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gbe_fork/mbedtls/bignum_core.h
otavepto 92c77cee31 added a new cryptography library Mbed TLS
2023-12-24 14:33:40 +02:00

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/**
* Core bignum functions
*
* This interface should only be used by the legacy bignum module (bignum.h)
* and the modular bignum modules (bignum_mod.c, bignum_mod_raw.c). All other
* modules should use the high-level modular bignum interface (bignum_mod.h)
* or the legacy bignum interface (bignum.h).
*
* This module is about processing non-negative integers with a fixed upper
* bound that's of the form 2^n-1 where n is a multiple of #biL.
* These can be thought of integers written in base 2^#biL with a fixed
* number of digits. Digits in this base are called *limbs*.
* Many operations treat these numbers as the principal representation of
* a number modulo 2^n or a smaller bound.
*
* The functions in this module obey the following conventions unless
* explicitly indicated otherwise:
*
* - **Overflow**: some functions indicate overflow from the range
* [0, 2^n-1] by returning carry parameters, while others operate
* modulo and so cannot overflow. This should be clear from the function
* documentation.
* - **Bignum parameters**: Bignums are passed as pointers to an array of
* limbs. A limb has the type #mbedtls_mpi_uint. Unless otherwise specified:
* - Bignum parameters called \p A, \p B, ... are inputs, and are
* not modified by the function.
* - For operations modulo some number, the modulus is called \p N
* and is input-only.
* - Bignum parameters called \p X, \p Y are outputs or input-output.
* The initial content of output-only parameters is ignored.
* - Some functions use different names that reflect traditional
* naming of operands of certain operations (e.g.
* divisor/dividend/quotient/remainder).
* - \p T is a temporary storage area. The initial content of such
* parameter is ignored and the final content is unspecified.
* - **Bignum sizes**: bignum sizes are always expressed in limbs.
* Most functions work on bignums of a given size and take a single
* \p limbs parameter that applies to all parameters that are limb arrays.
* All bignum sizes must be at least 1 and must be significantly less than
* #SIZE_MAX. The behavior if a size is 0 is undefined. The behavior if the
* total size of all parameters overflows #SIZE_MAX is undefined.
* - **Parameter ordering**: for bignum parameters, outputs come before inputs.
* Temporaries come last.
* - **Aliasing**: in general, output bignums may be aliased to one or more
* inputs. As an exception, parameters that are documented as a modulus value
* may not be aliased to an output. Outputs may not be aliased to one another.
* Temporaries may not be aliased to any other parameter.
* - **Overlap**: apart from aliasing of limb array pointers (where two
* arguments are equal pointers), overlap is not supported and may result
* in undefined behavior.
* - **Error handling**: This is a low-level module. Functions generally do not
* try to protect against invalid arguments such as nonsensical sizes or
* null pointers. Note that some functions that operate on bignums of
* different sizes have constraints about their size, and violating those
* constraints may lead to buffer overflows.
* - **Modular representatives**: functions that operate modulo \p N expect
* all modular inputs to be in the range [0, \p N - 1] and guarantee outputs
* in the range [0, \p N - 1]. If an input is out of range, outputs are
* fully unspecified, though bignum values out of range should not cause
* buffer overflows (beware that this is not extensively tested).
*/
/*
* Copyright The Mbed TLS Contributors
* SPDX-License-Identifier: Apache-2.0 OR GPL-2.0-or-later
*/
#ifndef MBEDTLS_BIGNUM_CORE_H
#define MBEDTLS_BIGNUM_CORE_H
#include "common.h"
#if defined(MBEDTLS_BIGNUM_C)
#include "mbedtls/bignum.h"
#endif
#include "constant_time_internal.h"
#define ciL (sizeof(mbedtls_mpi_uint)) /** chars in limb */
#define biL (ciL << 3) /** bits in limb */
#define biH (ciL << 2) /** half limb size */
/*
* Convert between bits/chars and number of limbs
* Divide first in order to avoid potential overflows
*/
#define BITS_TO_LIMBS(i) ((i) / biL + ((i) % biL != 0))
#define CHARS_TO_LIMBS(i) ((i) / ciL + ((i) % ciL != 0))
/* Get a specific byte, without range checks. */
#define GET_BYTE(X, i) \
(((X)[(i) / ciL] >> (((i) % ciL) * 8)) & 0xff)
/** Count leading zero bits in a given integer.
