Public-Mirror/gbe_fork
1
0
Fork 0
mirror of https://github.com/Detanup01/gbe_fork.git synced 2024-11-24 03:35:35 +08:00
Code Issues 1 Projects Releases Wiki Activity
0b8eb76bdd
gbe_fork/mbedtls/bignum_mod.h
otavepto 92c77cee31 added a new cryptography library Mbed TLS
2023-12-24 14:33:40 +02:00

453 lines
20 KiB
C
Raw Blame History

/**
* 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 §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 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 */
Reference in New Issue View Git Blame Copy Permalink