mbedtls/library/ecp.c

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2012-10-31 08:26:55 +00:00
/*
* Elliptic curves over GF(p)
*
* Copyright (C) 2012, Brainspark B.V.
*
* This file is part of PolarSSL (http://www.polarssl.org)
* Lead Maintainer: Paul Bakker <polarssl_maintainer at polarssl.org>
*
* All rights reserved.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License along
* with this program; if not, write to the Free Software Foundation, Inc.,
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
*/
/*
* References:
*
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* SEC1 http://www.secg.org/index.php?action=secg,docs_secg
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* Guide to Elliptic Curve Cryptography - Hankerson, Menezes, Vanstone
*/
#include "polarssl/config.h"
#if defined(POLARSSL_ECP_C)
#include "polarssl/ecp.h"
/*
* Initialize (the components of) a point
*/
void ecp_point_init( ecp_point *pt )
{
if( pt == NULL )
return;
pt->is_zero = 1;
mpi_init( &pt->X );
mpi_init( &pt->Y );
}
/*
* Initialize (the components of) a group
*/
void ecp_group_init( ecp_group *grp )
{
if( grp == NULL )
return;
mpi_init( &grp->P );
mpi_init( &grp->B );
ecp_point_init( &grp->G );
mpi_init( &grp->N );
}
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/*
* Unallocate (the components of) a point
*/
void ecp_point_free( ecp_point *pt )
{
if( pt == NULL )
return;
pt->is_zero = 1;
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mpi_free( &( pt->X ) );
mpi_free( &( pt->Y ) );
}
/*
* Unallocate (the components of) a group
*/
void ecp_group_free( ecp_group *grp )
{
if( grp == NULL )
return;
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mpi_free( &grp->P );
mpi_free( &grp->B );
ecp_point_free( &grp->G );
mpi_free( &grp->N );
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}
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/*
* Set point to zero
*/
void ecp_set_zero( ecp_point *pt )
{
pt->is_zero = 1;
mpi_free( &pt->X );
mpi_free( &pt->Y );
}
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/*
* Copy the contents of Q into P
*/
int ecp_copy( ecp_point *P, const ecp_point *Q )
{
int ret = 0;
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if( Q->is_zero ) {
ecp_set_zero( P );
return( ret );
}
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P->is_zero = Q->is_zero;
MPI_CHK( mpi_copy( &P->X, &Q->X ) );
MPI_CHK( mpi_copy( &P->Y, &Q->Y ) );
cleanup:
return( ret );
}
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/*
* Import a non-zero point from ASCII strings
*/
int ecp_point_read_string( ecp_point *P, int radix,
const char *x, const char *y )
{
int ret = 0;
P->is_zero = 0;
MPI_CHK( mpi_read_string( &P->X, radix, x ) );
MPI_CHK( mpi_read_string( &P->Y, radix, y ) );
cleanup:
return( ret );
}
/*
* Import an ECP group from ASCII strings
*/
int ecp_group_read_string( ecp_group *grp, int radix,
const char *p, const char *b,
const char *gx, const char *gy, const char *n)
{
int ret = 0;
MPI_CHK( mpi_read_string( &grp->P, radix, p ) );
MPI_CHK( mpi_read_string( &grp->B, radix, b ) );
MPI_CHK( ecp_point_read_string( &grp->G, radix, gx, gy ) );
MPI_CHK( mpi_read_string( &grp->N, radix, n ) );
cleanup:
return( ret );
}
/*
* Addition: R = P + Q, generic case (P != Q, P != 0, Q != 0, R != 0)
* Cf SEC1 v2 p. 7, item 4
*/
static int ecp_add_generic( const ecp_group *grp, ecp_point *R,
const ecp_point *P, const ecp_point *Q )
{
int ret = 0;
mpi DX, DY, K, L, LL, M, X, Y;
mpi_init( &DX ); mpi_init( &DY ); mpi_init( &K ); mpi_init( &L );
mpi_init( &LL ); mpi_init( &M ); mpi_init( &X ); mpi_init( &Y );
/*
* L = (Q.Y - P.Y) / (Q.X - P.X) mod p
*/
MPI_CHK( mpi_sub_mpi( &DY, &Q->Y, &P->Y ) );
MPI_CHK( mpi_sub_mpi( &DX, &Q->X, &P->X ) );
MPI_CHK( mpi_inv_mod( &K, &DX, &grp->P ) );
MPI_CHK( mpi_mul_mpi( &K, &K, &DY ) );
MPI_CHK( mpi_mod_mpi( &L, &K, &grp->P ) );
/*
* LL = L^2 mod p
* M = L^2 - Q.X
* X = L^2 - P.X - Q.X
*/
MPI_CHK( mpi_mul_mpi( &LL, &L, &L ) );
MPI_CHK( mpi_mod_mpi( &LL, &LL, &grp->P ) );
MPI_CHK( mpi_sub_mpi( &M, &LL, &Q->X ) );
MPI_CHK( mpi_sub_mpi( &X, &M, &P->X ) );
/*
* Y = L * (P.X - X) - P.Y = L * (-M) - P.Y
*/
MPI_CHK( mpi_copy( &Y, &M ) );
Y.s = - Y.s;
MPI_CHK( mpi_mul_mpi( &Y, &Y, &L ) );