*
* \warning The result is undefined if \p a == 0
*
* \param a Integer to count leading zero bits.
*
* \return The number of leading zero bits in \p a, if \p a != 0.
* If \p a == 0, the result is undefined.
*/
size_t mbedtls_mpi_core_clz(mbedtls_mpi_uint a);
/** Return the minimum number of bits required to represent the value held
* in the MPI.
*
* \note This function returns 0 if all the limbs of \p A are 0.
*
* \param[in] A The address of the MPI.
* \param A_limbs The number of limbs of \p A.
*
* \return The number of bits in \p A.
*/
size_t mbedtls_mpi_core_bitlen(const mbedtls_mpi_uint *A, size_t A_limbs);
/** Convert a big-endian byte array aligned to the size of mbedtls_mpi_uint
* into the storage form used by mbedtls_mpi.
*
* \param[in,out] A The address of the MPI.
* \param A_limbs The number of limbs of \p A.
*/
void mbedtls_mpi_core_bigendian_to_host(mbedtls_mpi_uint *A,
size_t A_limbs);
/** \brief Compare a machine integer with an MPI.
*
* This function operates in constant time with respect
* to the values of \p min and \p A.
*
* \param min A machine integer.
* \param[in] A An MPI.
* \param A_limbs The number of limbs of \p A.
* This must be at least 1.
*
* \return MBEDTLS_CT_TRUE if \p min is less than or equal to \p A, otherwise MBEDTLS_CT_FALSE.
*/
mbedtls_ct_condition_t mbedtls_mpi_core_uint_le_mpi(mbedtls_mpi_uint min,
const mbedtls_mpi_uint *A,
size_t A_limbs);
/**
* \brief Check if one unsigned MPI is less than another in constant
* time.
*
* \param A The left-hand MPI. This must point to an array of limbs
* with the same allocated length as \p B.
* \param B The right-hand MPI. This must point to an array of limbs
* with the same allocated length as \p A.
* \param limbs The number of limbs in \p A and \p B.
* This must not be 0.
*
* \return MBEDTLS_CT_TRUE if \p A is less than \p B.
* MBEDTLS_CT_FALSE if \p A is greater than or equal to \p B.
*/
mbedtls_ct_condition_t mbedtls_mpi_core_lt_ct(const mbedtls_mpi_uint *A,
const mbedtls_mpi_uint *B,
size_t limbs);
/**
* \brief Perform a safe conditional copy of an MPI which doesn't reveal
* whether assignment was done or not.
*
* \param[out] X The address of the destination MPI.
* This must be initialized. Must have enough limbs to
* store the full value of \p A.
* \param[in] A The address of the source MPI. This must be initialized.
* \param limbs The number of limbs of \p A.
* \param assign The condition deciding whether to perform the
* assignment or not. Callers will need to use
* the constant time interface (e.g. `mbedtls_ct_bool()`)
* to construct this argument.
*
* \note This function avoids leaking any information about whether
* the assignment was done or not.
*/
void mbedtls_mpi_core_cond_assign(mbedtls_mpi_uint *X,
const mbedtls_mpi_uint *A,
size_t limbs,
mbedtls_ct_condition_t assign);
/**
* \brief Perform a safe conditional swap of two MPIs which doesn't reveal
* whether the swap was done or not.
*
* \param[in,out] X The address of the first MPI.
* This must be initialized.
* \param[in,out] Y The address of the second MPI.
* This must be initialized.
* \param limbs The number of limbs of \p X and \p Y.
* \param swap The condition deciding whether to perform
* the swap or not.
*
* \note This function avoids leaking any information about whether
* the swap was done or not.
*/
void mbedtls_mpi_core_cond_swap(mbedtls_mpi_uint *X,
mbedtls_mpi_uint *Y,
size_t limbs,
mbedtls_ct_condition_t swap);
/** Import X from unsigned binary data, little-endian.
*
* The MPI needs to have enough limbs to store the full value (including any
* most significant zero bytes in the input).
*
* \param[out] X The address of the MPI.
* \param X_limbs The number of limbs of \p X.
