463 lines
21 KiB
C
463 lines
21 KiB
C
/**
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* Modular bignum functions
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*
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* This module implements operations on integers modulo some fixed modulus.
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*
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* The functions in this module obey the following conventions unless
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* explicitly indicated otherwise:
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*
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* - **Modulus parameters**: the modulus is passed as a pointer to a structure
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* of type #mbedtls_mpi_mod_modulus. The structure must be set up with an
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* array of limbs storing the bignum value of the modulus. The modulus must
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* be odd and is assumed to have no leading zeroes. The modulus is usually
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* named \c N and is usually input-only. Functions which take a parameter
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* of type \c const #mbedtls_mpi_mod_modulus* must not modify its value.
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* - **Bignum parameters**: Bignums are passed as pointers to an array of
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* limbs or to a #mbedtls_mpi_mod_residue structure. A limb has the type
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* #mbedtls_mpi_uint. Residues must be initialized before use, and must be
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* associated with the modulus \c N. Unless otherwise specified:
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* - Bignum parameters called \c A, \c B, ... are inputs and are not
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* modified by the function. Functions which take a parameter of
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* type \c const #mbedtls_mpi_mod_residue* must not modify its value.
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* - Bignum parameters called \c X, \c Y, ... are outputs or input-output.
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* The initial bignum value of output-only parameters is ignored, but
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* they must be set up and associated with the modulus \c N. Some
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* functions (typically constant-flow) require that the limbs in an
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* output residue are initialized.
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* - Bignum parameters called \c p are inputs used to set up a modulus or
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* residue. These must be pointers to an array of limbs.
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* - \c T is a temporary storage area. The initial content of such a
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* parameter is ignored and the final content is unspecified.
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* - Some functions use different names, such as \c r for the residue.
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* - **Bignum sizes**: bignum sizes are always expressed in limbs. Both
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* #mbedtls_mpi_mod_modulus and #mbedtls_mpi_mod_residue have a \c limbs
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* member storing its size. All bignum parameters must have the same
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* number of limbs as the modulus. All bignum sizes must be at least 1 and
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* must be significantly less than #SIZE_MAX. The behavior if a size is 0 is
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* undefined.
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* - **Bignum representation**: the representation of inputs and outputs is
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* specified by the \c int_rep field of the modulus.
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* - **Parameter ordering**: for bignum parameters, outputs come before inputs.
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* The modulus is passed after residues. Temporaries come last.
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* - **Aliasing**: in general, output bignums may be aliased to one or more
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* inputs. Modulus values may not be aliased to any other parameter. Outputs
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* may not be aliased to one another. Temporaries may not be aliased to any
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* other parameter.
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* - **Overlap**: apart from aliasing of residue pointers (where two residue
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* arguments are equal pointers), overlap is not supported and may result
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* in undefined behavior.
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* - **Error handling**: functions generally check compatibility of input
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* sizes. Most functions will not check that input values are in canonical
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* form (i.e. that \c A < \c N), this is only checked during setup of a
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* residue structure.
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* - **Modular representatives**: all functions expect inputs to be in the
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* range [0, \c N - 1] and guarantee outputs in the range [0, \c N - 1].
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* Residues are set up with an associated modulus, and operations are only
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* guaranteed to work if the modulus is associated with all residue
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* parameters. If a residue is passed with a modulus other than the one it
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* is associated with, then it may be out of range. If an input is out of
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* range, outputs are fully unspecified, though bignum values out of range
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* should not cause buffer overflows (beware that this is not extensively
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* tested).
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*/
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/*
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* Copyright The Mbed TLS Contributors
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* SPDX-License-Identifier: Apache-2.0
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*
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* Licensed under the Apache License, Version 2.0 (the "License"); you may
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* not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
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* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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#ifndef MBEDTLS_BIGNUM_MOD_H
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#define MBEDTLS_BIGNUM_MOD_H
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#include "common.h"
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#if defined(MBEDTLS_BIGNUM_C)
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#include "mbedtls/bignum.h"
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#endif
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/** How residues associated with a modulus are represented.
