library/ecdsa.c - security/mbedtls - Rivoreo Source Code Repositories

 /*
  *  Elliptic curve DSA
  *
  *  Copyright (C) 2006-2014, ARM Limited, All Rights Reserved
  *
  *  This file is part of mbed TLS (https://tls.mbed.org)
  *
  *  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:
  *
  * SEC1 http://www.secg.org/index.php?action=secg,docs_secg
  */

 #if !defined(POLARSSL_CONFIG_FILE)
 #include "mbedtls/config.h"
 #else
 #include POLARSSL_CONFIG_FILE
 #endif

 #if defined(POLARSSL_ECDSA_C)

 #include "mbedtls/ecdsa.h"
 #include "mbedtls/asn1write.h"

 #include <string.h>

 #if defined(POLARSSL_ECDSA_DETERMINISTIC)
 #include "mbedtls/hmac_drbg.h"
 #endif

 /*
  * Derive a suitable integer for group grp from a buffer of length len
  * SEC1 4.1.3 step 5 aka SEC1 4.1.4 step 3
  */
 static int derive_mpi( const ecp_group *grp, mpi *x,
                        const unsigned char *buf, size_t blen )
 {
     int ret;
     size_t n_size = ( grp->nbits + 7 ) / 8;
     size_t use_size = blen > n_size ? n_size : blen;

     MPI_CHK( mpi_read_binary( x, buf, use_size ) );
     if( use_size * 8 > grp->nbits )
         MPI_CHK( mpi_shift_r( x, use_size * 8 - grp->nbits ) );

     /* While at it, reduce modulo N */
     if( mpi_cmp_mpi( x, &grp->N ) >= 0 )
         MPI_CHK( mpi_sub_mpi( x, x, &grp->N ) );

 cleanup:
     return( ret );
 }

 /*
  * Compute ECDSA signature of a hashed message (SEC1 4.1.3)
  * Obviously, compared to SEC1 4.1.3, we skip step 4 (hash message)
  */
 int ecdsa_sign( ecp_group *grp, mpi *r, mpi *s,
                 const mpi *d, const unsigned char *buf, size_t blen,
                 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
 {
     int ret, key_tries, sign_tries, blind_tries;
     ecp_point R;
     mpi k, e, t;

     /* Fail cleanly on curves such as Curve25519 that can't be used for ECDSA */
     if( grp->N.p == NULL )
         return( POLARSSL_ERR_ECP_BAD_INPUT_DATA );

     ecp_point_init( &R );
     mpi_init( &k ); mpi_init( &e ); mpi_init( &t );

     sign_tries = 0;
     do
     {
         /*
          * Steps 1-3: generate a suitable ephemeral keypair
          * and set r = xR mod n
          */
         key_tries = 0;
         do
         {
             MPI_CHK( ecp_gen_keypair( grp, &k, &R, f_rng, p_rng ) );
             MPI_CHK( mpi_mod_mpi( r, &R.X, &grp->N ) );

             if( key_tries++ > 10 )
             {
                 ret = POLARSSL_ERR_ECP_RANDOM_FAILED;
                 goto cleanup;
             }
         }
         while( mpi_cmp_int( r, 0 ) == 0 );

         /*
          * Step 5: derive MPI from hashed message
          */
         MPI_CHK( derive_mpi( grp, &e, buf, blen ) );

         /*
          * Generate a random value to blind inv_mod in next step,
          * avoiding a potential timing leak.
          */
         blind_tries = 0;
         do
         {
             size_t n_size = ( grp->nbits + 7 ) / 8;
             MPI_CHK( mpi_fill_random( &t, n_size, f_rng, p_rng ) );
             MPI_CHK( mpi_shift_r( &t, 8 * n_size - grp->nbits ) );

             /* See ecp_gen_keypair() */
             if( ++blind_tries > 30 )
                 return( POLARSSL_ERR_ECP_RANDOM_FAILED );
         }
         while( mpi_cmp_int( &t, 1 ) < 0 ||
                mpi_cmp_mpi( &t, &grp->N ) >= 0 );

         /*
          * Step 6: compute s = (e + r * d) / k = t (e + rd) / (kt) mod n
          */
         MPI_CHK( mpi_mul_mpi( s, r, d ) );
         MPI_CHK( mpi_add_mpi( &e, &e, s ) );
         MPI_CHK( mpi_mul_mpi( &e, &e, &t ) );
         MPI_CHK( mpi_mul_mpi( &k, &k, &t ) );
         MPI_CHK( mpi_inv_mod( s, &k, &grp->N ) );
         MPI_CHK( mpi_mul_mpi( s, s, &e ) );
         MPI_CHK( mpi_mod_mpi( s, s, &grp->N ) );

         if( sign_tries++ > 10 )
         {
             ret = POLARSSL_ERR_ECP_RANDOM_FAILED;
             goto cleanup;
         }
     }
     while( mpi_cmp_int( s, 0 ) == 0 );

