
| * |
| * This module implements operations on integers modulo some fixed modulus. |
| * |
| * 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. Functions which take a parameter |
| * of type \c const #mbedtls_mpi_mod_modulus* must not modify its value. |
| * - **Bignum parameters**: Bignums are passed as pointers to an array of |
| * limbs or to a #mbedtls_mpi_mod_residue structure. A limb has the type |
| * #mbedtls_mpi_uint. Residues must be initialized before use, and must be |
| * associated with the modulus \c N. Unless otherwise specified: |
| * - Bignum parameters called \c A, \c B, ... are inputs and are not |
| * modified by the function. Functions which take a parameter of |
| * type \c const #mbedtls_mpi_mod_residue* must not modify its value. |
| * - Bignum parameters called \c X, \c Y, ... are outputs or input-output. |
| * The initial bignum value of output-only parameters is ignored, but |
| * they must be set up and associated with the modulus \c N. Some |
| * functions (typically constant-flow) require that the limbs in an |
| * output residue are initialized. |
| * - Bignum parameters called \c p are inputs used to set up a modulus or |
| * residue. These must be pointers to an array of limbs. |
| * - \c T is a temporary storage area. The initial content of such a |
| * parameter is ignored and the final content is unspecified. |
| * - Some functions use different names, such as \c r for the residue. |
| * - **Bignum sizes**: bignum sizes are always expressed in limbs. Both |
| * #mbedtls_mpi_mod_modulus and #mbedtls_mpi_mod_residue have a \c limbs |
| * member storing its size. 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. |
| * - **Parameter ordering**: for bignum parameters, outputs come before inputs. |
| * The modulus is passed after residues. 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 residue pointers (where two residue |
| * arguments are equal pointers), overlap is not supported and may result |
| * in undefined behavior. |
| * - **Error handling**: functions generally check compatibility of input |
| * sizes. Most functions will not check that input values are in canonical |
| * form (i.e. that \c A < \c N), this is only checked during setup of a |
| * residue structure. |
| * - **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]. |
| * Residues are set up with an associated modulus, and operations are only |
| * guaranteed to work if the modulus is associated with all residue |
| * parameters. If a residue is passed with a modulus other than the one it |
| * is associated with, then it may be out of range. 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_MOD_H |
| #define MBEDTLS_BIGNUM_MOD_H |
| |
| #include "common.h" |
| |
| #if defined(MBEDTLS_BIGNUM_C) |
| #include "mbedtls/bignum.h" |
| #endif |
| |
| /** How residues associated with a modulus are represented. |
| * |
| * This also determines which fields of the modulus structure are valid and |
| * what their contents are (see #mbedtls_mpi_mod_modulus). |
| */ |
| typedef enum { |
| /** Representation not chosen (makes the modulus structure invalid). */ |
| MBEDTLS_MPI_MOD_REP_INVALID = 0, |
| /* Skip 1 as it is slightly easier to accidentally pass to functions. */ |
| /** Montgomery representation. */ |
| MBEDTLS_MPI_MOD_REP_MONTGOMERY = 2, |
| /* Optimised reduction available. This indicates a coordinate modulus (P) |
| * and one or more of the following have been configured: |
| * - A nist curve (MBEDTLS_ECP_DP_SECPXXXR1_ENABLED) & MBEDTLS_ECP_NIST_OPTIM. |
| * - A Kobliz Curve. |
| * - A Fast Reduction Curve CURVE25519 or CURVE448. */ |
| 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 int (*mbedtls_mpi_modp_fn)(mbedtls_mpi_uint *X, size_t X_limbs); |
| |
| typedef struct { |
| mbedtls_mpi_modp_fn modp; /* The optimised reduction function pointer */ |
| } 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 { |
| /* if int_rep == #MBEDTLS_MPI_MOD_REP_MONTGOMERY */ |
| mbedtls_mpi_mont_struct mont; |
| /* if int_rep == #MBEDTLS_MPI_MOD_REP_OPT_RED */ |
| 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 N. |
| * |
| * 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 `N->int_rep` field. |
| * |
| * The modulus \p N will be the modulus associated with \p r. The residue \p r |
| * should only be used in operations where the modulus is \p N. |
| * |
| * \param[out] r The address of the residue to setup. |
| * \param[in] N 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 `N->p`) and already in the representation |
| * indicated by `N->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 N. |
| * |
| * \return \c 0 if successful. |
| * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \p p_limbs is less than the |
| * limbs in \p N or if \p p is not less than \p N. |
| */ |
| int mbedtls_mpi_mod_residue_setup(mbedtls_mpi_mod_residue *r, |
| const mbedtls_mpi_mod_modulus *N, |
| 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] N The address of the modulus structure to initialize. |
| */ |
| void mbedtls_mpi_mod_modulus_init(mbedtls_mpi_mod_modulus *N); |
| |
| /** Setup a modulus structure. |
| * |
| * \param[out] N The address of the modulus structure to populate. |
| * \param[in] p The address of the limb array storing the value of \p N. |