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*
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* This also determines which fields of the modulus structure are valid and
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* what their contents are (see #mbedtls_mpi_mod_modulus).
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*/
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typedef enum {
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/** Representation not chosen (makes the modulus structure invalid). */
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MBEDTLS_MPI_MOD_REP_INVALID = 0,
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/* Skip 1 as it is slightly easier to accidentally pass to functions. */
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/** Montgomery representation. */
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MBEDTLS_MPI_MOD_REP_MONTGOMERY = 2,
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/** TODO: document this.
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*
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* Residues are in canonical representation.
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*/
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MBEDTLS_MPI_MOD_REP_OPT_RED,
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} mbedtls_mpi_mod_rep_selector;
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/* Make mbedtls_mpi_mod_rep_selector and mbedtls_mpi_mod_ext_rep disjoint to
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* make it easier to catch when they are accidentally swapped. */
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typedef enum {
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MBEDTLS_MPI_MOD_EXT_REP_INVALID = 0,
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MBEDTLS_MPI_MOD_EXT_REP_LE = 8,
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MBEDTLS_MPI_MOD_EXT_REP_BE
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} mbedtls_mpi_mod_ext_rep;
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typedef struct {
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mbedtls_mpi_uint *p;
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size_t limbs;
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} mbedtls_mpi_mod_residue;
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typedef struct {
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mbedtls_mpi_uint const *rr; /* The residue for 2^{2*n*biL} mod N */
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mbedtls_mpi_uint mm; /* Montgomery const for -N^{-1} mod 2^{ciL} */
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} mbedtls_mpi_mont_struct;
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typedef void *mbedtls_mpi_opt_red_struct;
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typedef struct {
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const mbedtls_mpi_uint *p;
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size_t limbs; // number of limbs
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size_t bits; // bitlen of p
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mbedtls_mpi_mod_rep_selector int_rep; // selector to signal the active member of the union
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union rep {
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/* if int_rep == #MBEDTLS_MPI_MOD_REP_MONTGOMERY */
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mbedtls_mpi_mont_struct mont;
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/* if int_rep == #MBEDTLS_MPI_MOD_REP_OPT_RED */
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mbedtls_mpi_opt_red_struct ored;
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} rep;
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} mbedtls_mpi_mod_modulus;
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/** Setup a residue structure.
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*
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* The residue will be set up with the buffer \p p and modulus \p N.
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*
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* The memory pointed to by \p p will be used by the resulting residue structure.
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* The value at the pointed-to memory will be the initial value of \p r and must
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* hold a value that is less than the modulus. This value will be used as-is
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* and interpreted according to the value of the `N->int_rep` field.
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*
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* The modulus \p N will be the modulus associated with \p r. The residue \p r
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* should only be used in operations where the modulus is \p N.
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*
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* \param[out] r The address of the residue to setup.
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* \param[in] N The address of the modulus related to \p r.
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* \param[in] p The address of the limb array containing the value of \p r.
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* The memory pointed to by \p p will be used by \p r and must
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* not be modified in any way until after
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* mbedtls_mpi_mod_residue_release() is called. The data
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* pointed to by \p p must be less than the modulus (the value
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* pointed to by `N->p`) and already in the representation
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* indicated by `N->int_rep`.
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* \param p_limbs The number of limbs of \p p. Must be the same as the number
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* of limbs in the modulus \p N.
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*
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* \return \c 0 if successful.
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* \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \p p_limbs is less than the
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* limbs in \p N or if \p p is not less than \p N.
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*/
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int mbedtls_mpi_mod_residue_setup(mbedtls_mpi_mod_residue *r,
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const mbedtls_mpi_mod_modulus *N,
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mbedtls_mpi_uint *p,
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size_t p_limbs);
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/** Unbind elements of a residue structure.