 cleanup:
     ecp_point_free( &R );
     mpi_free( &k ); mpi_free( &e ); mpi_free( &t );

     return( ret );
 }

 #if defined(POLARSSL_ECDSA_DETERMINISTIC)
 /*
  * Deterministic signature wrapper
  */
 int ecdsa_sign_det( ecp_group *grp, mpi *r, mpi *s,
                     const mpi *d, const unsigned char *buf, size_t blen,
                     md_type_t md_alg )
 {
     int ret;
     hmac_drbg_context rng_ctx;
     unsigned char data[2 * POLARSSL_ECP_MAX_BYTES];
     size_t grp_len = ( grp->nbits + 7 ) / 8;
     const md_info_t *md_info;
     mpi h;

     if( ( md_info = md_info_from_type( md_alg ) ) == NULL )
         return( POLARSSL_ERR_ECP_BAD_INPUT_DATA );

     mpi_init( &h );
     memset( &rng_ctx, 0, sizeof( hmac_drbg_context ) );

     /* Use private key and message hash (reduced) to initialize HMAC_DRBG */
     MPI_CHK( mpi_write_binary( d, data, grp_len ) );
     MPI_CHK( derive_mpi( grp, &h, buf, blen ) );
     MPI_CHK( mpi_write_binary( &h, data + grp_len, grp_len ) );
     hmac_drbg_init_buf( &rng_ctx, md_info, data, 2 * grp_len );

     ret = ecdsa_sign( grp, r, s, d, buf, blen,
                       hmac_drbg_random, &rng_ctx );

 cleanup:
     hmac_drbg_free( &rng_ctx );
     mpi_free( &h );

     return( ret );
 }
 #endif /* POLARSSL_ECDSA_DETERMINISTIC */

 /*
  * Verify ECDSA signature of hashed message (SEC1 4.1.4)
  * Obviously, compared to SEC1 4.1.3, we skip step 2 (hash message)
  */
 int ecdsa_verify( ecp_group *grp,
                   const unsigned char *buf, size_t blen,
                   const ecp_point *Q, const mpi *r, const mpi *s)
 {
     int ret;
     mpi e, s_inv, u1, u2;
     ecp_point R, P;

     ecp_point_init( &R ); ecp_point_init( &P );
     mpi_init( &e ); mpi_init( &s_inv ); mpi_init( &u1 ); mpi_init( &u2 );

     /* Fail cleanly on curves such as Curve25519 that can't be used for ECDSA */
     if( grp->N.p == NULL )
         return( POLARSSL_ERR_ECP_BAD_INPUT_DATA );

     /*
      * Step 1: make sure r and s are in range 1..n-1
      */
     if( mpi_cmp_int( r, 1 ) < 0 || mpi_cmp_mpi( r, &grp->N ) >= 0 ||
         mpi_cmp_int( s, 1 ) < 0 || mpi_cmp_mpi( s, &grp->N ) >= 0 )
     {
         ret = POLARSSL_ERR_ECP_VERIFY_FAILED;
         goto cleanup;
     }

     /*
      * Additional precaution: make sure Q is valid
      */
     MPI_CHK( ecp_check_pubkey( grp, Q ) );

     /*
      * Step 3: derive MPI from hashed message
      */
     MPI_CHK( derive_mpi( grp, &e, buf, blen ) );

     /*
      * Step 4: u1 = e / s mod n, u2 = r / s mod n
      */
     MPI_CHK( mpi_inv_mod( &s_inv, s, &grp->N ) );

     MPI_CHK( mpi_mul_mpi( &u1, &e, &s_inv ) );
     MPI_CHK( mpi_mod_mpi( &u1, &u1, &grp->N ) );

     MPI_CHK( mpi_mul_mpi( &u2, r, &s_inv ) );
     MPI_CHK( mpi_mod_mpi( &u2, &u2, &grp->N ) );

     /*
      * Step 5: R = u1 G + u2 Q
      *
      * Since we're not using any secret data, no need to pass a RNG to
      * ecp_mul() for countermesures.
      */
     MPI_CHK( ecp_mul( grp, &R, &u1, &grp->G, NULL, NULL ) );
     MPI_CHK( ecp_mul( grp, &P, &u2, Q, NULL, NULL ) );
     MPI_CHK( ecp_add( grp, &R, &R, &P ) );

     if( ecp_is_zero( &R ) )
     {
         ret = POLARSSL_ERR_ECP_VERIFY_FAILED;
         goto cleanup;
     }

     /*
      * Step 6: convert xR to an integer (no-op)
      * Step 7: reduce xR mod n (gives v)
      */
     MPI_CHK( mpi_mod_mpi( &R.X, &R.X, &grp->N ) );

