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First version of ecp_mul_comb()

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This commit is contained in:
Manuel Pégourié-Gonnard 2013-11-16 15:50:12 +01:00
parent d1bac4ae55
commit d1c1ba90ca
2 changed files with 303 additions and 21 deletions
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12
include/polarssl/ecp.h
View File

@ -476,10 +476,14 @@ int ecp_sub( const ecp_group *grp, ecp_point *R,
* has very low overhead, it is recommended to always provide
* a non-NULL f_rng parameter when using secret inputs.
*/
int ecp_mul( ecp_group *grp, ecp_point *R,
const mpi *m, const ecp_point *P,
int (*f_rng)(void *, unsigned char *, size_t), void *p_rng );
// Temporary, WIP
int ecp_mul_wnaf( ecp_group *grp, ecp_point *R,
const mpi *m, const ecp_point *P,
int (*f_rng)(void *, unsigned char *, size_t), void *p_rng );
int ecp_mul_comb( ecp_group *grp, ecp_point *R,
const mpi *m, const ecp_point *P,
int (*f_rng)(void *, unsigned char *, size_t), void *p_rng );
#define ecp_mul ecp_mul_comb
/**
* \brief Check that a point is a valid public key on this curve

312
library/ecp.c
View File

@ -41,6 +41,11 @@
* 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>
*
* [3] HEDABOU, Mustapha, PINEL, Pierre, et BÉNÉTEAU, Lucien. A comb method to
* render ECC resistant against Side Channel Attacks. IACR Cryptology
* ePrint Archive, 2004, vol. 2004, p. 342.
* <http://eprint.iacr.org/2004/342.pdf>
*/
#include "polarssl/config.h"
@ -902,7 +907,7 @@ cleanup:
}
/*
* Normalize jacobian coordinates of an array of points,
* Normalize jacobian coordinates of an array of (pointers to) points,
* using Montgomery's trick to perform only one inversion mod P.
* (See for example Cohen's "A Course in Computational Algebraic Number
* Theory", Algorithm 10.3.4.)
@ -911,14 +916,14 @@ cleanup:
* This should never happen, see choice of w in ecp_mul().
*/
static int ecp_normalize_many( const ecp_group *grp,
ecp_point T[], size_t t_len )
ecp_point *T[], size_t t_len )
{
int ret;
size_t i;
mpi *c, u, Zi, ZZi;
if( t_len < 2 )
return( ecp_normalize( grp, T ) );
return( ecp_normalize( grp, *T ) );
if( ( c = (mpi *) polarssl_malloc( t_len * sizeof( mpi ) ) ) == NULL )
return( POLARSSL_ERR_ECP_MALLOC_FAILED );
@ -930,10 +935,10 @@ static int ecp_normalize_many( const ecp_group *grp,
/*
* c[i] = Z_0 * ... * Z_i
*/
MPI_CHK( mpi_copy( &c[0], &T[0].Z ) );
MPI_CHK( mpi_copy( &c[0], &T[0]->Z ) );
for( i = 1; i < t_len; i++ )
{
MPI_CHK( mpi_mul_mpi( &c[i], &c[i-1], &T[i].Z ) );
MPI_CHK( mpi_mul_mpi( &c[i], &c[i-1], &T[i]->Z ) );
MOD_MUL( c[i] );
}
@ -953,18 +958,18 @@ static int ecp_normalize_many( const ecp_group *grp,
}
else
{
MPI_CHK( mpi_mul_mpi( &Zi, &u, &c[i-1] ) ); MOD_MUL( Zi );
MPI_CHK( mpi_mul_mpi( &u, &u, &T[i].Z ) ); MOD_MUL( u );
MPI_CHK( mpi_mul_mpi( &Zi, &u, &c[i-1] ) ); MOD_MUL( Zi );
MPI_CHK( mpi_mul_mpi( &u, &u, &T[i]->Z ) ); MOD_MUL( u );
}
/*
* proceed as in normalize()
*/
MPI_CHK( mpi_mul_mpi( &ZZi, &Zi, &Zi ) ); MOD_MUL( ZZi );
MPI_CHK( mpi_mul_mpi( &T[i].X, &T[i].X, &ZZi ) ); MOD_MUL( T[i].X );
MPI_CHK( mpi_mul_mpi( &T[i].Y, &T[i].Y, &ZZi ) ); MOD_MUL( T[i].Y );
MPI_CHK( mpi_mul_mpi( &T[i].Y, &T[i].Y, &Zi ) ); MOD_MUL( T[i].Y );
MPI_CHK( mpi_lset( &T[i].Z, 1 ) );
MPI_CHK( mpi_mul_mpi( &ZZi, &Zi, &Zi ) ); MOD_MUL( ZZi );
MPI_CHK( mpi_mul_mpi( &T[i]->X, &T[i]->X, &ZZi ) ); MOD_MUL( T[i]->X );
MPI_CHK( mpi_mul_mpi( &T[i]->Y, &T[i]->Y, &ZZi ) ); MOD_MUL( T[i]->Y );
MPI_CHK( mpi_mul_mpi( &T[i]->Y, &T[i]->Y, &Zi ) ); MOD_MUL( T[i]->Y );
MPI_CHK( mpi_lset( &T[i]->Z, 1 ) );
if( i == 0 )
break;
@ -1250,6 +1255,7 @@ static int ecp_precompute( const ecp_group *grp,
int ret;
size_t i;
ecp_point PP;
ecp_point *TT[ 1 << ( POLARSSL_ECP_WINDOW_SIZE - 1 ) ];
ecp_point_init( &PP );
@ -1261,9 +1267,11 @@ static int ecp_precompute( const ecp_group *grp,
MPI_CHK( ecp_add_mixed( grp, &T[i], &T[i-1], &PP, +1 ) );
/*
* T[0] = P already has normalized coordinates
* T[0] = P already has normalized coordinates, normalize others
*/
MPI_CHK( ecp_normalize_many( grp, T + 1, t_len - 1 ) );
for( i = 1; i < t_len; i++ )
TT[i-1] = &T[i];
MPI_CHK( ecp_normalize_many( grp, TT, t_len - 1 ) );
cleanup:
@ -1342,9 +1350,9 @@ cleanup:
* countermeasure against DPA in 5.3 of [2] (with the obvious adaptation that
* we use jacobian coordinates, not standard projective coordinates).
