417 lines
19 KiB
C++
417 lines
19 KiB
C++
/**
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* Low-level modular bignum functions
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*
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* This interface should only be used by the higher-level modular bignum
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* module (bignum_mod.c) and the ECP module (ecp.c, ecp_curves.c). All other
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* modules should use the high-level modular bignum interface (bignum_mod.h)
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* or the legacy bignum interface (bignum.h).
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*
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* This is a low-level interface to operations on integers modulo which
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* has no protection against passing invalid arguments such as arrays of
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* the wrong size. The functions in bignum_mod.h provide a higher-level
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* interface that includes protections against accidental misuse, at the
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* expense of code size and sometimes more cumbersome memory management.
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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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* - **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.
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* - **Bignum parameters**: Bignums are passed as pointers to an array of
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* limbs. A limb has the type #mbedtls_mpi_uint. 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.
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* - Bignum parameters called \c X, \c Y are outputs or input-output.
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* The initial content of output-only parameters is ignored.
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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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* - **Bignum sizes**: bignum sizes are usually expressed by the \c limbs
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* member of the modulus argument. 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 for arithmetic
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* functions. Utility functions may allow for different representation.
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* - **Parameter ordering**: for bignum parameters, outputs come before inputs.
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* The modulus is passed after other bignum input parameters. Temporaries
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* 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 limb array pointers (where two
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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**: This is a low-level module. Functions generally do not
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* try to protect against invalid arguments such as nonsensical sizes or
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* null pointers. Note that passing bignums with a different size than the
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* modulus may lead to buffer overflows. Some functions which allocate
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* memory or handle reading/writing of bignums will return an error if
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* memory allocation fails or if buffer sizes are invalid.
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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]. If
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* an input is out of range, outputs are fully unspecified, though bignum
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* values out of range should not cause buffer overflows (beware that this is
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* not extensively 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 OR GPL-2.0-or-later
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*/
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#ifndef MBEDTLS_BIGNUM_MOD_RAW_H
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#define MBEDTLS_BIGNUM_MOD_RAW_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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#include "bignum_mod.h"
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/**
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* \brief Perform a safe conditional copy of an MPI which doesn't reveal
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* whether the assignment was done or not.
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*
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* The size to copy is determined by \p N.
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*
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* \param[out] X The address of the destination MPI.
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* This must be initialized. Must have enough limbs to
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* store the full value of \p A.
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* \param[in] A The address of the source MPI. This must be initialized.
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* \param[in] N The address of the modulus related to \p X and \p A.
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* \param assign The condition deciding whether to perform the
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* assignment or not. Must be either 0 or 1:
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* * \c 1: Perform the assignment `X = A`.
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* * \c 0: Keep the original value of \p X.
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*
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* \note This function avoids leaking any information about whether
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* the assignment was done or not.
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*
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* \warning If \p assign is neither 0 nor 1, the result of this function
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* is indeterminate, and the resulting value in \p X might be
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* neither its original value nor the value in \p A.
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*/
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void mbedtls_mpi_mod_raw_cond_assign(mbedtls_mpi_uint *X,
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const mbedtls_mpi_uint *A,
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const mbedtls_mpi_mod_modulus *N,
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unsigned char assign);
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/**
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* \brief Perform a safe conditional swap of two MPIs which doesn't reveal
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* whether the swap was done or not.
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*
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* The size to swap is determined by \p N.
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*
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* \param[in,out] X The address of the first MPI. This must be initialized.
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* \param[in,out] Y The address of the second MPI. This must be initialized.
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* \param[in] N The address of the modulus related to \p X and \p Y.
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* \param swap The condition deciding whether to perform
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* the swap or not. Must be either 0 or 1:
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* * \c 1: Swap the values of \p X and \p Y.
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* * \c 0: Keep the original values of \p X and \p Y.
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*
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* \note This function avoids leaking any information about whether
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* the swap was done or not.
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*
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* \warning If \p swap is neither 0 nor 1, the result of this function
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* is indeterminate, and both \p X and \p Y might end up with
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* values different to either of the original ones.
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*/
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void mbedtls_mpi_mod_raw_cond_swap(mbedtls_mpi_uint *X,
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mbedtls_mpi_uint *Y,
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const mbedtls_mpi_mod_modulus *N,
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unsigned char swap);
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/** Import X from unsigned binary data.
