531 lines
16 KiB
C
531 lines
16 KiB
C
/**
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* \brief Multi-precision integer library, ESP32 hardware accelerated parts
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*
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* based on mbedTLS implementation
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*
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* Copyright (C) 2006-2015, ARM Limited, All Rights Reserved
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* Additions Copyright (C) 2016, Espressif Systems (Shanghai) PTE Ltd
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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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*/
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#include <stdio.h>
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#include <string.h>
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#include <malloc.h>
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#include <limits.h>
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#include <assert.h>
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#include <stdlib.h>
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#include <sys/param.h>
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#include "soc/hwcrypto_periph.h"
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#include "esp_system.h"
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#include "esp_log.h"
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#include "esp_attr.h"
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#include "bignum_impl.h"
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#include <mbedtls/bignum.h>
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/* Some implementation notes:
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*
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* - Naming convention x_words, y_words, z_words for number of words (limbs) used in a particular
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* bignum. This number may be less than the size of the bignum
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*
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* - Naming convention hw_words for the hardware length of the operation. This number maybe be rounded up
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* for targets that requres this (e.g. ESP32), and may be larger than any of the numbers
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* involved in the calculation.
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*
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* - Timing behaviour of these functions will depend on the length of the inputs. This is fundamentally
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* the same constraint as the software mbedTLS implementations, and relies on the same
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* countermeasures (exponent blinding, etc) which are used in mbedTLS.
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*/
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static const __attribute__((unused)) char *TAG = "bignum";
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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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/* Convert bit count to word count
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*/
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static inline size_t bits_to_words(size_t bits)
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{
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return (bits + 31) / 32;
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}
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/* Return the number of words actually used to represent an mpi
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number.
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*/
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#if defined(MBEDTLS_MPI_EXP_MOD_ALT)
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static size_t mpi_words(const mbedtls_mpi *mpi)
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{
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for (size_t i = mpi->n; i > 0; i--) {
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if (mpi->p[i - 1] != 0) {
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return i;
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}
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}
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return 0;
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}
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#endif //MBEDTLS_MPI_EXP_MOD_ALT
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/**
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*
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* There is a need for the value of integer N' such that B^-1(B-1)-N^-1N'=1,
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* where B^-1(B-1) mod N=1. Actually, only the least significant part of
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* N' is needed, hence the definition N0'=N' mod b. We reproduce below the
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* simple algorithm from an article by Dusse and Kaliski to efficiently
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* find N0' from N0 and b
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*/
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static mbedtls_mpi_uint modular_inverse(const mbedtls_mpi *M)
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{
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int i;
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uint64_t t = 1;
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uint64_t two_2_i_minus_1 = 2; /* 2^(i-1) */
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uint64_t two_2_i = 4; /* 2^i */
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uint64_t N = M->p[0];
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for (i = 2; i <= 32; i++) {
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if ((mbedtls_mpi_uint) N * t % two_2_i >= two_2_i_minus_1) {
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t += two_2_i_minus_1;
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}
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two_2_i_minus_1 <<= 1;
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two_2_i <<= 1;
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}
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return (mbedtls_mpi_uint)(UINT32_MAX - t + 1);
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}
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/* Calculate Rinv = RR^2 mod M, where:
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*
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* R = b^n where b = 2^32, n=num_words,
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* R = 2^N (where N=num_bits)
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* RR = R^2 = 2^(2*N) (where N=num_bits=num_words*32)
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*
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* This calculation is computationally expensive (mbedtls_mpi_mod_mpi)
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* so caller should cache the result where possible.
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*
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* DO NOT call this function while holding esp_mpi_enable_hardware_hw_op().