*/
int ecp_mul( ecp_group *grp, ecp_point *R,
const mpi *m, const ecp_point *P,
int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
int ecp_mul_wnaf( ecp_group *grp, ecp_point *R,
const mpi *m, const ecp_point *P,
int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
{
int ret;
unsigned char w, m_is_odd, p_eq_g;
@ -1503,6 +1511,276 @@ cleanup:
return( ret );
}
/*
* Compute the representation of m that will be used with the comb method.
*
* The basic comb method is described in GECC 3.44 for example. We use a
* modified version [3] that provides resistance to SPA by avoiding zero
* digits in the representation. We represent (K_i, s_i) from the paper as a
* single signed char.
*
* Calling conventions:
* - x is an array of size d
* - w is the size, ie number of teeth, of the comb
* - m is the MPI, expected to be odd and such that, if l = bitlength(m):
* ceil( l / w ) <= d (these two assumptions are not checked, an incorrect
* result my be returned if they are not satisfied)
*/
static void ecp_comb_fixed( signed char x[], size_t d,
unsigned char w, const mpi *m )
{
size_t i, j;
memset( x, 0, d );
/* For x[0] use the classical comb value without adjustement */
for( j = 0; j < w; j++ )
x[0] |= mpi_get_bit( m, d * j ) << j;
for( i = 1; i < d; i++ )
{
/* Get the classical comb value */
for( j = 0; j < w; j++ )
x[i] |= mpi_get_bit( m, i + d * j ) << j;
/* Adjust if it's zero */
if( x[i] == 0 )
{
x[i] = x[i-1];
x[i-1] *= -1;
}
}
}
/*
* Precompute points for the comb method
*
* If i = i_{w-1} ... i_0 is the binary representation of i, then
* T[i-1] = i_{w-1} 2^{(w-1)d} P + ... + i_1 2^d P + i_0 P
*
* T must be able to hold at least 2^w - 1 elements
*/
static int ecp_precompute_comb( const ecp_group *grp,
ecp_point T[], const ecp_point *P,
unsigned char w, size_t d )
{
int ret;
unsigned char i, mask;
size_t j, t_len = ( 1U << w ) - 1;
ecp_point *cur, *TT[t_len - 1];
/*
* Compute the 2^{di}
*/
MPI_CHK( ecp_copy( &T[0], P ) );
for( i = 1; i < w; i++ )
{
cur = T + ( 1 << i ) - 1;
ecp_copy( cur, T + ( 1 << (i-1) ) - 1 );
for( j = 0; j < d; j++ )
MPI_CHK( ecp_double_jac( grp, cur, cur ) );
TT[i-1] = cur;
}
/* P already normalized, so w - 1 points to do */
ecp_normalize_many( grp, TT, w - 1);
/*
* Compute the remaining ones using the minimal number of additions
*/
j = 0;
for( i = 3; i < (1U << w); i++ )
{
if( T[i - 1].X.p != NULL )
continue;
/* Find the least significant non-zero bit of the index */
for( mask = 1; mask != 0; mask <<=1 )
if( ( i & mask ) != 0 )
break;
/* Use the previously computed values */
ecp_add_mixed( grp, &T[i - 1], &T[i - mask - 1], &T[mask - 1], +1 );
/* Register for normalisation */
TT[j++] = &T[i - 1];
}
ecp_normalize_many( grp, TT, j );
cleanup:
return( ret );
}
/*
* Select precomputed point: R = sign(i) * T[ abs(i) ]
*/
static int ecp_select_comb( const ecp_group *grp, ecp_point *R,
const ecp_point T[], signed char i )
{
int ret;
if( i > 0 )
return( ecp_copy( R, &T[i - 1] ) );
MPI_CHK( ecp_copy( R, &T[-i - 1] ) );
/*
* -R = (R.X, -R.Y, R.Z), and
* -R.Y mod P = P - R.Y unless R.Y == 0
*/
if( mpi_cmp_int( &R->Y, 0 ) != 0 )
MPI_CHK( mpi_sub_mpi( &R->Y, &grp->P, &R->Y ) );
cleanup:
return( ret );
}
/*
* Core multiplication algorithm for the (modified) comb method.
