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Merge pull request #975 from yanesca/issue-946

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Fix RSA side channel
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Manuel Pégourié-Gonnard 2022-11-23 10:30:35 +01:00 committed by GitHub
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2 changed files with 112 additions and 36 deletions
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10
ChangeLog.d/rsa-fix-priviliged-side-channel.txt Normal file
View file

@ -0,0 +1,10 @@
Security
* An adversary with access to precise enough information about memory
accesses (typically, an untrusted operating system attacking a secure
enclave) could recover an RSA private key after observing the victim
performing a single private-key operation if the window size used for the
exponentiation was 3 or smaller. Found and reported by Zili KOU,
Wenjian HE, Sharad Sinha, and Wei ZHANG. See "Cache Side-channel Attacks
and Defenses of the Sliding Window Algorithm in TEEs" - Design, Automation
and Test in Europe 2023.

138
library/bignum.c
View file

@ -1588,11 +1588,11 @@ int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A,
mbedtls_mpi *prec_RR ) mbedtls_mpi *prec_RR )
{ {
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
size_t wbits, wsize, one = 1; size_t window_bitsize;
size_t i, j, nblimbs; size_t i, j, nblimbs;
size_t bufsize, nbits; size_t bufsize, nbits;
mbedtls_mpi_uint ei, mm, state; mbedtls_mpi_uint ei, mm, state;
mbedtls_mpi RR, T, W[ 1 << MBEDTLS_MPI_WINDOW_SIZE ], WW, Apos; mbedtls_mpi RR, T, W[ (size_t) 1 << MBEDTLS_MPI_WINDOW_SIZE ], WW, Apos;
int neg; int neg;
MPI_VALIDATE_RET( X != NULL ); MPI_VALIDATE_RET( X != NULL );
@ -1621,21 +1621,59 @@ int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A,
i = mbedtls_mpi_bitlen( E ); i = mbedtls_mpi_bitlen( E );
wsize = ( i > 671 ) ? 6 : ( i > 239 ) ? 5 : window_bitsize = ( i > 671 ) ? 6 : ( i > 239 ) ? 5 :
( i > 79 ) ? 4 : ( i > 23 ) ? 3 : 1; ( i > 79 ) ? 4 : ( i > 23 ) ? 3 : 1;
#if( MBEDTLS_MPI_WINDOW_SIZE < 6 ) #if( MBEDTLS_MPI_WINDOW_SIZE < 6 )
if( wsize > MBEDTLS_MPI_WINDOW_SIZE ) if( window_bitsize > MBEDTLS_MPI_WINDOW_SIZE )
wsize = MBEDTLS_MPI_WINDOW_SIZE; window_bitsize = MBEDTLS_MPI_WINDOW_SIZE;
#endif #endif
const size_t w_table_used_size = (size_t) 1 << window_bitsize;
/*
* This function is not constant-trace: its memory accesses depend on the
* exponent value. To defend against timing attacks, callers (such as RSA
* and DHM) should use exponent blinding. However this is not enough if the
* adversary can find the exponent in a single trace, so this function
* takes extra precautions against adversaries who can observe memory
* access patterns.
*
* This function performs a series of multiplications by table elements and
* squarings, and we want the prevent the adversary from finding out which
* table element was used, and from distinguishing between multiplications
* and squarings. Firstly, when multiplying by an element of the window
* W[i], we do a constant-trace table lookup to obfuscate i. This leaves
* squarings as having a different memory access patterns from other
* multiplications. So secondly, we put the accumulator X in the table as
* well, and also do a constant-trace table lookup to multiply by X.
*
* This way, all multiplications take the form of a lookup-and-multiply.
* The number of lookup-and-multiply operations inside each iteration of
* the main loop still depends on the bits of the exponent, but since the
* other operations in the loop don't have an easily recognizable memory
* trace, an adversary is unlikely to be able to observe the exact
* patterns.
*
* An adversary may still be able to recover the exponent if they can
* observe both memory accesses and branches. However, branch prediction
* exploitation typically requires many traces of execution over the same
* data, which is defeated by randomized blinding.
*
* To achieve this, we make a copy of X and we use the table entry in each
* calculation from this point on.
*/
const size_t x_index = 0;
mbedtls_mpi_init( &W[x_index] );
mbedtls_mpi_copy( &W[x_index], X );
j = N->n + 1; j = N->n + 1;
/* All W[i] and X must have at least N->n limbs for the mpi_montmul() /* All W[i] and X must have at least N->n limbs for the mpi_montmul()
* and mpi_montred() calls later. Here we ensure that W[1] and X are * and mpi_montred() calls later. Here we ensure that W[1] and X are
* large enough, and later we'll grow other W[i] to the same length. * large enough, and later we'll grow other W[i] to the same length.
* They must not be shrunk midway through this function! * They must not be shrunk midway through this function!
*/ */
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, j ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &W[x_index], j ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &W[1], j ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &W[1], j ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &T, j * 2 ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &T, j * 2 ) );
@ -1684,28 +1722,36 @@ int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A,