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*
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*/
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static int calculate_rinv(mbedtls_mpi *Rinv, const mbedtls_mpi *M, int num_words)
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{
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int ret;
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size_t num_bits = num_words * 32;
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mbedtls_mpi RR;
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mbedtls_mpi_init(&RR);
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MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(&RR, num_bits * 2, 1));
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MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(Rinv, &RR, M));
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cleanup:
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mbedtls_mpi_free(&RR);
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return ret;
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}
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/* Z = (X * Y) mod M
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Not an mbedTLS function
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*/
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int esp_mpi_mul_mpi_mod(mbedtls_mpi *Z, const mbedtls_mpi *X, const mbedtls_mpi *Y, const mbedtls_mpi *M)
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{
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int ret = 0;
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size_t x_bits = mbedtls_mpi_bitlen(X);
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size_t y_bits = mbedtls_mpi_bitlen(Y);
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size_t m_bits = mbedtls_mpi_bitlen(M);
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size_t z_bits = MIN(m_bits, x_bits + y_bits);
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size_t x_words = bits_to_words(x_bits);
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size_t y_words = bits_to_words(y_bits);
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size_t m_words = bits_to_words(m_bits);
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size_t z_words = bits_to_words(z_bits);
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size_t hw_words = esp_mpi_hardware_words(MAX(x_words, MAX(y_words, m_words))); /* longest operand */
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mbedtls_mpi Rinv;
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mbedtls_mpi_uint Mprime;
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/* Calculate and load the first stage montgomery multiplication */
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mbedtls_mpi_init(&Rinv);
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MBEDTLS_MPI_CHK(calculate_rinv(&Rinv, M, hw_words));
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Mprime = modular_inverse(M);
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esp_mpi_enable_hardware_hw_op();
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/* Load and start a (X * Y) mod M calculation */
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esp_mpi_mul_mpi_mod_hw_op(X, Y, M, &Rinv, Mprime, hw_words);
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MBEDTLS_MPI_CHK(mbedtls_mpi_grow(Z, z_words));
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esp_mpi_read_result_hw_op(Z, z_words);
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Z->s = X->s * Y->s;
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cleanup:
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mbedtls_mpi_free(&Rinv);
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esp_mpi_disable_hardware_hw_op();
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return ret;
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}
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#if defined(MBEDTLS_MPI_EXP_MOD_ALT)
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#ifdef ESP_MPI_USE_MONT_EXP
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/*
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* Return the most significant one-bit.
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*/
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static size_t mbedtls_mpi_msb( const mbedtls_mpi *X )
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{
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int i, j;
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if (X != NULL && X->n != 0) {
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for (i = X->n - 1; i >= 0; i--) {
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if (X->p[i] != 0) {
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for (j = biL - 1; j >= 0; j--) {
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if ((X->p[i] & (1 << j)) != 0) {
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return (i * biL) + j;
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}
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}
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}
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}
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}
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return 0;
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}
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/*
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* Montgomery exponentiation: Z = X ^ Y mod M (HAC 14.94)
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*/
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static int mpi_montgomery_exp_calc( mbedtls_mpi *Z, const mbedtls_mpi *X, const mbedtls_mpi *Y, const mbedtls_mpi *M,
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mbedtls_mpi *Rinv,
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size_t hw_words,
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mbedtls_mpi_uint Mprime )
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{
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int ret = 0;
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mbedtls_mpi X_, one;
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mbedtls_mpi_init(&X_);
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mbedtls_mpi_init(&one);
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if ( ( ( ret = mbedtls_mpi_grow(&one, hw_words) ) != 0 ) ||
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( ( ret = mbedtls_mpi_set_bit(&one, 0, 1) ) != 0 ) ) {
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goto cleanup2;
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}
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// Algorithm from HAC 14.94
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{
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// 0 determine t (highest bit set in y)
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int t = mbedtls_mpi_msb(Y);
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esp_mpi_enable_hardware_hw_op();
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// 1.1 x_ = mont(x, R^2 mod m)
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// = mont(x, rb)
