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Added ecp_normalize_many() for faster precompute()

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Manuel Pégourié-Gonnard 2012-11-21 16:00:55 +01:00 committed by Paul Bakker
parent b63f9e98f5
commit cdd44324e9
1 changed files with 90 additions and 8 deletions
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98
library/ecp.c
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@ -37,6 +37,7 @@
#include "polarssl/ecp.h"
#include <limits.h>
#include <stdlib.h>
#if defined(POLARSSL_SELF_TEST)
/*
@ -472,12 +473,12 @@ int ecp_use_known_dp( ecp_group *grp, size_t index )
static int ecp_normalize( const ecp_group *grp, ecp_point *pt )
{
int ret;
mpi Zi, ZZi, T;
mpi Zi, ZZi;
if( mpi_cmp_int( &pt->Z, 0 ) == 0 )
return( 0 );
mpi_init( &Zi ); mpi_init( &ZZi ); mpi_init( &T );
mpi_init( &Zi ); mpi_init( &ZZi );
/*
* X = X / Z^2 mod p
@ -499,11 +500,90 @@ static int ecp_normalize( const ecp_group *grp, ecp_point *pt )
cleanup:
mpi_free( &Zi ); mpi_free( &ZZi ); mpi_free( &T );
mpi_free( &Zi ); mpi_free( &ZZi );
return( ret );
}
/*
* Normalize jacobian coordinates of an array of points,
* using Montgomery's trick to perform only one division.
* (See for example Cohen's "A Course in Computational Algebraic Number
* Theory", Algorithm 10.3.4.)
*
* FIXME: assumes all points are non zero
*/
static int ecp_normalize_many( const ecp_group *grp,
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 ) );
if( ( c = (mpi *) malloc( t_len * sizeof( mpi ) ) ) == NULL )
return( POLARSSL_ERR_ECP_GENERIC );
mpi_init( &u ); mpi_init( &Zi ); mpi_init( &ZZi );
for( i = 0; i < t_len; i++ )
mpi_init( &c[i] );
/*
* c[i] = Z_0 * ... * Z_i
*/
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 ) );
MOD_MUL( c[i] );
}
/*
* u = 1 / (Z_0 * ... * Z_n) mod P
*/
MPI_CHK( mpi_inv_mod( &u, &c[t_len-1], &grp->P ) );
for( i = t_len - 1; ; i-- )
{
/*
* Zi = 1 / Z_i mod p
* u = 1 / (Z_0 * ... * Z_i) mod P
*/
if( i == 0 ) {
MPI_CHK( mpi_copy( &Zi, &u ) );
}
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 );
}
/*
* 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 ) );
if( i == 0 )
break;
}
cleanup:
mpi_free( &u ); mpi_free( &Zi ); mpi_free( &ZZi );
for( i = 0; i < t_len; i++ )
mpi_free( &c[i] );
free( c );
return( ret );
}
/*
* Point doubling R = 2 P, Jacobian coordinates (GECC 3.21)
*/
@ -782,11 +862,13 @@ static int ecp_precompute( const ecp_group *grp,
MPI_CHK( ecp_copy( &T[0], P ) );
/*
* TODO: use Montgomery's trick for less inversions
*/
for( i = 1; i < t_len; i++ )
MPI_CHK( ecp_add( grp, &T[i], &T[i-1], &PP ) );
MPI_CHK( ecp_add_mixed( grp, &T[i], &T[i-1], &PP, +1 ) );
/*
* T[0] = P already has normalized coordinates
*/
ecp_normalize_many( grp, T + 1, t_len - 1 );
cleanup:
@ -829,7 +911,7 @@ int ecp_mul( const ecp_group *grp, ecp_point *R,
if( mpi_cmp_int( m, 0 ) < 0 || mpi_msb( m ) > grp->nbits )
return( POLARSSL_ERR_ECP_GENERIC );
w = 3; // TODO: find optimal values once precompute() is optimized
w = 5; // TODO: find optimal values once precompute() is optimized
if( w < 2 )
w = 2;