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*
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* The MPI needs to have enough limbs to store the full value (including any
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* most significant zero bytes in the input).
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*
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* \param[out] X The address of the MPI. The size is determined by \p N.
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* (In particular, it must have at least as many limbs as
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* the modulus \p N.)
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* \param[in] N The address of the modulus related to \p X.
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* \param[in] input The input buffer to import from.
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* \param input_length The length in bytes of \p input.
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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 X isn't
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* large enough to hold the value in \p input.
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* \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if the external representation
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* of \p N is invalid or \p X is not less than \p N.
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*/
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int mbedtls_mpi_mod_raw_read(mbedtls_mpi_uint *X,
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const mbedtls_mpi_mod_modulus *N,
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const unsigned char *input,
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size_t input_length,
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mbedtls_mpi_mod_ext_rep ext_rep);
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/** Export A into unsigned binary data.
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*
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* \param[in] A The address of the MPI. The size is determined by \p N.
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* (In particular, it must have at least as many limbs as
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* the modulus \p N.)
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* \param[in] N The address of the modulus related to \p A.
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* \param[out] output The output buffer to export to.
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* \param output_length The length in bytes of \p output.
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* \param ext_rep The endianness in which the number should be written into 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 output isn't
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* large enough to hold the value of \p A.
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* \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if the external representation
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* of \p N is invalid.
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*/
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int mbedtls_mpi_mod_raw_write(const mbedtls_mpi_uint *A,
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const mbedtls_mpi_mod_modulus *N,
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unsigned char *output,
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size_t output_length,
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mbedtls_mpi_mod_ext_rep ext_rep);
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/** \brief Subtract two MPIs, returning the residue modulo the specified
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* modulus.
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*
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* The size of the operation is determined by \p N. \p A and \p B must have
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* 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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* \param[out] X The address of the result MPI.
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* This must be initialized. Must have enough limbs to
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* store the full value of the result.
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* \param[in] A The address of the first MPI. This must be initialized.
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* \param[in] B The address of the second MPI. This must be initialized.
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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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void mbedtls_mpi_mod_raw_sub(mbedtls_mpi_uint *X,
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const mbedtls_mpi_uint *A,
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const mbedtls_mpi_uint *B,
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const mbedtls_mpi_mod_modulus *N);
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/** \brief Multiply two MPIs, 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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* \param[in,out] T Temporary storage of size at least 2 * N->limbs + 1
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* limbs. Its initial content is unused and
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* its final content is indeterminate.
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* It must not alias or otherwise overlap any of the
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* other parameters.
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*/
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void mbedtls_mpi_mod_raw_mul(mbedtls_mpi_uint *X,
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const mbedtls_mpi_uint *A,
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const mbedtls_mpi_uint *B,
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const mbedtls_mpi_mod_modulus *N,
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mbedtls_mpi_uint *T);
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/**
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* \brief Returns the number of limbs of working memory required for
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* a call to `mbedtls_mpi_mod_raw_inv_prime()`.
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*
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* \note This will always be at least
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* `mbedtls_mpi_core_montmul_working_limbs(AN_limbs)`,
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* i.e. sufficient for a call to `mbedtls_mpi_core_montmul()`.
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*
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* \param AN_limbs The number of limbs in the input `A` and the modulus `N`
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* (they must be the same size) that will be given to
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* `mbedtls_mpi_mod_raw_inv_prime()`.
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*
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* \return The number of limbs of working memory required by
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* `mbedtls_mpi_mod_raw_inv_prime()`.
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*/
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size_t mbedtls_mpi_mod_raw_inv_prime_working_limbs(size_t AN_limbs);
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/**
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* \brief Perform fixed-width modular inversion of a Montgomery-form MPI with
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* respect to a modulus \p N that must be prime.
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*
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* \p X may be aliased to \p A, but not to \p N or \p RR.
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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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* Will be in Montgomery form.
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* \param[in] A The number to calculate the modular inverse of.
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* Must be in Montgomery form. Must not be 0.
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* \param[in] N The modulus, as a little-endian array of length \p AN_limbs.
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* Must be prime.
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* \param AN_limbs The number of limbs in \p A, \p N and \p RR.