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MBEDTLS_MPI_CHK( esp_mont_hw_op(&X_, X, Rinv, M, Mprime, hw_words, false) );
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// 1.2 z = R mod m
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// now z = R mod m = Mont (R^2 mod m, 1) mod M (as Mont(x) = X&R^-1 mod M)
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MBEDTLS_MPI_CHK( esp_mont_hw_op(Z, Rinv, &one, M, Mprime, hw_words, true) );
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// 2 for i from t down to 0
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for (int i = t; i >= 0; i--) {
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// 2.1 z = mont(z,z)
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if (i != t) { // skip on the first iteration as is still unity
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MBEDTLS_MPI_CHK( esp_mont_hw_op(Z, Z, Z, M, Mprime, hw_words, true) );
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}
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// 2.2 if y[i] = 1 then z = mont(A, x_)
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if (mbedtls_mpi_get_bit(Y, i)) {
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MBEDTLS_MPI_CHK( esp_mont_hw_op(Z, Z, &X_, M, Mprime, hw_words, true) );
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}
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}
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// 3 z = Mont(z, 1)
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MBEDTLS_MPI_CHK( esp_mont_hw_op(Z, Z, &one, M, Mprime, hw_words, true) );
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}
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cleanup:
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esp_mpi_disable_hardware_hw_op();
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cleanup2:
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mbedtls_mpi_free(&X_);
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mbedtls_mpi_free(&one);
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return ret;
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}
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#endif //USE_MONT_EXPONENATIATION
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/*
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* Z = X ^ Y mod M
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*
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* _Rinv is optional pre-calculated version of Rinv (via calculate_rinv()).
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*
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* (See RSA Accelerator section in Technical Reference for more about Mprime, Rinv)
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*
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*/
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int mbedtls_mpi_exp_mod( mbedtls_mpi *Z, const mbedtls_mpi *X, const mbedtls_mpi *Y, const mbedtls_mpi *M, mbedtls_mpi *_Rinv )
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{
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int ret = 0;
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size_t x_words = mpi_words(X);
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size_t y_words = mpi_words(Y);
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size_t m_words = mpi_words(M);
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/* "all numbers must be the same length", so choose longest number
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as cardinal length of operation...
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*/
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size_t num_words = esp_mpi_hardware_words(MAX(m_words, MAX(x_words, y_words)));
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mbedtls_mpi Rinv_new; /* used if _Rinv == NULL */
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mbedtls_mpi *Rinv; /* points to _Rinv (if not NULL) othwerwise &RR_new */
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mbedtls_mpi_uint Mprime;
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if (mbedtls_mpi_cmp_int(M, 0) <= 0 || (M->p[0] & 1) == 0) {
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return MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
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}
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if (mbedtls_mpi_cmp_int(Y, 0) < 0) {
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return MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
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}
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if (mbedtls_mpi_cmp_int(Y, 0) == 0) {
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return mbedtls_mpi_lset(Z, 1);
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}
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if (num_words * 32 > 4096) {
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return MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
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}
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/* Determine RR pointer, either _RR for cached value
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or local RR_new */
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if (_Rinv == NULL) {
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mbedtls_mpi_init(&Rinv_new);
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Rinv = &Rinv_new;
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} else {
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Rinv = _Rinv;
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}
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if (Rinv->p == NULL) {
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MBEDTLS_MPI_CHK(calculate_rinv(Rinv, M, num_words));
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}
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Mprime = modular_inverse(M);
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// Montgomery exponentiation: Z = X ^ Y mod M (HAC 14.94)
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#ifdef ESP_MPI_USE_MONT_EXP
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ret = mpi_montgomery_exp_calc(Z, X, Y, M, Rinv, num_words, Mprime) ;
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MBEDTLS_MPI_CHK(ret);
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#else
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esp_mpi_enable_hardware_hw_op();
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esp_mpi_exp_mpi_mod_hw_op(X, Y, M, Rinv, Mprime, num_words);
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ret = mbedtls_mpi_grow(Z, m_words);
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if (ret != 0) {
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esp_mpi_disable_hardware_hw_op();
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goto cleanup;
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}
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esp_mpi_read_result_hw_op(Z, m_words);
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esp_mpi_disable_hardware_hw_op();