* \param[in] input The input buffer to import from.
* \param input_length The length bytes of \p input.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p X isn't
* large enough to hold the value in \p input.
*/
int mbedtls_mpi_core_read_le(mbedtls_mpi_uint *X,
size_t X_limbs,
const unsigned char *input,
size_t input_length);
/** Import X from unsigned binary data, big-endian.
*
* The MPI needs to have enough limbs to store the full value (including any
* most significant zero bytes in the input).
*
* \param[out] X The address of the MPI.
* May only be #NULL if \p X_limbs is 0 and \p input_length
* is 0.
* \param X_limbs The number of limbs of \p X.
* \param[in] input The input buffer to import from.
* May only be #NULL if \p input_length is 0.
* \param input_length The length in bytes of \p input.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p X isn't
* large enough to hold the value in \p input.
*/
int mbedtls_mpi_core_read_be(mbedtls_mpi_uint *X,
size_t X_limbs,
const unsigned char *input,
size_t input_length);
/** Export A into unsigned binary data, little-endian.
*
* \note If \p output is shorter than \p A the export is still successful if the
* value held in \p A fits in the buffer (that is, if enough of the most
* significant bytes of \p A are 0).
*
* \param[in] A The address of the MPI.
* \param A_limbs The number of limbs of \p A.
* \param[out] output The output buffer to export to.
* \param output_length The length in bytes of \p output.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p output isn't
* large enough to hold the value of \p A.
*/
int mbedtls_mpi_core_write_le(const mbedtls_mpi_uint *A,
size_t A_limbs,
unsigned char *output,
size_t output_length);
/** Export A into unsigned binary data, big-endian.
*
* \note If \p output is shorter than \p A the export is still successful if the
* value held in \p A fits in the buffer (that is, if enough of the most
* significant bytes of \p A are 0).
*
* \param[in] A The address of the MPI.
* \param A_limbs The number of limbs of \p A.
* \param[out] output The output buffer to export to.
* \param output_length The length in bytes of \p output.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p output isn't
* large enough to hold the value of \p A.
*/
int mbedtls_mpi_core_write_be(const mbedtls_mpi_uint *A,
size_t A_limbs,
unsigned char *output,
size_t output_length);
/** \brief Shift an MPI in-place right by a number of bits.
*
* Shifting by more bits than there are bit positions
* in \p X is valid and results in setting \p X to 0.
*
* This function's execution time depends on the value
* of \p count (and of course \p limbs).
*
* \param[in,out] X The number to shift.
* \param limbs The number of limbs of \p X. This must be at least 1.
* \param count The number of bits to shift by.
*/
void mbedtls_mpi_core_shift_r(mbedtls_mpi_uint *X, size_t limbs,
size_t count);
/**
* \brief Shift an MPI in-place left by a number of bits.
*
* Shifting by more bits than there are bit positions
* in \p X will produce an unspecified result.
*
* This function's execution time depends on the value
* of \p count (and of course \p limbs).
* \param[in,out] X The number to shift.
* \param limbs The number of limbs of \p X. This must be at least 1.
* \param count The number of bits to shift by.
*/
void mbedtls_mpi_core_shift_l(mbedtls_mpi_uint *X, size_t limbs,
size_t count);
/**
* \brief Add two fixed-size large unsigned integers, returning the carry.
*
* Calculates `A + B` where `A` and `B` have the same size.
*
* This function operates modulo `2^(biL*limbs)` and returns the carry
* (1 if there was a wraparound, and 0 otherwise).
*
* \p X may be aliased to \p A or \p B.
*
* \param[out] X The result of the addition.
* \param[in] A Little-endian presentation of the left operand.
* \param[in] B Little-endian presentation of the right operand.
* \param limbs Number of limbs of \p X, \p A and \p B.
*
* \return 1 if `A + B >= 2^(biL*limbs)`, 0 otherwise.
*/
mbedtls_mpi_uint mbedtls_mpi_core_add(mbedtls_mpi_uint *X,
const mbedtls_mpi_uint *A,
const mbedtls_mpi_uint *B,
size_t limbs);
/**
* \brief Conditional addition of two fixed-size large unsigned integers,
* returning the carry.
*
* Functionally equivalent to
*
* ```
* if( cond )
* X += A;
* return carry;
* ```
*
* This function operates modulo `2^(biL*limbs)`.