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* \param[in] RR The precomputed residue of 2^{2*biL} modulo N, as a little-
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* endian array of length \p AN_limbs.
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* \param[in,out] T Temporary storage of at least the number of limbs returned
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* by `mbedtls_mpi_mod_raw_inv_prime_working_limbs()`.
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* Its initial content is unused and its final content is
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* indeterminate.
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* It must not alias or otherwise overlap any of the other
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* parameters.
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* It is up to the caller to zeroize \p T when it is no
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* longer needed, and before freeing it if it was dynamically
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* allocated.
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*/
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void mbedtls_mpi_mod_raw_inv_prime(mbedtls_mpi_uint *X,
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const mbedtls_mpi_uint *A,
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const mbedtls_mpi_uint *N,
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size_t AN_limbs,
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const mbedtls_mpi_uint *RR,
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mbedtls_mpi_uint *T);
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/**
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* \brief Perform a known-size modular addition.
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*
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* Calculate `A + B modulo N`.
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*
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* The number of limbs in each operand, and the result, is given by the
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* modulus \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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* \param[out] X The result of the modular addition.
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* \param[in] A Little-endian presentation of the left operand. This
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* must be smaller than \p N.
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* \param[in] B Little-endian presentation of the right operand. This
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* must be smaller than \p N.
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* \param[in] N The address of the modulus.
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*/
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void mbedtls_mpi_mod_raw_add(mbedtls_mpi_uint *X,
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const mbedtls_mpi_uint *A,
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const mbedtls_mpi_uint *B,
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const mbedtls_mpi_mod_modulus *N);
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/** Convert an MPI from canonical representation (little-endian limb array)
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* to the representation associated with the modulus.
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*
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* \param[in,out] X The limb array to convert.
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* It must have as many limbs as \p N.
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* It is converted in place.
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* If this function returns an error, the content of \p X
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* is unspecified.
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* \param[in] N The modulus structure.
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*
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* \return \c 0 if successful.
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* Otherwise an \c MBEDTLS_ERR_MPI_xxx error code.
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*/
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int mbedtls_mpi_mod_raw_canonical_to_modulus_rep(
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mbedtls_mpi_uint *X,
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const mbedtls_mpi_mod_modulus *N);
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/** Convert an MPI from the representation associated with the modulus
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* to canonical representation (little-endian limb array).
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*
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* \param[in,out] X The limb array to convert.
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* It must have as many limbs as \p N.
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* It is converted in place.
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* If this function returns an error, the content of \p X
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* is unspecified.
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* \param[in] N The modulus structure.
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*
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* \return \c 0 if successful.
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* Otherwise an \c MBEDTLS_ERR_MPI_xxx error code.
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*/
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int mbedtls_mpi_mod_raw_modulus_to_canonical_rep(
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mbedtls_mpi_uint *X,
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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 MPI, in canonical representation modulo \p N.
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* It must not be aliased with \p N or otherwise overlap it.
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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_raw_random(mbedtls_mpi_uint *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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/** Convert an MPI into Montgomery form.
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*
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* \param X The address of the MPI.
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* Must have the same number of limbs as \p N.
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* \param N The address of the modulus, which gives the size of
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* the base `R` = 2^(biL*N->limbs).
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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_raw_to_mont_rep(mbedtls_mpi_uint *X,
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const mbedtls_mpi_mod_modulus *N);
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/** Convert an MPI back from Montgomery representation.
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*
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* \param X The address of the MPI.
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* Must have the same number of limbs as \p N.
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* \param N The address of the modulus, which gives the size of
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* the base `R`= 2^(biL*N->limbs).
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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_raw_from_mont_rep(mbedtls_mpi_uint *X,
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const mbedtls_mpi_mod_modulus *N);
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/** \brief Perform fixed width modular negation.
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*
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* The size of the operation is determined by \p N. \p A must have
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* 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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* \param[out] X The result of the modular negation.
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* This must be initialized.
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* \param[in] A Little-endian presentation of the input operand. This
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* must be less than or equal to \p N.
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* \param[in] N The modulus to use.
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*/
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void mbedtls_mpi_mod_raw_neg(mbedtls_mpi_uint *X,
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const mbedtls_mpi_uint *A,
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const mbedtls_mpi_mod_modulus *N);
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#endif /* MBEDTLS_BIGNUM_MOD_RAW_H */
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