437 lines
19 KiB
C
437 lines
19 KiB
C
/**
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* Core bignum functions
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*
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* This interface should only be used by the legacy bignum module (bignum.h)
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* and the modular bignum modules (bignum_mod.c, bignum_mod_raw.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 module is about processing non-negative integers with a fixed upper
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* bound that's of the form 2^n-1 where n is a multiple of #biL.
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* These can be thought of integers written in base 2^#biL with a fixed
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* number of digits. Digits in this base are called *limbs*.
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* Many operations treat these numbers as the principal representation of
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* a number modulo 2^n or a smaller bound.
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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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* - **Overflow**: some functions indicate overflow from the range
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* [0, 2^n-1] by returning carry parameters, while others operate
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* modulo and so cannot overflow. This should be clear from the function
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* documentation.
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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 \p A, \p B, ... are inputs, and are
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* not modified by the function.
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* - For operations modulo some number, the modulus is called \p N
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* and is input-only.
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* - Bignum parameters called \p X, \p Y are outputs or input-output.
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* The initial content of output-only parameters is ignored.
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* - Some functions use different names that reflect traditional
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* naming of operands of certain operations (e.g.
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* divisor/dividend/quotient/remainder).
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* - \p T is a temporary storage area. The initial content of such
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* parameter is ignored and the final content is unspecified.
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* - **Bignum sizes**: bignum sizes are always expressed in limbs.
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* Most functions work on bignums of a given size and take a single
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* \p limbs parameter that applies to all parameters that are limb arrays.
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* All bignum sizes must be at least 1 and must be significantly less than
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* #SIZE_MAX. The behavior if a size is 0 is undefined. The behavior if the
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* total size of all parameters overflows #SIZE_MAX is undefined.
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* - **Parameter ordering**: for bignum parameters, outputs come before inputs.
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* Temporaries come last.
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* - **Aliasing**: in general, output bignums may be aliased to one or more
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* inputs. As an exception, parameters that are documented as a modulus value
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* may not be aliased to an output. Outputs may not be aliased to one another.
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* Temporaries may not be aliased to any 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 some functions that operate on bignums of
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* different sizes have constraints about their size, and violating those
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* constraints may lead to buffer overflows.
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* - **Modular representatives**: functions that operate modulo \p N expect
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* all modular inputs to be in the range [0, \p N - 1] and guarantee outputs
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* in the range [0, \p N - 1]. If an input is out of range, outputs are
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* fully unspecified, though bignum values out of range should not cause
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* buffer overflows (beware that this is 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
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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_CORE_H
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#define MBEDTLS_BIGNUM_CORE_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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#define ciL ( sizeof(mbedtls_mpi_uint) ) /** chars in limb */
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#define biL ( ciL << 3 ) /** bits in limb */
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#define biH ( ciL << 2 ) /** half limb size */
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/*
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* Convert between bits/chars and number of limbs
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* Divide first in order to avoid potential overflows
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*/
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#define BITS_TO_LIMBS(i) ( (i) / biL + ( (i) % biL != 0 ) )
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#define CHARS_TO_LIMBS(i) ( (i) / ciL + ( (i) % ciL != 0 ) )
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/* Get a specific byte, without range checks. */
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#define GET_BYTE( X, i ) \
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( ( (X)[(i) / ciL] >> ( ( (i) % ciL ) * 8 ) ) & 0xff )
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/** Count leading zero bits in a given integer.
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*
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* \param a Integer to count leading zero bits.
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*
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* \return The number of leading zero bits in \p a.
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*/
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size_t mbedtls_mpi_core_clz( mbedtls_mpi_uint a );
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/** Return the minimum number of bits required to represent the value held
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* in the MPI.
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*
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* \note This function returns 0 if all the limbs of \p A are 0.
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*
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* \param[in] A The address of the MPI.
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* \param A_limbs The number of limbs of \p A.
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*
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* \return The number of bits in \p A.
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*/
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size_t mbedtls_mpi_core_bitlen( const mbedtls_mpi_uint *A, size_t A_limbs );
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/** Convert a big-endian byte array aligned to the size of mbedtls_mpi_uint
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* into the storage form used by mbedtls_mpi.
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*
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* \param[in,out] A The address of the MPI.
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* \param A_limbs The number of limbs of \p A.
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*/
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void mbedtls_mpi_core_bigendian_to_host( mbedtls_mpi_uint *A,
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size_t A_limbs );
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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 assignment was done or not.