*
* \param[in,out] X The pointer to the (little-endian) array
* representing the bignum to accumulate onto.
* \param[in] A The pointer to the (little-endian) array
* representing the bignum to conditionally add
* to \p X. This may be aliased to \p X but may not
* overlap otherwise.
* \param limbs Number of limbs of \p X and \p A.
* \param cond Condition bit dictating whether addition should
* happen or not. This must be \c 0 or \c 1.
*
* \warning If \p cond is neither 0 nor 1, the result of this function
* is unspecified, and the resulting value in \p X might be
* neither its original value nor \p X + \p A.
*
* \return 1 if `X + cond * A >= 2^(biL*limbs)`, 0 otherwise.
*/
mbedtls_mpi_uint mbedtls_mpi_core_add_if(mbedtls_mpi_uint *X,
const mbedtls_mpi_uint *A,
size_t limbs,
unsigned cond);
/**
* \brief Subtract two fixed-size large unsigned integers, returning the borrow.
*
* Calculate `A - B` where \p A and \p B have the same size.
* This function operates modulo `2^(biL*limbs)` and returns the carry
* (1 if there was a wraparound, i.e. if `A < B`, and 0 otherwise).
*
* \p X may be aliased to \p A or \p B, or even both, but may not overlap
* either otherwise.
*
* \param[out] X The result of the subtraction.
* \param[in] A Little-endian presentation of left operand.
* \param[in] B Little-endian presentation of right operand.
* \param limbs Number of limbs of \p X, \p A and \p B.
*
* \return 1 if `A < B`.
* 0 if `A >= B`.
*/
mbedtls_mpi_uint mbedtls_mpi_core_sub(mbedtls_mpi_uint *X,
const mbedtls_mpi_uint *A,
const mbedtls_mpi_uint *B,
size_t limbs);
/**
* \brief Perform a fixed-size multiply accumulate operation: X += b * A
*
* \p X may be aliased to \p A (when \p X_limbs == \p A_limbs), but may not
* otherwise overlap.
*
* This function operates modulo `2^(biL*X_limbs)`.
*
* \param[in,out] X The pointer to the (little-endian) array
* representing the bignum to accumulate onto.
* \param X_limbs The number of limbs of \p X. This must be
* at least \p A_limbs.
* \param[in] A The pointer to the (little-endian) array
* representing the bignum to multiply with.
* This may be aliased to \p X but may not overlap
* otherwise.
* \param A_limbs The number of limbs of \p A.
* \param b X scalar to multiply with.
*
* \return The carry at the end of the operation.
*/
mbedtls_mpi_uint mbedtls_mpi_core_mla(mbedtls_mpi_uint *X, size_t X_limbs,
const mbedtls_mpi_uint *A, size_t A_limbs,
mbedtls_mpi_uint b);
/**
* \brief Perform a known-size multiplication
*
* \p X may not be aliased to any of the inputs for this function.
* \p A may be aliased to \p B.
*
* \param[out] X The pointer to the (little-endian) array to receive
* the product of \p A_limbs and \p B_limbs.
* This must be of length \p A_limbs + \p B_limbs.
* \param[in] A The pointer to the (little-endian) array
* representing the first factor.
* \param A_limbs The number of limbs in \p A.
* \param[in] B The pointer to the (little-endian) array
* representing the second factor.
* \param B_limbs The number of limbs in \p B.
*/
void mbedtls_mpi_core_mul(mbedtls_mpi_uint *X,
const mbedtls_mpi_uint *A, size_t A_limbs,
const mbedtls_mpi_uint *B, size_t B_limbs);
/**
* \brief Calculate initialisation value for fast Montgomery modular
* multiplication
*
* \param[in] N Little-endian presentation of the modulus. This must have
* at least one limb.
*
* \return The initialisation value for fast Montgomery modular multiplication
*/
mbedtls_mpi_uint mbedtls_mpi_core_montmul_init(const mbedtls_mpi_uint *N);
/**
* \brief Montgomery multiplication: X = A * B * R^-1 mod N (HAC 14.36)
*
* \p A and \p B must be in canonical form. That is, < \p N.