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*
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* This function removes the reference to the limb array that was passed to
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* mbedtls_mpi_mod_residue_setup() to make it safe to free or use again.
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*
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* This function invalidates \p r and it must not be used until after
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* mbedtls_mpi_mod_residue_setup() is called on it again.
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*
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* \param[out] r The address of residue to release.
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*/
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void mbedtls_mpi_mod_residue_release(mbedtls_mpi_mod_residue *r);
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/** Initialize a modulus structure.
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*
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* \param[out] N The address of the modulus structure to initialize.
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*/
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void mbedtls_mpi_mod_modulus_init(mbedtls_mpi_mod_modulus *N);
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/** Setup a modulus structure.
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*
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* \param[out] N The address of the modulus structure to populate.
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* \param[in] p The address of the limb array storing the value of \p N.
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* The memory pointed to by \p p will be used by \p N and must
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* not be modified in any way until after
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* mbedtls_mpi_mod_modulus_free() is called.
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* \param p_limbs The number of limbs of \p p.
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* \param int_rep The internal representation to be used for residues
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* associated with \p N (see #mbedtls_mpi_mod_rep_selector).
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*
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* \return \c 0 if successful.
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* \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \p int_rep is invalid.
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*/
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int mbedtls_mpi_mod_modulus_setup(mbedtls_mpi_mod_modulus *N,
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const mbedtls_mpi_uint *p,
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size_t p_limbs,
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mbedtls_mpi_mod_rep_selector int_rep);
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/** Setup an optimised-reduction compatible modulus structure.
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*
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* \param[out] N The address of the modulus structure to populate.
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* \param[in] p The address of the limb array storing the value of \p N.
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* The memory pointed to by \p p will be used by \p N and must
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* not be modified in any way until after
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* mbedtls_mpi_mod_modulus_free() is called.
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* \param p_limbs The number of limbs of \p p.
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* \param ored The optimized reduction structure to use. \p p.
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*
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* \return \c 0 if successful.
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*/
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int mbedtls_mpi_mod_optred_modulus_setup(mbedtls_mpi_mod_modulus *N,
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const mbedtls_mpi_uint *p,
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size_t p_limbs,
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mbedtls_mpi_opt_red_struct *ored);
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/** Free elements of a modulus structure.
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*
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* This function frees any memory allocated by mbedtls_mpi_mod_modulus_setup().
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*
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* \warning This function does not free the limb array passed to
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* mbedtls_mpi_mod_modulus_setup() only removes the reference to it,
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* making it safe to free or to use it again.
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*
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* \param[in,out] N The address of the modulus structure to free.
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*/
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void mbedtls_mpi_mod_modulus_free(mbedtls_mpi_mod_modulus *N);
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/** \brief Multiply two residues, returning the residue modulo the specified
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* modulus.
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*
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* \note Currently handles the case when `N->int_rep` is
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* MBEDTLS_MPI_MOD_REP_MONTGOMERY.
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*
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* The size of the operation is determined by \p N. \p A, \p B and \p X must
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* all be associated with the modulus \p N and must all have the same number
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* of limbs as \p N.
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*
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* \p X may be aliased to \p A or \p B, or even both, but may not overlap
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* either otherwise. They may not alias \p N (since they must be in canonical
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* form, they cannot == \p N).
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*
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* \param[out] X The address of the result MPI. Must have the same
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* number of limbs as \p N.
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* On successful completion, \p X contains the result of
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* the multiplication `A * B * R^-1` mod N where
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* `R = 2^(biL * N->limbs)`.
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* \param[in] A The address of the first MPI.
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* \param[in] B The address of the second MPI.
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* \param[in] N The address of the modulus. Used to perform a modulo
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* operation on the result of the multiplication.
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*
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* \return \c 0 if successful.
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* \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if all the parameters do not
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* have the same number of limbs or \p N is invalid.