mpi_montmul( &W[1], &RR, N, mm, &T ); mpi_montmul( &W[1], &RR, N, mm, &T );
/* /*
* X = R^2 * R^-1 mod N = R mod N * W[x_index] = R^2 * R^-1 mod N = R mod N
*/ */
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( X, &RR ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &W[x_index], &RR ) );
mpi_montred( X, N, mm, &T ); mpi_montred( &W[x_index], N, mm, &T );
if( wsize > 1 )
if( window_bitsize > 1 )
{ {
/* /*
* W[1 << (wsize - 1)] = W[1] ^ (wsize - 1) * W[i] = W[1] ^ i
*
* The first bit of the sliding window is always 1 and therefore we
* only need to store the second half of the table.
*
* (There are two special elements in the table: W[0] for the
* accumulator/result and W[1] for A in Montgomery form. Both of these
* are already set at this point.)
*/ */
j = one << ( wsize - 1 ); j = w_table_used_size / 2;
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &W[j], N->n + 1 ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &W[j], N->n + 1 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &W[j], &W[1] ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &W[j], &W[1] ) );
for( i = 0; i < wsize - 1; i++ ) for( i = 0; i < window_bitsize - 1; i++ )
mpi_montmul( &W[j], &W[j], N, mm, &T ); mpi_montmul( &W[j], &W[j], N, mm, &T );
/* /*
* W[i] = W[i - 1] * W[1] * W[i] = W[i - 1] * W[1]
*/ */
for( i = j + 1; i < ( one << wsize ); i++ ) for( i = j + 1; i < w_table_used_size; i++ )
{ {
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &W[i], N->n + 1 ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &W[i], N->n + 1 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &W[i], &W[i - 1] ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &W[i], &W[i - 1] ) );
@ -1717,7 +1763,7 @@ int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A,
nblimbs = E->n; nblimbs = E->n;
bufsize = 0; bufsize = 0;
nbits = 0; nbits = 0;
wbits = 0; size_t exponent_bits_in_window = 0;
state = 0; state = 0;
while( 1 ) while( 1 )
@ -1745,9 +1791,10 @@ int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A,
if( ei == 0 && state == 1 ) if( ei == 0 && state == 1 )
{ {
/* /*
* out of window, square X * out of window, square W[x_index]
*/ */
mpi_montmul( X, X, N, mm, &T ); MBEDTLS_MPI_CHK( mpi_select( &WW, W, w_table_used_size, x_index ) );
mpi_montmul( &W[x_index], &WW, N, mm, &T );
continue; continue;
} }
@ -1757,25 +1804,30 @@ int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A,
state = 2; state = 2;
nbits++; nbits++;
wbits |= ( ei << ( wsize - nbits ) ); exponent_bits_in_window |= ( ei << ( window_bitsize - nbits ) );
if( nbits == wsize ) if( nbits == window_bitsize )
{ {
/* /*
* X = X^wsize R^-1 mod N * W[x_index] = W[x_index]^window_bitsize R^-1 mod N
*/ */
for( i = 0; i < wsize; i++ ) for( i = 0; i < window_bitsize; i++ )
mpi_montmul( X, X, N, mm, &T ); {
MBEDTLS_MPI_CHK( mpi_select( &WW, W, w_table_used_size,
x_index ) );
mpi_montmul( &W[x_index], &WW, N, mm, &T );
}
/* /*
* X = X * W[wbits] R^-1 mod N * W[x_index] = W[x_index] * W[exponent_bits_in_window] R^-1 mod N
*/ */
MBEDTLS_MPI_CHK( mpi_select( &WW, W, (size_t) 1 << wsize, wbits ) ); MBEDTLS_MPI_CHK( mpi_select( &WW, W, w_table_used_size,
mpi_montmul( X, &WW, N, mm, &T ); exponent_bits_in_window ) );
mpi_montmul( &W[x_index], &WW, N, mm, &T );
state--; state--;
nbits = 0; nbits = 0;
wbits = 0; exponent_bits_in_window = 0;
} }
} }
@ -1784,31 +1836,45 @@ int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A,
*/ */
for( i = 0; i < nbits; i++ ) for( i = 0; i < nbits; i++ )
{ {
mpi_montmul( X, X, N, mm, &T ); MBEDTLS_MPI_CHK( mpi_select( &WW, W, w_table_used_size, x_index ) );
mpi_montmul( &W[x_index], &WW, N, mm, &T );
wbits <<= 1; exponent_bits_in_window <<= 1;
if( ( wbits & ( one << wsize ) ) != 0 ) if( ( exponent_bits_in_window & ( (size_t) 1 << window_bitsize ) ) != 0 )
mpi_montmul( X, &W[1], N, mm, &T ); {
MBEDTLS_MPI_CHK( mpi_select( &WW, W, w_table_used_size, 1 ) );
mpi_montmul( &W[x_index], &WW, N, mm, &T );
}
} }
/* /*
* X = A^E * R * R^-1 mod N = A^E mod N * W[x_index] = A^E * R * R^-1 mod N = A^E mod N
*/ */
mpi_montred( X, N, mm, &T ); mpi_montred( &W[x_index], N, mm, &T );
if( neg && E->n != 0 && ( E->p[0] & 1 ) != 0 ) if( neg && E->n != 0 && ( E->p[0] & 1 ) != 0 )
{ {
X->s = -1; W[x_index].s = -1;
MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( X, N, X ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &W[x_index], N, &W[x_index] ) );
} }
/*
* Load the result in the output variable.
*/
mbedtls_mpi_copy( X, &W[x_index] );
cleanup: cleanup:
for( i = ( one << ( wsize - 1 ) ); i < ( one << wsize ); i++ ) /* The first bit of the sliding window is always 1 and therefore the first
* half of the table was unused. */
for( i = w_table_used_size/2; i < w_table_used_size; i++ )
mbedtls_mpi_free( &W[i] ); mbedtls_mpi_free( &W[i] );
mbedtls_mpi_free( &W[1] ); mbedtls_mpi_free( &T ); mbedtls_mpi_free( &Apos ); mbedtls_mpi_free( &W[x_index] );
mbedtls_mpi_free( &W[1] );
mbedtls_mpi_free( &T );
mbedtls_mpi_free( &Apos );
mbedtls_mpi_free( &WW ); mbedtls_mpi_free( &WW );
if( prec_RR == NULL || prec_RR->p == NULL ) if( prec_RR == NULL || prec_RR->p == NULL )