*
* \p X may be aliased to \p A or \p N, or even \p B (if \p AN_limbs ==
* \p B_limbs) but may not overlap any parameters otherwise.
*
* \p A and \p B may alias each other, if \p AN_limbs == \p B_limbs. They may
* not alias \p N (since they must be in canonical form, they cannot == \p N).
*
* \param[out] X The destination MPI, as a little-endian array of
* length \p AN_limbs.
* On successful completion, X contains the result of
* the multiplication `A * B * R^-1` mod N where
* `R = 2^(biL*AN_limbs)`.
* \param[in] A Little-endian presentation of first operand.
* Must have the same number of limbs as \p N.
* \param[in] B Little-endian presentation of second operand.
* \param[in] B_limbs The number of limbs in \p B.
* Must be <= \p AN_limbs.
* \param[in] N Little-endian presentation of the modulus.
* This must be odd, and have exactly the same number
* of limbs as \p A.
* It may alias \p X, but must not alias or otherwise
* overlap any of the other parameters.
* \param[in] AN_limbs The number of limbs in \p X, \p A and \p N.
* \param mm The Montgomery constant for \p N: -N^-1 mod 2^biL.
* This can be calculated by `mbedtls_mpi_core_montmul_init()`.
* \param[in,out] T Temporary storage of size at least 2*AN_limbs+1 limbs.
* Its initial content is unused and
* its final content is indeterminate.
* It must not alias or otherwise overlap any of the
* other parameters.
*/
void mbedtls_mpi_core_montmul(mbedtls_mpi_uint *X,
const mbedtls_mpi_uint *A,
const mbedtls_mpi_uint *B, size_t B_limbs,
const mbedtls_mpi_uint *N, size_t AN_limbs,
mbedtls_mpi_uint mm, mbedtls_mpi_uint *T);
/**
* \brief Calculate the square of the Montgomery constant. (Needed
* for conversion and operations in Montgomery form.)
*
* \param[out] X A pointer to the result of the calculation of
* the square of the Montgomery constant:
* 2^{2*n*biL} mod N.
* \param[in] N Little-endian presentation of the modulus, which must be odd.
*
* \return 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if there is not enough space
* to store the value of Montgomery constant squared.
* \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p N modulus is zero.
* \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p N modulus is negative.
*/
int mbedtls_mpi_core_get_mont_r2_unsafe(mbedtls_mpi *X,
const mbedtls_mpi *N);
#if defined(MBEDTLS_TEST_HOOKS)
/**
* Copy an MPI from a table without leaking the index.
*
* \param dest The destination buffer. This must point to a writable
* buffer of at least \p limbs limbs.
* \param table The address of the table. This must point to a readable
* array of \p count elements of \p limbs limbs each.
* \param limbs The number of limbs in each table entry.
* \param count The number of entries in \p table.
* \param index The (secret) table index to look up. This must be in the
* range `0 .. count-1`.
*/
void mbedtls_mpi_core_ct_uint_table_lookup(mbedtls_mpi_uint *dest,
const mbedtls_mpi_uint *table,
size_t limbs,
size_t count,
size_t index);
#endif /* MBEDTLS_TEST_HOOKS */
/**
* \brief Fill an integer with a number of random bytes.
*
* \param X The destination MPI.
* \param X_limbs The number of limbs of \p X.
* \param bytes The number of random bytes to generate.
* \param f_rng The RNG function to use. This must not be \c NULL.
* \param p_rng The RNG parameter to be passed to \p f_rng. This may be
* \c NULL if \p f_rng doesn't need a context argument.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \p X does not have
* enough room for \p bytes bytes.
* \return A negative error code on RNG failure.
*
* \note The bytes obtained from the RNG are interpreted
* as a big-endian representation of an MPI; this can
* be relevant in applications like deterministic ECDSA.
*/
int mbedtls_mpi_core_fill_random(mbedtls_mpi_uint *X, size_t X_limbs,
size_t bytes,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng);
/** Generate a random number uniformly in a range.
*
* This function generates a random number between \p min inclusive and
* \p N exclusive.
*
* The procedure complies with RFC 6979 §3.3 (deterministic ECDSA)
* when the RNG is a suitably parametrized instance of HMAC_DRBG
* and \p min is \c 1.