| * The memory pointed to by \p p will be used by \p N 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. |
| * |
| * \return \c 0 if successful. |
| */ |
| int mbedtls_mpi_mod_modulus_setup(mbedtls_mpi_mod_modulus *N, |
| const mbedtls_mpi_uint *p, |
| size_t p_limbs); |
| |
| /** Setup an optimised-reduction compatible modulus structure. |
| * |
| * \param[out] N The address of the modulus structure to populate. |
| * \param[in] p The address of the limb array storing the value of \p N. |
| * The memory pointed to by \p p will be used by \p N 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 modp A pointer to the optimised reduction function to use. \p p. |
| * |
| * \return \c 0 if successful. |
| */ |
| int mbedtls_mpi_mod_optred_modulus_setup(mbedtls_mpi_mod_modulus *N, |
| const mbedtls_mpi_uint *p, |
| size_t p_limbs, |
| mbedtls_mpi_modp_fn modp); |
| |
| /** 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] N The address of the modulus structure to free. |
| */ |
| void mbedtls_mpi_mod_modulus_free(mbedtls_mpi_mod_modulus *N); |
| |
| /** \brief Multiply two residues, 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. |
| * |
| * \return \c 0 if successful. |
| * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if all the parameters do not |
| * have the same number of limbs or \p N is invalid. |
| * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure. |
| */ |
| int mbedtls_mpi_mod_mul(mbedtls_mpi_mod_residue *X, |
| const mbedtls_mpi_mod_residue *A, |
| const mbedtls_mpi_mod_residue *B, |
| const mbedtls_mpi_mod_modulus *N); |
| |
| /** |
| * \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); |
| |
| /** |
| * \brief Perform modular inversion of an MPI with respect to a modulus \p N. |
| * |
| * \p A and \p X must be associated with the modulus \p N and will therefore |
| * have the same number of limbs as \p N. |
| * |
| * \p X may be aliased to \p A. |
| * |
| * \warning Currently only supports prime moduli, but does not check for them. |
| * |
| * \param[out] X The modular inverse of \p A with respect to \p N. |
| * \param[in] A The number to calculate the modular inverse of. |
| * Must not be 0. |
| * \param[in] N The modulus to use. |
| * |
| * \return \c 0 if successful. |
| * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \p A and \p N do not |
| * have the same number of limbs. |
| * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \p A is zero. |
| * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if couldn't allocate enough |
| * memory (needed for conversion to and from Mongtomery form |
| * when not in Montgomery form already, and for temporary use |
| * by the inversion calculation itself). |
| */ |
| |
| int mbedtls_mpi_mod_inv(mbedtls_mpi_mod_residue *X, |
| const mbedtls_mpi_mod_residue *A, |
| const mbedtls_mpi_mod_modulus *N); |
| /** |
| * \brief Perform a fixed-size modular addition. |
| * |
| * Calculate `A + B modulo 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. |
| * |
| * \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 residue. Must be initialized. |
| * Must have the same number of limbs as the modulus \p N. |
| * \param[in] A The address of the first input residue. |
| * \param[in] B The address of the second input residue. |
| * \param[in] N The address of the modulus. Used to perform a modulo |
| * operation on the result of the addition. |
| * |
| * \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_add(mbedtls_mpi_mod_residue *X, |
| const mbedtls_mpi_mod_residue *A, |
| const mbedtls_mpi_mod_residue *B, |
| 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 residue. |
| * \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_random(mbedtls_mpi_mod_residue *X, |
| mbedtls_mpi_uint min, |
| const mbedtls_mpi_mod_modulus *N, |
| int (*f_rng)(void *, unsigned char *, size_t), |
| void *p_rng); |
| |
| /** Read a residue from a byte buffer. |
| * |
| * The residue will be automatically converted to the internal representation |
| * based on the value of the `N->int_rep` field. |
| * |
| * The modulus \p N will be the modulus associated with \p r. The residue \p r |
| * should only be used in operations where the modulus is \p N or a modulus |
| * equivalent to \p N (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 N. |
| * \param[in] N 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 N. |
| */ |
| int mbedtls_mpi_mod_read(mbedtls_mpi_mod_residue *r, |
| const mbedtls_mpi_mod_modulus *N, |
| const unsigned char *buf, |
| size_t buflen, |
| mbedtls_mpi_mod_ext_rep ext_rep); |
| |
| /** Write a residue into a byte buffer. |
| * |
| * The modulus \p N 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 `N->int_rep` field. |
| * |
| * \warning If the buffer is smaller than `N->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 |
| * (`N->bits`+7)/8. |
| * |
| * \param[in] r The address of the residue. It must have the same number of |
| * limbs as the modulus \p N. (\p r is an input parameter, but |
| * its value will be modified during execution and restored |
| * before the function returns.) |
| * \param[in] N The address of the modulus associated with \p 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 *N, |
| unsigned char *buf, |
| size_t buflen, |
| mbedtls_mpi_mod_ext_rep ext_rep); |
| |
| #endif /* MBEDTLS_BIGNUM_MOD_H */ |
