| /** |
| * 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 |
| * |
| * Licensed under the Apache License, Version 2.0 (the "License"); you may |
| * not use this file except in compliance with the License. |
| * You may obtain a copy of the License at |
| * |
| * http://www.apache.org/licenses/LICENSE-2.0 |
| * |
| * Unless required by applicable law or agreed to in writing, software |
| * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT |
| * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| * See the License for the specific language governing permissions and |
| * limitations under the License. |
| */ |
| |
| #ifndef MBEDTLS_BIGNUM_CORE_H |
| #define MBEDTLS_BIGNUM_CORE_H |
| |
| #include "common.h" |
| |
| #if defined(MBEDTLS_BIGNUM_C) |
| #include "mbedtls/bignum.h" |
| #endif |
| |
| #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. |
| * |
| * \param a Integer to count leading zero bits. |
| * |
| * \return The number of leading zero bits in \p a. |
| */ |
| 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 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. Must be either 0 or 1: |
| * * \c 1: Perform the assignment `X = A`. |
| * * \c 0: Keep the original value of \p X. |
| * |
| * \note This function avoids leaking any information about whether |
| * the assignment was done or not. |
| * |
| * \warning If \p assign is neither 0 nor 1, the result of this function |
| * is indeterminate, and the resulting value in \p X might be |
| * neither its original value nor the value in \p A. |
| */ |
| void mbedtls_mpi_core_cond_assign( mbedtls_mpi_uint *X, |
| const mbedtls_mpi_uint *A, |
| size_t limbs, |
| unsigned char 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. Must be either 0 or 1: |
| * * \c 1: Swap the values of \p X and \p Y. |
| * * \c 0: Keep the original values of \p X and \p Y. |
| * |
| * \note This function avoids leaking any information about whether |
| * the swap was done or not. |
| * |
| * \warning If \p swap is neither 0 nor 1, the result of this function |
| * is indeterminate, and both \p X and \p Y might end up with |
| * values different to either of the original ones. |
| */ |
| void mbedtls_mpi_core_cond_swap( mbedtls_mpi_uint *X, |
| mbedtls_mpi_uint *Y, |
| size_t limbs, |
| unsigned char 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 \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 right in place 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 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 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 ); |
| |
| #endif /* MBEDTLS_BIGNUM_CORE_H */ |