*
* \note There are `N - min` possible outputs. The lower bound
* \p min can be reached, but the upper bound \p N cannot.
*
* \param X The destination MPI, with \p limbs limbs.
* It must not be aliased with \p N or otherwise overlap it.
* \param min The minimum value to return.
* \param N The upper bound of the range, exclusive, with \p limbs limbs.
* In other words, this is one plus the maximum value to return.
* \p N must be strictly larger than \p min.
* \param limbs The number of limbs of \p N and \p X.
* This must not be 0.
* \param f_rng The RNG function to use. This must not be \c NULL.
* \param p_rng The RNG parameter to be passed to \p f_rng.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if the implementation was
* unable to find a suitable value within a limited number
* of attempts. This has a negligible probability if \p N
* is significantly larger than \p min, which is the case
* for all usual cryptographic applications.
*/
int mbedtls_mpi_core_random(mbedtls_mpi_uint *X,
mbedtls_mpi_uint min,
const mbedtls_mpi_uint *N,
size_t limbs,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng);
/**
* \brief Returns the number of limbs of working memory required for
* a call to `mbedtls_mpi_core_exp_mod()`.
*
* \note This will always be at least
* `mbedtls_mpi_core_montmul_working_limbs(AN_limbs)`,
* i.e. sufficient for a call to `mbedtls_mpi_core_montmul()`.
*
* \param AN_limbs The number of limbs in the input `A` and the modulus `N`
* (they must be the same size) that will be given to
* `mbedtls_mpi_core_exp_mod()`.
* \param E_limbs The number of limbs in the exponent `E` that will be given
* to `mbedtls_mpi_core_exp_mod()`.
*
* \return The number of limbs of working memory required by
* `mbedtls_mpi_core_exp_mod()`.
*/
size_t mbedtls_mpi_core_exp_mod_working_limbs(size_t AN_limbs, size_t E_limbs);
/**
* \brief Perform a modular exponentiation with secret exponent:
* X = A^E mod N, where \p A is already in Montgomery form.
*
* \p X may be aliased to \p A, but not to \p RR or \p E, even if \p E_limbs ==
* \p AN_limbs.
*
* \param[out] X The destination MPI, as a little endian array of length
* \p AN_limbs.
* \param[in] A The base MPI, as a little endian array of length \p AN_limbs.
* Must be in Montgomery form.
* \param[in] N The modulus, as a little endian array of length \p AN_limbs.
* \param AN_limbs The number of limbs in \p X, \p A, \p N, \p RR.
* \param[in] E The exponent, as a little endian array of length \p E_limbs.
* \param E_limbs The number of limbs in \p E.
* \param[in] RR The precomputed residue of 2^{2*biL} modulo N, as a little
* endian array of length \p AN_limbs.
* \param[in,out] T Temporary storage of at least the number of limbs returned
* by `mbedtls_mpi_core_exp_mod_working_limbs()`.
* Its initial content is unused and its final content is
* indeterminate.
* It must not alias or otherwise overlap any of the other
* parameters.
* It is up to the caller to zeroize \p T when it is no
* longer needed, and before freeing it if it was dynamically
* allocated.
*/
void mbedtls_mpi_core_exp_mod(mbedtls_mpi_uint *X,
const mbedtls_mpi_uint *A,
const mbedtls_mpi_uint *N, size_t AN_limbs,
const mbedtls_mpi_uint *E, size_t E_limbs,
const mbedtls_mpi_uint *RR,
mbedtls_mpi_uint *T);
/**
* \brief Subtract unsigned integer from known-size large unsigned integers.
* Return the borrow.
*
* \param[out] X The result of the subtraction.
* \param[in] A The left operand.
* \param b The unsigned scalar to subtract.
* \param limbs Number of limbs of \p X and \p A.
*
* \return 1 if `A < b`.
* 0 if `A >= b`.
*/
mbedtls_mpi_uint mbedtls_mpi_core_sub_int(mbedtls_mpi_uint *X,
const mbedtls_mpi_uint *A,
mbedtls_mpi_uint b,
size_t limbs);
/**
* \brief Determine if a given MPI has the value \c 0 in constant time with
* respect to the value (but not with respect to the number of limbs).
*
* \param[in] A The MPI to test.