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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 limbs The number of limbs of \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_core_cond_assign( mbedtls_mpi_uint *X,
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const mbedtls_mpi_uint *A,
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size_t limbs,
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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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* \param[in,out] X The address of the first MPI.
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* This must be initialized.
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* \param[in,out] Y The address of the second MPI.
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* This must be initialized.
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* \param limbs The number of limbs of \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_core_cond_swap( mbedtls_mpi_uint *X,
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mbedtls_mpi_uint *Y,
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size_t limbs,
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unsigned char swap );
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/** Import X from unsigned binary data, little-endian.
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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.
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* \param X_limbs The number of limbs of \p X.
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* \param[in] input The input buffer to import from.
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* \param input_length The length bytes of \p input.
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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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*/
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int mbedtls_mpi_core_read_le( mbedtls_mpi_uint *X,
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size_t X_limbs,
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const unsigned char *input,
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size_t input_length );
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/** Import X from unsigned binary data, big-endian.
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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.
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* May only be #NULL if \X_limbs is 0 and \p input_length
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* is 0.
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* \param X_limbs The number of limbs of \p X.
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* \param[in] input The input buffer to import from.
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* May only be #NULL if \p input_length is 0.
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* \param input_length The length in bytes of \p input.
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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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*/
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int mbedtls_mpi_core_read_be( mbedtls_mpi_uint *X,
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size_t X_limbs,
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const unsigned char *input,
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size_t input_length );
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/** Export A into unsigned binary data, little-endian.
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*
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* \note If \p output is shorter than \p A the export is still successful if the
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* value held in \p A fits in the buffer (that is, if enough of the most
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* significant bytes of \p A are 0).
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*
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* \param[in] A The address of the MPI.
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* \param A_limbs The number of limbs of \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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*
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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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*/
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int mbedtls_mpi_core_write_le( const mbedtls_mpi_uint *A,
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size_t A_limbs,
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unsigned char *output,
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size_t output_length );
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/** Export A into unsigned binary data, big-endian.
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*
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* \note If \p output is shorter than \p A the export is still successful if the
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* value held in \p A fits in the buffer (that is, if enough of the most
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* significant bytes of \p A are 0).
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*
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* \param[in] A The address of the MPI.
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* \param A_limbs The number of limbs of \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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*
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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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*/
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int mbedtls_mpi_core_write_be( const mbedtls_mpi_uint *A,
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size_t A_limbs,
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unsigned char *output,
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size_t output_length );
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/** \brief Shift an MPI right in place by a number of bits.
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*
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* Shifting by more bits than there are bit positions
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* in \p X is valid and results in setting \p X to 0.
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*
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* This function's execution time depends on the value
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* of \p count (and of course \p limbs).
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*
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* \param[in,out] X The number to shift.
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* \param limbs The number of limbs of \p X. This must be at least 1.
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* \param count The number of bits to shift by.
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*/
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void mbedtls_mpi_core_shift_r( mbedtls_mpi_uint *X, size_t limbs,
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size_t count );
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/**
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* \brief Add two fixed-size large unsigned integers, returning the carry.
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*
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* Calculates `A + B` where `A` and `B` have the same size.
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*
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* This function operates modulo `2^(biL*limbs)` and returns the carry
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* (1 if there was a wraparound, and 0 otherwise).
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*
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* \p X may be aliased to \p A or \p B.
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*
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* \param[out] X The result of the addition.
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* \param[in] A Little-endian presentation of the left operand.
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* \param[in] B Little-endian presentation of the right operand.
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* \param limbs Number of limbs of \p X, \p A and \p B.
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*
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* \return 1 if `A + B >= 2^(biL*limbs)`, 0 otherwise.
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*/
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mbedtls_mpi_uint mbedtls_mpi_core_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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size_t limbs );
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/**
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* \brief Conditional addition of two fixed-size large unsigned integers,
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* returning the carry.
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*
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* Functionally equivalent to
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*
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* ```
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* if( cond )
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* X += A;
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* return carry;
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* ```
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*
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* This function operates modulo `2^(biL*limbs)`.
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*
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* \param[in,out] X The pointer to the (little-endian) array
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* representing the bignum to accumulate onto.
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* \param[in] A The pointer to the (little-endian) array
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* representing the bignum to conditionally add
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* to \p X. This may be aliased to \p X but may not
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* overlap otherwise.
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* \param limbs Number of limbs of \p X and \p A.
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* \param cond Condition bit dictating whether addition should
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* happen or not. This must be \c 0 or \c 1.
