/**
* \brief Multi-precision integer library, ESP32 hardware accelerated parts
*
* based on mbedTLS implementation
*
* Copyright (C) 2006-2015, ARM Limited, All Rights Reserved
* Additions Copyright (C) 2016, Espressif Systems (Shanghai) PTE Ltd
* 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.
*
*/
#include <stdio.h>
#include <string.h>
#include <malloc.h>
#include "mbedtls/bignum.h"
#include "mbedtls/bn_mul.h"
#include "rom/bigint.h"
#if defined(MBEDTLS_MPI_MUL_MPI_ALT) || defined(MBEDTLS_MPI_EXP_MOD_ALT)
/* Constants from mbedTLS bignum.c */
#define ciL (sizeof(mbedtls_mpi_uint)) /* chars in limb */
#define biL (ciL << 3) /* bits in limb */
static _lock_t mpi_lock;
/* At the moment these hardware locking functions aren't exposed publically
for MPI. If you want to use the ROM bigint functions and co-exist with mbedTLS,
please raise a feature request.
*/
static void esp_mpi_acquire_hardware( void )
{
/* newlib locks lazy initialize on ESP-IDF */
_lock_acquire(&mpi_lock);
ets_bigint_enable();
}
static void esp_mpi_release_hardware( void )
{
ets_bigint_disable();
_lock_release(&mpi_lock);
}
/*
* Helper for mbedtls_mpi multiplication
* copied/trimmed from mbedtls bignum.c
*/
static void mpi_mul_hlp( size_t i, mbedtls_mpi_uint *s, mbedtls_mpi_uint *d, mbedtls_mpi_uint b )
{
mbedtls_mpi_uint c = 0, t = 0;
for( ; i >= 16; i -= 16 )
{
MULADDC_INIT
MULADDC_CORE MULADDC_CORE
MULADDC_CORE MULADDC_CORE
MULADDC_CORE MULADDC_CORE
MULADDC_CORE MULADDC_CORE
MULADDC_CORE MULADDC_CORE
MULADDC_CORE MULADDC_CORE
MULADDC_CORE MULADDC_CORE
MULADDC_CORE MULADDC_CORE
MULADDC_STOP
}
for( ; i >= 8; i -= 8 )
{
MULADDC_INIT
MULADDC_CORE MULADDC_CORE
MULADDC_CORE MULADDC_CORE
MULADDC_CORE MULADDC_CORE
MULADDC_CORE MULADDC_CORE
MULADDC_STOP
}
for( ; i > 0; i-- )
{
MULADDC_INIT
MULADDC_CORE
MULADDC_STOP
}
t++;
do {
*d += c; c = ( *d < c ); d++;
}
while( c != 0 );
}
/*
* Helper for mbedtls_mpi subtraction
* Copied/adapter from mbedTLS bignum.c
*/
static void mpi_sub_hlp( size_t n, mbedtls_mpi_uint *s, mbedtls_mpi_uint *d )
{
size_t i;
mbedtls_mpi_uint c, z;
for( i = c = 0; i < n; i++, s++, d++ )
{
z = ( *d < c ); *d -= c;
c = ( *d < *s ) + z; *d -= *s;
}
while( c != 0 )
{
z = ( *d < c ); *d -= c;
c = z; i++; d++;
}
}
/* The following 3 Montgomery arithmetic function are
copied from mbedTLS bigint.c verbatim as they are static.
TODO: find a way to support making the versions in mbedtls
non-static.