* \param limbs Number of limbs in \p A.
*
* \return 0 if `A == 0`
* non-0 (may be any value) if `A != 0`.
*/
mbedtls_mpi_uint mbedtls_mpi_core_check_zero_ct(const mbedtls_mpi_uint *A,
size_t limbs);
/**
* \brief Returns the number of limbs of working memory required for
* a call to `mbedtls_mpi_core_montmul()`.
*
* \param AN_limbs The number of limbs in the input `A` and the modulus `N`
* (they must be the same size) that will be given to
* `mbedtls_mpi_core_montmul()` or one of the other functions
* that specifies this as the amount of working memory needed.
*
* \return The number of limbs of working memory required by
* `mbedtls_mpi_core_montmul()` (or other similar function).
*/
static inline size_t mbedtls_mpi_core_montmul_working_limbs(size_t AN_limbs)
{
return 2 * AN_limbs + 1;
}
/** Convert an MPI into Montgomery form.
*
* \p X may be aliased to \p A, but may not otherwise overlap it.
*
* \p X may not alias \p N (it is in canonical form, so must be strictly less
* than \p N). Nor may it alias or overlap \p rr (this is unlikely to be
* required in practice.)
*
* This function is a thin wrapper around `mbedtls_mpi_core_montmul()` that is
* an alternative to calling `mbedtls_mpi_mod_raw_to_mont_rep()` when we
* don't want to allocate memory.
*
* \param[out] X The result of the conversion.
* Must have the same number of limbs as \p A.
* \param[in] A The MPI to convert into Montgomery form.
* Must have the same number of limbs as the modulus.
* \param[in] N The address of the modulus, which gives the size of
* the base `R` = 2^(biL*N->limbs).
* \param[in] AN_limbs The number of limbs in \p X, \p A, \p N and \p rr.
* \param mm The Montgomery constant for \p N: -N^-1 mod 2^biL.
* This can be determined by calling
* `mbedtls_mpi_core_montmul_init()`.
* \param[in] rr The residue for `2^{2*n*biL} mod N`.
* \param[in,out] T Temporary storage of size at least
* `mbedtls_mpi_core_montmul_working_limbs(AN_limbs)`
* limbs.
* Its initial content is unused and
* its final content is indeterminate.
* It must not alias or otherwise overlap any of the
* other parameters.
*/
void mbedtls_mpi_core_to_mont_rep(mbedtls_mpi_uint *X,
const mbedtls_mpi_uint *A,
const mbedtls_mpi_uint *N,
size_t AN_limbs,
mbedtls_mpi_uint mm,
const mbedtls_mpi_uint *rr,
mbedtls_mpi_uint *T);
/** Convert an MPI from Montgomery form.
*
* \p X may be aliased to \p A, but may not otherwise overlap it.
*
* \p X may not alias \p N (it is in canonical form, so must be strictly less
* than \p N).
*
* This function is a thin wrapper around `mbedtls_mpi_core_montmul()` that is
* an alternative to calling `mbedtls_mpi_mod_raw_from_mont_rep()` when we
* don't want to allocate memory.
*
* \param[out] X The result of the conversion.
* Must have the same number of limbs as \p A.
* \param[in] A The MPI to convert from Montgomery form.
* Must have the same number of limbs as the modulus.
* \param[in] N The address of the modulus, which gives the size of
* the base `R` = 2^(biL*N->limbs).
* \param[in] AN_limbs The number of limbs in \p X, \p A and \p N.
* \param mm The Montgomery constant for \p N: -N^-1 mod 2^biL.
* This can be determined by calling
* `mbedtls_mpi_core_montmul_init()`.
* \param[in,out] T Temporary storage of size at least
* `mbedtls_mpi_core_montmul_working_limbs(AN_limbs)`
* limbs.
* Its initial content is unused and
* its final content is indeterminate.
* It must not alias or otherwise overlap any of the
* other parameters.
*/
void mbedtls_mpi_core_from_mont_rep(mbedtls_mpi_uint *X,
const mbedtls_mpi_uint *A,
const mbedtls_mpi_uint *N,
size_t AN_limbs,
mbedtls_mpi_uint mm,
mbedtls_mpi_uint *T);
#endif /* MBEDTLS_BIGNUM_CORE_H */
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