MPI_CHK( mpi_sub_mpi( &Y, &Y, &P->Y ) );
/*
* R = (X mod p, Y mod p)
*/
R->is_zero = 0;
MPI_CHK( mpi_mod_mpi( &R->X, &X, &grp->P ) );
MPI_CHK( mpi_mod_mpi( &R->Y, &Y, &grp->P ) );
cleanup:
mpi_free( &DX ); mpi_free( &DY ); mpi_free( &K ); mpi_free( &L );
mpi_free( &LL ); mpi_free( &M ); mpi_free( &X ); mpi_free( &Y );
return( ret );
}
/*
* Doubling: R = 2 * P, generic case (P != 0, R != 0)
*/
static int ecp_double_generic( const ecp_group *grp, ecp_point *R,
const ecp_point *P )
{
int ret = 0;
(void) grp;
(void) R;
(void) P;
return( ret );
}
/*
* Addition: R = P + Q, cf p. 7 of SEC1 v2
*/
int ecp_add( const ecp_group *grp, ecp_point *R,
const ecp_point *P, const ecp_point *Q )
{
int ret = 0;
if( P->is_zero )
{
ret = ecp_copy( R, Q );
}
else if( Q->is_zero )
{
ret = ecp_copy( R, P );
}
else if( mpi_cmp_mpi( &P->X, &Q->X ) != 0 )
{
ret = ecp_add_generic( grp, R, P, Q );
}
else if( mpi_cmp_int( &P->Y, 0 ) == 0 ||
mpi_cmp_mpi( &P->Y, &Q->Y ) != 0 )
{
ecp_set_zero( R );
}
else
{
/*
* P == Q
*/
ret = ecp_double_generic( grp, R, P );
}
return ret;
}
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#if defined(POLARSSL_SELF_TEST)
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/*
* Return true iff P and Q are the same point
*/
static int ecp_point_eq( const ecp_point *P, const ecp_point *Q )
{
if( P->is_zero || Q->is_zero )
return( P->is_zero && Q->is_zero );
return( mpi_cmp_mpi( &P->X, &Q->X ) == 0 &&
mpi_cmp_mpi( &P->Y, &Q->Y ) == 0 );
}
/*
* Print a point assuming its components are small
*/
static void ecp_point_print( const ecp_point *P )
{
if( P->is_zero )
printf("zero\n");
else
printf("(%lu, %lu)\n", P->X.p[0], P->Y.p[0]);
}
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/*
* Checkup routine
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*
* Data for basic tests with small values gathered from
* http://danher6.100webspace.net/ecc/#EFp_interactivo and double-checked
* using Pari-GP.
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*/
int ecp_self_test( int verbose )
{
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int ret = 0;
unsigned i;
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ecp_group grp;
ecp_point O, A, B, C, D, E, F, G, TMP;
ecp_point *add_tbl[][3] =
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{
{&O, &O, &O},
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};
ecp_group_init( &grp );
ecp_point_init( &O ); ecp_point_init( &A ); ecp_point_init( &B );
ecp_point_init( &C ); ecp_point_init( &D ); ecp_point_init( &E );
ecp_point_init( &F ); ecp_point_init( &G ); ecp_point_init( &TMP );
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ecp_set_zero( &O );
MPI_CHK( ecp_group_read_string( &grp, 10, "47", "4", "17", "42", "13" ) );
MPI_CHK( ecp_point_read_string( &A, 10, "13", "0" ) );
MPI_CHK( ecp_point_read_string( &B, 10, "14", "11" ) );
MPI_CHK( ecp_point_read_string( &C, 10, "14", "36" ) );
MPI_CHK( ecp_point_read_string( &D, 10, "37", "31" ) );
MPI_CHK( ecp_point_read_string( &E, 10, "34", "14" ) );
MPI_CHK( ecp_point_read_string( &F, 10, "45", "7" ) );
MPI_CHK( ecp_point_read_string( &G, 10, "21", "32" ) );
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if( verbose != 0 )
printf( " ECP test #1 (ecp_add): " );
for( i = 0; i < sizeof( add_tbl ) / sizeof( add_tbl[0] ); i++ )
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{
MPI_CHK( ecp_add( &grp, &TMP, add_tbl[i][0], add_tbl[i][1] ) );
if( ! ecp_point_eq( &TMP, add_tbl[i][2] ) )
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{
if( verbose != 0 )
{
printf(" failed\n");
printf(" GOT: ");
ecp_point_print( &TMP );
printf(" EXPECTED: ");
ecp_point_print( add_tbl[i][2] );
}
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return( 1 );
}
}
if (verbose != 0 )
printf( " passed\n" );
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cleanup:
if( ret != 0 && verbose != 0 )
printf( "Unexpected error, return code = %08X\n", ret );
ecp_group_free( &grp );
ecp_point_free( &O ); ecp_point_free( &A ); ecp_point_free( &B );
ecp_point_free( &C ); ecp_point_free( &D ); ecp_point_free( &E );
ecp_point_free( &F ); ecp_point_free( &G );
if( verbose != 0 )
printf( "\n" );
return( ret );
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}
#endif
#endif