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#endif
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// Compensate for negative X
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if (X->s == -1 && (Y->p[0] & 1) != 0) {
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Z->s = -1;
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MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(Z, M, Z));
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} else {
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Z->s = 1;
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}
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cleanup:
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if (_Rinv == NULL) {
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mbedtls_mpi_free(&Rinv_new);
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}
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return ret;
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}
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#endif /* MBEDTLS_MPI_EXP_MOD_ALT */
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#if defined(MBEDTLS_MPI_MUL_MPI_ALT) /* MBEDTLS_MPI_MUL_MPI_ALT */
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static int mpi_mult_mpi_failover_mod_mult( mbedtls_mpi *Z, const mbedtls_mpi *X, const mbedtls_mpi *Y, size_t z_words);
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static int mpi_mult_mpi_overlong(mbedtls_mpi *Z, const mbedtls_mpi *X, const mbedtls_mpi *Y, size_t y_words, size_t z_words);
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/* Z = X * Y */
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int mbedtls_mpi_mul_mpi( mbedtls_mpi *Z, const mbedtls_mpi *X, const mbedtls_mpi *Y )
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{
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int ret = 0;
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size_t x_bits = mbedtls_mpi_bitlen(X);
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size_t y_bits = mbedtls_mpi_bitlen(Y);
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size_t x_words = bits_to_words(x_bits);
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size_t y_words = bits_to_words(y_bits);
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size_t z_words = bits_to_words(x_bits + y_bits);
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size_t hw_words = esp_mpi_hardware_words(MAX(x_words, y_words)); // length of one operand in hardware
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/* Short-circuit eval if either argument is 0 or 1.
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This is needed as the mpi modular division
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argument will sometimes call in here when one
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argument is too large for the hardware unit, but the other
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argument is zero or one.
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*/
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if (x_bits == 0 || y_bits == 0) {
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mbedtls_mpi_lset(Z, 0);
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return 0;
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}
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if (x_bits == 1) {
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ret = mbedtls_mpi_copy(Z, Y);
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Z->s *= X->s;
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return ret;
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}
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if (y_bits == 1) {
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ret = mbedtls_mpi_copy(Z, X);
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Z->s *= Y->s;
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return ret;
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}
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/* Grow Z to result size early, avoid interim allocations */
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MBEDTLS_MPI_CHK( mbedtls_mpi_grow(Z, z_words) );
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/* If either factor is over 2048 bits, we can't use the standard hardware multiplier
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(it assumes result is double longest factor, and result is max 4096 bits.)
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However, we can fail over to mod_mult for up to 4096 bits of result (modulo
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multiplication doesn't have the same restriction, so result is simply the
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number of bits in X plus number of bits in in Y.)
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*/
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if (hw_words * 32 > 2048) {
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if (z_words * 32 <= 4096) {
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/* Note: it's possible to use mpi_mult_mpi_overlong
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for this case as well, but it's very slightly
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slower and requires a memory allocation.
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*/
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return mpi_mult_mpi_failover_mod_mult(Z, X, Y, z_words);
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} else {
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/* Still too long for the hardware unit... */
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if (y_words > x_words) {
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return mpi_mult_mpi_overlong(Z, X, Y, y_words, z_words);
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} else {
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return mpi_mult_mpi_overlong(Z, Y, X, x_words, z_words);
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}
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}
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}
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/* Otherwise, we can use the (faster) multiply hardware unit */
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esp_mpi_enable_hardware_hw_op();
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esp_mpi_mul_mpi_hw_op(X, Y, hw_words);
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esp_mpi_read_result_hw_op(Z, z_words);
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esp_mpi_disable_hardware_hw_op();
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Z->s = X->s * Y->s;
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cleanup:
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return ret;
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}
|
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|
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/* Deal with the case when X & Y are too long for the hardware unit, by splitting one operand
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into two halves.