*/
/*
* Fast Montgomery initialization (thanks to Tom St Denis)
*/
static void mpi_montg_init( mbedtls_mpi_uint *mm, const mbedtls_mpi *N )
{
mbedtls_mpi_uint x, m0 = N->p[0];
unsigned int i;
x = m0;
x += ( ( m0 + 2 ) & 4 ) << 1;
for( i = biL; i >= 8; i /= 2 )
x *= ( 2 - ( m0 * x ) );
*mm = ~x + 1;
}
/*
* Montgomery multiplication: A = A * B * R^-1 mod N (HAC 14.36)
*/
static int mpi_montmul( mbedtls_mpi *A, const mbedtls_mpi *B, const mbedtls_mpi *N, mbedtls_mpi_uint mm,
const mbedtls_mpi *T )
{
size_t i, n, m;
mbedtls_mpi_uint u0, u1, *d;
if( T->n < N->n + 1 || T->p == NULL )
return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
memset( T->p, 0, T->n * ciL );
d = T->p;
n = N->n;
m = ( B->n < n ) ? B->n : n;
for( i = 0; i < n; i++ )
{
/*
* T = (T + u0*B + u1*N) / 2^biL
*/
u0 = A->p[i];
u1 = ( d[0] + u0 * B->p[0] ) * mm;
mpi_mul_hlp( m, B->p, d, u0 );
mpi_mul_hlp( n, N->p, d, u1 );
*d++ = u0; d[n + 1] = 0;
}
memcpy( A->p, d, ( n + 1 ) * ciL );
if( mbedtls_mpi_cmp_abs( A, N ) >= 0 )
mpi_sub_hlp( n, N->p, A->p );
else
/* prevent timing attacks */
mpi_sub_hlp( n, A->p, T->p );
return( 0 );
}
/*
* Montgomery reduction: A = A * R^-1 mod N
*/
static int mpi_montred( mbedtls_mpi *A, const mbedtls_mpi *N, mbedtls_mpi_uint mm, const mbedtls_mpi *T )
{
mbedtls_mpi_uint z = 1;
mbedtls_mpi U;
U.n = U.s = (int) z;
U.p = &z;
return( mpi_montmul( A, &U, N, mm, T ) );
}
/* Allocate parameters used by hardware MPI multiply,
and copy mbedtls_mpi structures into them */
static int mul_pram_alloc(const mbedtls_mpi *A, const mbedtls_mpi *B, char **pA, char **pB, char **pX, size_t *bites)
{
char *sa, *sb, *sx;
// int algn;
int words, bytes;
int abytes, bbytes;
if (A->n > B->n)
words = A->n;
else
words = B->n;
bytes = (words / 16 + ((words % 16) ? 1 : 0 )) * 16 * 4 * 2;
abytes = A->n * 4;
bbytes = B->n * 4;
sa = malloc(bytes);
if (!sa) {
return -1;
}
sb = malloc(bytes);
if (!sb) {
free(sa);
return -1;
}
sx = malloc(bytes);
if (!sx) {
free(sa);
free(sb);
return -1;
}
memcpy(sa, A->p, abytes);
memset(sa + abytes, 0, bytes - abytes);
memcpy(sb, B->p, bbytes);
memset(sb + bbytes, 0, bytes - bbytes);
*pA = sa;
*pB = sb;
*pX = sx;
*bites = bytes * 4;
return 0;
}
#if defined(MBEDTLS_MPI_MUL_MPI_ALT)
int mbedtls_mpi_mul_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B )
{
int ret = -1;
size_t i, j;
char *s1 = NULL, *s2 = NULL, *dest = NULL;
size_t bites;
mbedtls_mpi TA, TB;
mbedtls_mpi_init( &TA ); mbedtls_mpi_init( &TB );
if( X == A ) { MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TA, A ) ); A = &TA; }
if( X == B ) { MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TB, B ) ); B = &TB; }
for( i = A->n; i > 0; i-- )
if( A->p[i - 1] != 0 )
break;
for( j = B->n; j > 0; j-- )
if( B->p[j - 1] != 0 )
break;
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, i + j ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) );
if (mul_pram_alloc(A, B, &s1, &s2, &dest, &bites)) {
goto cleanup;
}
esp_mpi_acquire_hardware();
if (ets_bigint_mult_prepare((uint32_t *)s1, (uint32_t *)s2, bites)){
ets_bigint_wait_finish();
if (ets_bigint_mult_getz((uint32_t *)dest, bites) == true) {
memcpy(X->p, dest, (i + j) * 4);
ret = 0;
} else {
printf("ets_bigint_mult_getz failed\n");
}
} else{
printf("Baseline multiplication failed\n");
}
esp_mpi_release_hardware();
X->s = A->s * B->s;
free(s1);
free(s2);
free(dest);
cleanup:
mbedtls_mpi_free( &TB ); mbedtls_mpi_free( &TA );
return( ret );
}
#endif /* MBEDTLS_MPI_MUL_MPI_ALT */
#if defined(MBEDTLS_MPI_EXP_MOD_ALT)
/*
* Sliding-window exponentiation: X = A^E mod N (HAC 14.85)
*/
int mbedtls_mpi_exp_mod( mbedtls_mpi* X, const mbedtls_mpi* A, const mbedtls_mpi* E, const mbedtls_mpi* N, mbedtls_mpi* _RR )
{
int ret;
size_t wbits, wsize, one = 1;
size_t i, j, nblimbs;
size_t bufsize, nbits;
mbedtls_mpi_uint ei, mm, state;