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* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
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*/
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int mbedtls_mpi_mod_mul(mbedtls_mpi_mod_residue *X,
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const mbedtls_mpi_mod_residue *A,
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const mbedtls_mpi_mod_residue *B,
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const mbedtls_mpi_mod_modulus *N);
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/**
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* \brief Perform a fixed-size modular subtraction.
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*
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* Calculate `A - B modulo N`.
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*
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* \p A, \p B and \p X must all have the same number of limbs as \p N.
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*
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* \p X may be aliased to \p A or \p B, or even both, but may not overlap
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* either otherwise.
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*
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* \note This function does not check that \p A or \p B are in canonical
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* form (that is, are < \p N) - that will have been done by
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* mbedtls_mpi_mod_residue_setup().
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*
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* \param[out] X The address of the result MPI. Must be initialized.
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* Must have the same number of limbs as the modulus \p N.
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* \param[in] A The address of the first MPI.
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* \param[in] B The address of the second MPI.
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* \param[in] N The address of the modulus. Used to perform a modulo
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* operation on the result of the subtraction.
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*
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* \return \c 0 if successful.
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* \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if the given MPIs do not
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* have the correct number of limbs.
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*/
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int mbedtls_mpi_mod_sub(mbedtls_mpi_mod_residue *X,
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const mbedtls_mpi_mod_residue *A,
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const mbedtls_mpi_mod_residue *B,
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const mbedtls_mpi_mod_modulus *N);
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/**
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* \brief Perform modular inversion of an MPI with respect to a modulus \p N.
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*
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* \p A and \p X must be associated with the modulus \p N and will therefore
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* have the same number of limbs as \p N.
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*
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* \p X may be aliased to \p A.
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*
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* \warning Currently only supports prime moduli, but does not check for them.
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*
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* \param[out] X The modular inverse of \p A with respect to \p N.
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* \param[in] A The number to calculate the modular inverse of.
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* Must not be 0.
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* \param[in] N The modulus to use.
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*
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* \return \c 0 if successful.
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* \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \p A and \p N do not
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* have the same number of limbs.
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* \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \p A is zero.
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* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if couldn't allocate enough
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* memory (needed for conversion to and from Mongtomery form
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* when not in Montgomery form already, and for temporary use
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* by the inversion calculation itself).
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*/
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int mbedtls_mpi_mod_inv(mbedtls_mpi_mod_residue *X,
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const mbedtls_mpi_mod_residue *A,
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const mbedtls_mpi_mod_modulus *N);
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/**
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* \brief Perform a fixed-size modular addition.
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*
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* Calculate `A + B modulo N`.
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*
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* \p A, \p B and \p X must all be associated with the modulus \p N and must
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* all have the same number of limbs as \p N.
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*
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* \p X may be aliased to \p A or \p B, or even both, but may not overlap
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* either otherwise.
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*
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* \note This function does not check that \p A or \p B are in canonical
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* form (that is, are < \p N) - that will have been done by
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* mbedtls_mpi_mod_residue_setup().
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*
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* \param[out] X The address of the result residue. Must be initialized.
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* Must have the same number of limbs as the modulus \p N.
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* \param[in] A The address of the first input residue.
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* \param[in] B The address of the second input residue.
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* \param[in] N The address of the modulus. Used to perform a modulo
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* operation on the result of the addition.
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*
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* \return \c 0 if successful.
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* \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if the given MPIs do not
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* have the correct number of limbs.
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*/
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int mbedtls_mpi_mod_add(mbedtls_mpi_mod_residue *X,
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const mbedtls_mpi_mod_residue *A,
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const mbedtls_mpi_mod_residue *B,
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const mbedtls_mpi_mod_modulus *N);
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/** Generate a random number uniformly in a range.
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*
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* This function generates a random number between \p min inclusive and
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* \p N exclusive.
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*
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* The procedure complies with RFC 6979 §3.3 (deterministic ECDSA)
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* when the RNG is a suitably parametrized instance of HMAC_DRBG
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* and \p min is \c 1.
