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