mbedtls_mpi RR, T, W[ 2 << MBEDTLS_MPI_WINDOW_SIZE ], Apos;
int neg;
if( mbedtls_mpi_cmp_int( N, 0 ) < 0 || ( N->p[0] & 1 ) == 0 )
return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
if( mbedtls_mpi_cmp_int( E, 0 ) < 0 )
return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
/*
* Init temps and window size
*/
mpi_montg_init( &mm, N );
mbedtls_mpi_init( &RR ); mbedtls_mpi_init( &T );
mbedtls_mpi_init( &Apos );
memset( W, 0, sizeof( W ) );
i = mbedtls_mpi_bitlen( E );
wsize = ( i > 671 ) ? 6 : ( i > 239 ) ? 5 :
( i > 79 ) ? 4 : ( i > 23 ) ? 3 : 1;
if( wsize > MBEDTLS_MPI_WINDOW_SIZE )
wsize = MBEDTLS_MPI_WINDOW_SIZE;
j = N->n + 1;
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, j ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &W[1], j ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &T, j * 2 ) );
/*
* Compensate for negative A (and correct at the end)
*/
neg = ( A->s == -1 );
if( neg )
{
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &Apos, A ) );
Apos.s = 1;
A = &Apos;
}
/*
* If 1st call, pre-compute R^2 mod N
*/
if( _RR == NULL || _RR->p == NULL )
{
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &RR, 1 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &RR, N->n * 2 * biL ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &RR, &RR, N ) );
if( _RR != NULL )
memcpy( _RR, &RR, sizeof( mbedtls_mpi) );
}
else
memcpy( &RR, _RR, sizeof( mbedtls_mpi) );
/*
* W[1] = A * R^2 * R^-1 mod N = A * R mod N
*/
if( mbedtls_mpi_cmp_mpi( A, N ) >= 0 )
MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &W[1], A, N ) );
else
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &W[1], A ) );
mpi_montmul( &W[1], &RR, N, mm, &T );
/*
* X = R^2 * R^-1 mod N = R mod N
*/
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( X, &RR ) );
mpi_montred( X, N, mm, &T );
if( wsize > 1 )
{
/*
* W[1 << (wsize - 1)] = W[1] ^ (wsize - 1)
*/
j = one << ( wsize - 1 );
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &W[j], N->n + 1 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &W[j], &W[1] ) );
for( i = 0; i < wsize - 1; i++ )
mpi_montmul( &W[j], &W[j], N, mm, &T );
/*
* W[i] = W[i - 1] * W[1]
*/
for( i = j + 1; i < ( one << wsize ); i++ )
{
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &W[i], N->n + 1 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &W[i], &W[i - 1] ) );
mpi_montmul( &W[i], &W[1], N, mm, &T );
}
}
nblimbs = E->n;
bufsize = 0;
nbits = 0;
wbits = 0;
state = 0;
while( 1 )
{
if( bufsize == 0 )
{
if( nblimbs == 0 )
break;
nblimbs--;
bufsize = sizeof( mbedtls_mpi_uint ) << 3;
}
bufsize--;
ei = (E->p[nblimbs] >> bufsize) & 1;
/*
* skip leading 0s
*/
if( ei == 0 && state == 0 )
continue;
if( ei == 0 && state == 1 )
{
/*
* out of window, square X
*/
mpi_montmul( X, X, N, mm, &T );
continue;
}
/*
* add ei to current window
*/
state = 2;
nbits++;
wbits |= ( ei << ( wsize - nbits ) );
if( nbits == wsize )
{
/*
* X = X^wsize R^-1 mod N
*/
for( i = 0; i < wsize; i++ )
mpi_montmul( X, X, N, mm, &T );
/*
* X = X * W[wbits] R^-1 mod N
*/
mpi_montmul( X, &W[wbits], N, mm, &T );
state--;
nbits = 0;
wbits = 0;
}
}
/*
* process the remaining bits
*/
for( i = 0; i < nbits; i++ )
{
mpi_montmul( X, X, N, mm, &T );
wbits <<= 1;
if( ( wbits & ( one << wsize ) ) != 0 )
mpi_montmul( X, &W[1], N, mm, &T );
}
/*
* X = A^E * R * R^-1 mod N = A^E mod N
*/
mpi_montred( X, N, mm, &T );
if( neg )
{
X->s = -1;
MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( X, N, X ) );
}
cleanup:
for( i = ( one << ( wsize - 1 ) ); i < ( one << wsize ); i++ )
mbedtls_mpi_free( &W[i] );
mbedtls_mpi_free( &W[1] ); mbedtls_mpi_free( &T ); mbedtls_mpi_free( &Apos );
if( _RR == NULL || _RR->p == NULL )
mbedtls_mpi_free( &RR );
return( ret );
}
#endif /* MBEDTLS_MPI_EXP_MOD_ALT */
#endif /* MBEDTLS_MPI_MUL_MPI_ALT || MBEDTLS_MPI_EXP_MOD_ALT */