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*
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* \note There are `N - min` possible outputs. The lower bound
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* \p min can be reached, but the upper bound \p N cannot.
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*
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* \param X The destination residue.
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* \param min The minimum value to return. It must be strictly smaller
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* than \b N.
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* \param N The modulus.
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* This is the upper bound of the output range, exclusive.
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* \param f_rng The RNG function to use. This must not be \c NULL.
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* \param p_rng The RNG parameter to be passed to \p f_rng.
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*
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* \return \c 0 if successful.
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* \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if the implementation was
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* unable to find a suitable value within a limited number
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* of attempts. This has a negligible probability if \p N
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* is significantly larger than \p min, which is the case
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* for all usual cryptographic applications.
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*/
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int mbedtls_mpi_mod_random(mbedtls_mpi_mod_residue *X,
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mbedtls_mpi_uint min,
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const mbedtls_mpi_mod_modulus *N,
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int (*f_rng)(void *, unsigned char *, size_t),
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void *p_rng);
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/** Read a residue from a byte buffer.
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*
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* The residue will be automatically converted to the internal representation
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* based on the value of the `N->int_rep` field.
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*
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* The modulus \p N will be the modulus associated with \p r. The residue \p r
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* should only be used in operations where the modulus is \p N or a modulus
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* equivalent to \p N (in the sense that all their fields or memory pointed by
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* their fields hold the same value).
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*
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* \param[out] r The address of the residue. It must have exactly the same
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* number of limbs as the modulus \p N.
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* \param[in] N The address of the modulus.
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* \param[in] buf The input buffer to import from.
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* \param buflen The length in bytes of \p buf.
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* \param ext_rep The endianness of the number in the input buffer.
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*
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* \return \c 0 if successful.
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* \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p r isn't
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* large enough to hold the value in \p buf.
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* \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \p ext_rep
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* is invalid or the value in the buffer is not less than \p N.
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*/
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int mbedtls_mpi_mod_read(mbedtls_mpi_mod_residue *r,
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const mbedtls_mpi_mod_modulus *N,
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const unsigned char *buf,
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size_t buflen,
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mbedtls_mpi_mod_ext_rep ext_rep);
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/** Write a residue into a byte buffer.
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*
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* The modulus \p N must be the modulus associated with \p r (see
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* mbedtls_mpi_mod_residue_setup() and mbedtls_mpi_mod_read()).
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*
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* The residue will be automatically converted from the internal representation
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* based on the value of `N->int_rep` field.
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*
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* \warning If the buffer is smaller than `N->bits`, the number of
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* leading zeroes is leaked through timing. If \p r is
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* secret, the caller must ensure that \p buflen is at least
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* (`N->bits`+7)/8.
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*
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* \param[in] r The address of the residue. It must have the same number of
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* limbs as the modulus \p N. (\p r is an input parameter, but
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* its value will be modified during execution and restored
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* before the function returns.)
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* \param[in] N The address of the modulus associated with \p r.
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* \param[out] buf The output buffer to export to.
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* \param buflen The length in bytes of \p buf.
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* \param ext_rep The endianness in which the number should be written into
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* the output buffer.
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*
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* \return \c 0 if successful.
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* \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p buf isn't
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* large enough to hold the value of \p r (without leading
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* zeroes).
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* \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \p ext_rep is invalid.
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* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if couldn't allocate enough
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* memory for conversion. Can occur only for moduli with
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* MBEDTLS_MPI_MOD_REP_MONTGOMERY.
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*/
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int mbedtls_mpi_mod_write(const mbedtls_mpi_mod_residue *r,
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const mbedtls_mpi_mod_modulus *N,
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unsigned char *buf,
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size_t buflen,
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mbedtls_mpi_mod_ext_rep ext_rep);
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#endif /* MBEDTLS_BIGNUM_MOD_H */
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