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*
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* \warning If \p cond is neither 0 nor 1, the result of this function
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* is unspecified, and the resulting value in \p X might be
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* neither its original value nor \p X + \p A.
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*
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* \return 1 if `X + cond * A >= 2^(biL*limbs)`, 0 otherwise.
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*/
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mbedtls_mpi_uint mbedtls_mpi_core_add_if( mbedtls_mpi_uint *X,
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const mbedtls_mpi_uint *A,
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size_t limbs,
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unsigned cond );
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/**
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* \brief Subtract two fixed-size large unsigned integers, returning the borrow.
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*
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* Calculate `A - B` where \p A and \p B have the same size.
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* This function operates modulo `2^(biL*limbs)` and returns the carry
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* (1 if there was a wraparound, i.e. if `A < B`, and 0 otherwise).
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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 subtraction.
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* \param[in] A Little-endian presentation of left operand.
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* \param[in] B Little-endian presentation of right operand.
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* \param limbs Number of limbs of \p X, \p A and \p B.
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*
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* \return 1 if `A < B`.
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* 0 if `A >= B`.
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*/
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mbedtls_mpi_uint mbedtls_mpi_core_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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size_t limbs );
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/**
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* \brief Perform a fixed-size multiply accumulate operation: X += b * A
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*
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* \p X may be aliased to \p A (when \p X_limbs == \p A_limbs), but may not
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* otherwise overlap.
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*
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* This function operates modulo `2^(biL*X_limbs)`.
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*
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* \param[in,out] X The pointer to the (little-endian) array
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* representing the bignum to accumulate onto.
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* \param X_limbs The number of limbs of \p X. This must be
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* at least \p A_limbs.
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* \param[in] A The pointer to the (little-endian) array
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* representing the bignum to multiply with.
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* This may be aliased to \p X but may not overlap
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* otherwise.
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* \param A_limbs The number of limbs of \p A.
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* \param b X scalar to multiply with.
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*
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* \return The carry at the end of the operation.
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*/
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mbedtls_mpi_uint mbedtls_mpi_core_mla( mbedtls_mpi_uint *X, size_t X_limbs,
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const mbedtls_mpi_uint *A, size_t A_limbs,
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mbedtls_mpi_uint b );
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/**
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* \brief Calculate initialisation value for fast Montgomery modular
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* multiplication
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*
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* \param[in] N Little-endian presentation of the modulus. This must have
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* at least one limb.
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*
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* \return The initialisation value for fast Montgomery modular multiplication
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*/
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mbedtls_mpi_uint mbedtls_mpi_core_montmul_init( const mbedtls_mpi_uint *N );
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/**
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* \brief Montgomery multiplication: X = A * B * R^-1 mod N (HAC 14.36)
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*
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* \p A and \p B must be in canonical form. That is, < \p N.
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*
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* \p X may be aliased to \p A or \p N, or even \p B (if \p AN_limbs ==
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* \p B_limbs) but may not overlap any parameters otherwise.
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*
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* \p A and \p B may alias each other, if \p AN_limbs == \p B_limbs. They may
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* not alias \p N (since they must be in canonical form, they cannot == \p N).
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*
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* \param[out] X The destination MPI, as a little-endian array of
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* length \p AN_limbs.
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* On successful completion, 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*AN_limbs)`.
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* \param[in] A Little-endian presentation of first operand.
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* Must have the same number of limbs as \p N.
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* \param[in] B Little-endian presentation of second operand.
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* \param[in] B_limbs The number of limbs in \p B.
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* Must be <= \p AN_limbs.
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* \param[in] N Little-endian presentation of the modulus.
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* This must be odd, and have exactly the same number
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* of limbs as \p A.
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* It may alias \p X, but must not alias or otherwise
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* overlap any of the other parameters.
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* \param[in] AN_limbs The number of limbs in \p X, \p A and \p N.
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* \param mm The Montgomery constant for \p N: -N^-1 mod 2^biL.
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* This can be calculated by `mbedtls_mpi_core_montmul_init()`.
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* \param[in,out] T Temporary storage of size at least 2*AN_limbs+1 limbs.
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* 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_core_montmul( mbedtls_mpi_uint *X,
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const mbedtls_mpi_uint *A,
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const mbedtls_mpi_uint *B, size_t B_limbs,
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const mbedtls_mpi_uint *N, size_t AN_limbs,
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mbedtls_mpi_uint mm, mbedtls_mpi_uint *T );
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#endif /* MBEDTLS_BIGNUM_CORE_H */
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