* This part is actually common with the basic comb method (GECC 3.44)
*/
static int ecp_mul_comb_core( const ecp_group *grp, ecp_point *R,
const ecp_point T[], const signed char x[],
size_t d )
{
int ret;
ecp_point Txi;
size_t i;
ecp_point_init( &Txi );
/* Avoid useless doubling/addition of 0 by better initialisation */
i = d - 1;
MPI_CHK( ecp_select_comb( grp, R, T, x[i] ) );
while( i-- != 0 )
{
MPI_CHK( ecp_double_jac( grp, R, R ) );
MPI_CHK( ecp_select_comb( grp, &Txi, T, x[i] ) );
MPI_CHK( ecp_add_mixed( grp, R, R, &Txi, +1 ) );
}
cleanup:
ecp_point_free( &Txi );
return( ret );
}
/*
* Multiplication using the comb method, WIP
*/
int ecp_mul_comb( ecp_group *grp, ecp_point *R,
const mpi *m, const ecp_point *P,
int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
{
int ret;
unsigned char w, m_is_odd, p_eq_g;
size_t pre_len, d, i;
signed char k[100]; // TODO
ecp_point Q, *T = NULL, S[2];
mpi M;
(void) f_rng;
(void) p_rng; // TODO
if( mpi_cmp_int( m, 0 ) < 0 || mpi_msb( m ) > grp->nbits )
return( POLARSSL_ERR_ECP_BAD_INPUT_DATA );
mpi_init( &M );
ecp_point_init( &Q );
ecp_point_init( &S[0] );
ecp_point_init( &S[1] );
/*
* Check if P == G
*/
p_eq_g = ( mpi_cmp_int( &P->Z, 1 ) == 0 &&
mpi_cmp_mpi( &P->Y, &grp->G.Y ) == 0 &&
mpi_cmp_mpi( &P->X, &grp->G.X ) == 0 );
/* TODO: adjust exact value */
w = grp->nbits >= 192 ? 5 : 2;
pre_len = 1U << w;
d = ( grp->nbits + w - 1 ) / w;
/*
* Prepare precomputed points: if P == G we want to
* use grp->T if already initialized, or initiliaze it.
*/
if( ! p_eq_g || grp->T == NULL )
{
T = (ecp_point *) polarssl_malloc( pre_len * sizeof( ecp_point ) );
if( T == NULL )
{
ret = POLARSSL_ERR_ECP_MALLOC_FAILED;
goto cleanup;
}
for( i = 0; i < pre_len; i++ )
ecp_point_init( &T[i] );
MPI_CHK( ecp_precompute_comb( grp, T, P, w, d ) );
if( p_eq_g )
{
grp->T = T;
grp->T_size = pre_len;
}
}
else
{
T = grp->T;
/* Should never happen, but we want to be extra sure */
if( pre_len != grp->T_size )
{
ret = POLARSSL_ERR_ECP_BAD_INPUT_DATA;
goto cleanup;
}
}
/*
* Make sure M is odd (M = m + 1 or M = m + 2)
* later we'll get m * P by subtracting P or 2 * P to M * P.
*/
m_is_odd = ( mpi_get_bit( m, 0 ) == 1 );
MPI_CHK( mpi_copy( &M, m ) );
MPI_CHK( mpi_add_int( &M, &M, 1 + m_is_odd ) );
/*
* Go for comb multiplication, Q = M * P
*/
ecp_comb_fixed( k, d, w, &M );
ecp_mul_comb_core( grp, &Q, T, k, d );
/*
* Now get m * P from M * P
*/
MPI_CHK( ecp_copy( &S[0], P ) );
MPI_CHK( ecp_add( grp, &S[1], P, P ) );
MPI_CHK( ecp_sub( grp, R, &Q, &S[m_is_odd] ) );
cleanup:
if( T != NULL && ! p_eq_g )
{
for( i = 0; i < pre_len; i++ )
ecp_point_free( &T[i] );
polarssl_free( T );
}
ecp_point_free( &S[1] );
ecp_point_free( &S[0] );
ecp_point_free( &Q );
mpi_free( &M );
return( ret );
}
/*
* Check that a point is valid as a public key (SEC1 3.2.3.1)
*/