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Y must be the longer operand
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Slice Y into Yp, Ypp such that:
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Yp = lower 'b' bits of Y
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Ypp = upper 'b' bits of Y (right shifted)
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Such that
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Z = X * Y
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Z = X * (Yp + Ypp<<b)
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Z = (X * Yp) + (X * Ypp<<b)
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Note that this function may recurse multiple times, if both X & Y
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are too long for the hardware multiplication unit.
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*/
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static int mpi_mult_mpi_overlong(mbedtls_mpi *Z, const mbedtls_mpi *X, const mbedtls_mpi *Y, size_t y_words, size_t z_words)
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{
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int ret = 0;
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mbedtls_mpi Ztemp;
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/* Rather than slicing in two on bits we slice on limbs (32 bit words) */
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const size_t words_slice = y_words / 2;
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/* Yp holds lower bits of Y (declared to reuse Y's array contents to save on copying) */
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const mbedtls_mpi Yp = {
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.p = Y->p,
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.n = words_slice,
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.s = Y->s
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};
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/* Ypp holds upper bits of Y, right shifted (also reuses Y's array contents) */
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const mbedtls_mpi Ypp = {
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.p = Y->p + words_slice,
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.n = y_words - words_slice,
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.s = Y->s
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};
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mbedtls_mpi_init(&Ztemp);
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/* Get result Ztemp = Yp * X (need temporary variable Ztemp) */
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MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi(&Ztemp, X, &Yp) );
|
|
|
|
/* Z = Ypp * Y */
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|
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi(Z, X, &Ypp) );
|
|
|
|
/* Z = Z << b */
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|
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l(Z, words_slice * 32) );
|
|
|
|
/* Z += Ztemp */
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi(Z, Z, &Ztemp) );
|
|
|
|
cleanup:
|
|
mbedtls_mpi_free(&Ztemp);
|
|
|
|
return ret;
|
|
}
|
|
|
|
/* Special-case of mbedtls_mpi_mult_mpi(), where we use hardware montgomery mod
|
|
multiplication to calculate an mbedtls_mpi_mult_mpi result where either
|
|
A or B are >2048 bits so can't use the standard multiplication method.
|
|
|
|
Result (number of words, based on A bits + B bits) must still be less than 4096 bits.
|
|
|
|
This case is simpler than the general case modulo multiply of
|
|
esp_mpi_mul_mpi_mod() because we can control the other arguments:
|
|
|
|
* Modulus is chosen with M=(2^num_bits - 1) (ie M=R-1), so output
|
|
* Mprime and Rinv are therefore predictable as follows:
|
|
isn't actually modulo anything.
|
|
Mprime 1
|
|
Rinv 1
|
|
|
|
(See RSA Accelerator section in Technical Reference for more about Mprime, Rinv)
|
|
*/
|
|
|
|
static int mpi_mult_mpi_failover_mod_mult( mbedtls_mpi *Z, const mbedtls_mpi *X, const mbedtls_mpi *Y, size_t z_words)
|
|
{
|
|
int ret;
|
|
size_t hw_words = esp_mpi_hardware_words(z_words);
|
|
|
|
esp_mpi_enable_hardware_hw_op();
|
|
|
|
esp_mpi_mult_mpi_failover_mod_mult_hw_op(X, Y, hw_words );
|
|
MBEDTLS_MPI_CHK( mbedtls_mpi_grow(Z, hw_words) );
|
|
esp_mpi_read_result_hw_op(Z, hw_words);
|
|
|
|
Z->s = X->s * Y->s;
|
|
cleanup:
|
|
esp_mpi_disable_hardware_hw_op();
|
|
return ret;
|
|
}
|
|
|
|
#endif /* MBEDTLS_MPI_MUL_MPI_ALT */
|
|
|