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Implement randomized coordinates in ecp_mul()

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Manuel Pégourié-Gonnard 2013-09-02 16:26:04 +02:00
parent c75c56fef7
commit 07de4b1d08
1 changed files with 72 additions and 12 deletions
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84
library/ecp.c
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@ -30,6 +30,17 @@
* GECC = Guide to Elliptic Curve Cryptography - Hankerson, Menezes, Vanstone
* FIPS 186-3 http://csrc.nist.gov/publications/fips/fips186-3/fips_186-3.pdf
* RFC 4492 for the related TLS structures and constants
*
* [1] OKEYA, Katsuyuki and TAKAGI, Tsuyoshi. The width-w NAF method provides
* small memory and fast elliptic scalar multiplications secure against
* side channel attacks. In : Topics in Cryptology—CT-RSA 2003. Springer
* Berlin Heidelberg, 2003. p. 328-343.
* <http://rd.springer.com/chapter/10.1007/3-540-36563-X_23>.
*
* [2] CORON, Jean-Sébastien. Resistance against differential power analysis
* for elliptic curve cryptosystems. In : Cryptographic Hardware and
* Embedded Systems. Springer Berlin Heidelberg, 1999. p. 292-302.
* <http://link.springer.com/chapter/10.1007/3-540-48059-5_25>
*/
#include "polarssl/config.h"
@ -51,7 +62,7 @@
#if defined(POLARSSL_SELF_TEST)
/*
* Counts of point addition and doubling operations.
* Used to test resistance of point multiplication to SPA/timing attacks.
* Used to test resistance of point multiplication to simple timing attacks.
*/
unsigned long add_count, dbl_count;
#endif
@ -777,7 +788,7 @@ cleanup:
* (See for example Cohen's "A Course in Computational Algebraic Number
* Theory", Algorithm 10.3.4.)
*
* Warning: fails if one of the points is zero!
* Warning: fails (returning an error) if one of the points is zero!
* This should never happen, see choice of w in ecp_mul().
*/
static int ecp_normalize_many( const ecp_group *grp,
@ -1049,11 +1060,10 @@ cleanup:
/*
* Compute a modified width-w non-adjacent form (NAF) of a number,
* with a fixed pattern for resistance to SPA/timing attacks,
* see <http://rd.springer.com/chapter/10.1007/3-540-36563-X_23>.
* (The resulting multiplication algorithm can also been seen as a
* modification of 2^w-ary multiplication, with signed coefficients,
* all of them odd.)
* with a fixed pattern for resistance to simple timing attacks (even SPA),
* see [1]. (The resulting multiplication algorithm can also been seen as a
* modification of 2^w-ary multiplication, with signed coefficients, all of
* them odd.)
*
* Input:
* m must be an odd positive mpi less than w * k bits long
@ -1144,6 +1154,51 @@ cleanup:
return( ret );
}
/*
* Randomize jacobian coordinates:
* (X, Y, Z) -> (l^2 X, l^3 Y, l Z) for random l
* This is sort of the reverse operation of ecp_normalize().
*/
static int ecp_randomize_coordinates( const ecp_group *grp, ecp_point *pt,
int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
{
int ret;
mpi l, ll;
size_t p_size = (grp->pbits + 7) / 8;
int count = 0;
mpi_init( &l ); mpi_init( &ll );
/* Generate l such that 1 < l < p */
do
{
mpi_fill_random( &l, p_size, f_rng, p_rng );
while( mpi_cmp_mpi( &l, &grp->P ) >= 0 )
mpi_shift_r( &l, 1 );
if( count++ > 10 )
return( POLARSSL_ERR_ECP_GENERIC );
}
while( mpi_cmp_int( &l, 1 ) <= 0 );
/* Z = l * Z */
MPI_CHK( mpi_mul_mpi( &pt->Z, &pt->Z, &l ) ); MOD_MUL( pt->Z );
/* X = l^2 * X */
MPI_CHK( mpi_mul_mpi( &ll, &l, &l ) ); MOD_MUL( ll );
MPI_CHK( mpi_mul_mpi( &pt->X, &pt->X, &ll ) ); MOD_MUL( pt->X );
/* Y = l^3 * Y */
MPI_CHK( mpi_mul_mpi( &ll, &ll, &l ) ); MOD_MUL( ll );
MPI_CHK( mpi_mul_mpi( &pt->Y, &pt->Y, &ll ) ); MOD_MUL( pt->Y );
cleanup:
mpi_free( &l ); mpi_free( &ll );
return( ret );
}
/*
* Maximum length of the precomputed table
*/
@ -1159,11 +1214,15 @@ cleanup:
/*
* Integer multiplication: R = m * P
*
* Based on fixed-pattern width-w NAF, see comments of ecp_w_naf_fixed()
* and <http://rd.springer.com/chapter/10.1007/3-540-36563-X_23>.
* Based on fixed-pattern width-w NAF, see comments of ecp_w_naf_fixed().
*
* This function executes a fixed number of operations for
* random m in the range 0 .. 2^nbits - 1.
*
* As an additional countermeasure against potential elaborate timing attacks,
* we randomize coordinates after each addition. This was suggested as a
* countermeasure against DPA in 5.3 of [2] (with the obvious adaptation that
* we use jacobian coordinates, not standard projective coordinates).
*/
int ecp_mul( const ecp_group *grp, ecp_point *R,
const mpi *m, const ecp_point *P,
@ -1176,9 +1235,6 @@ int ecp_mul( const ecp_group *grp, ecp_point *R,
ecp_point Q, T[ MAX_PRE_LEN ];
mpi M;
((void) f_rng);
((void) p_rng);
if( mpi_cmp_int( m, 0 ) < 0 || mpi_msb( m ) > grp->nbits )
return( POLARSSL_ERR_ECP_BAD_INPUT_DATA );
@ -1241,6 +1297,10 @@ int ecp_mul( const ecp_group *grp, ecp_point *R,
MPI_CHK( ecp_add_mixed( grp, &Q, &Q, &T[ naf[i] ], +1 ) );
}
/* Countermeasure (see comments above) */
if( f_rng != NULL )
ecp_randomize_coordinates( grp, &Q, f_rng, p_rng );
if( i == 0 )
break;
i--;