     /*
      * Step 8: check if v (that is, R.X) is equal to r
      */
     if( mpi_cmp_mpi( &R.X, r ) != 0 )
     {
         ret = POLARSSL_ERR_ECP_VERIFY_FAILED;
         goto cleanup;
     }

 cleanup:
     ecp_point_free( &R ); ecp_point_free( &P );
     mpi_free( &e ); mpi_free( &s_inv ); mpi_free( &u1 ); mpi_free( &u2 );

     return( ret );
 }

 /*
  * Convert a signature (given by context) to ASN.1
  */
 static int ecdsa_signature_to_asn1( const mpi *r, const mpi *s,
                                     unsigned char *sig, size_t *slen )
 {
     int ret;
     unsigned char buf[POLARSSL_ECDSA_MAX_LEN];
     unsigned char *p = buf + sizeof( buf );
     size_t len = 0;

     ASN1_CHK_ADD( len, asn1_write_mpi( &p, buf, s ) );
     ASN1_CHK_ADD( len, asn1_write_mpi( &p, buf, r ) );

     ASN1_CHK_ADD( len, asn1_write_len( &p, buf, len ) );
     ASN1_CHK_ADD( len, asn1_write_tag( &p, buf,
                                        ASN1_CONSTRUCTED | ASN1_SEQUENCE ) );

     memcpy( sig, p, len );
     *slen = len;

     return( 0 );
 }

 /*
  * Compute and write signature
  */
 int ecdsa_write_signature( ecdsa_context *ctx, md_type_t md_alg,
                            const unsigned char *hash, size_t hlen,
                            unsigned char *sig, size_t *slen,
                            int (*f_rng)(void *, unsigned char *, size_t),
                            void *p_rng )
 {
     int ret;
     mpi r, s;

     mpi_init( &r );
     mpi_init( &s );

 #if defined(POLARSSL_ECDSA_DETERMINISTIC)
     (void) f_rng;
     (void) p_rng;

     MPI_CHK( ecdsa_sign_det( &ctx->grp, &r, &s, &ctx->d,
                              hash, hlen, md_alg ) );
 #else
     (void) md_alg;

     MPI_CHK( ecdsa_sign( &ctx->grp, &r, &s, &ctx->d,
                          hash, hlen, f_rng, p_rng ) );
 #endif

     MPI_CHK( ecdsa_signature_to_asn1( &r, &s, sig, slen ) );

 cleanup:
     mpi_free( &r );
     mpi_free( &s );

     return( ret );
 }

 #if ! defined(POLARSSL_DEPRECATED_REMOVED)
 int ecdsa_write_signature_det( ecdsa_context *ctx,
                                const unsigned char *hash, size_t hlen,
                                unsigned char *sig, size_t *slen,
                                md_type_t md_alg )
 {
     return( ecdsa_write_signature( ctx, md_alg, hash, hlen, sig, slen,
                                    NULL, NULL ) );
 }
 #endif

 /*
  * Read and check signature
  */
 int ecdsa_read_signature( ecdsa_context *ctx,
                           const unsigned char *hash, size_t hlen,
                           const unsigned char *sig, size_t slen )
 {
     int ret;
     unsigned char *p = (unsigned char *) sig;
     const unsigned char *end = sig + slen;
     size_t len;
     mpi r, s;

     mpi_init( &r );
     mpi_init( &s );

     if( ( ret = asn1_get_tag( &p, end, &len,
                     ASN1_CONSTRUCTED | ASN1_SEQUENCE ) ) != 0 )
     {
         ret += POLARSSL_ERR_ECP_BAD_INPUT_DATA;
         goto cleanup;
     }

     if( p + len != end )
     {
         ret = POLARSSL_ERR_ECP_BAD_INPUT_DATA +
               POLARSSL_ERR_ASN1_LENGTH_MISMATCH;
         goto cleanup;
     }

     if( ( ret = asn1_get_mpi( &p, end, &r ) ) != 0 ||
         ( ret = asn1_get_mpi( &p, end, &s ) ) != 0 )
     {
         ret += POLARSSL_ERR_ECP_BAD_INPUT_DATA;
         goto cleanup;
     }

     if( ( ret = ecdsa_verify( &ctx->grp, hash, hlen,
                               &ctx->Q, &r, &s ) ) != 0 )
         goto cleanup;

     if( p != end )
         ret = POLARSSL_ERR_ECP_SIG_LEN_MISMATCH;

 cleanup:
     mpi_free( &r );
     mpi_free( &s );

     return( ret );
 }

 /*
  * Generate key pair
  */
 int ecdsa_genkey( ecdsa_context *ctx, ecp_group_id gid,
                   int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
 {
     return( ecp_use_known_dp( &ctx->grp, gid ) ||
             ecp_gen_keypair( &ctx->grp, &ctx->d, &ctx->Q, f_rng, p_rng ) );
 }

 /*
  * Set context from an ecp_keypair
  */
 int ecdsa_from_keypair( ecdsa_context *ctx, const ecp_keypair *key )
 {
     int ret;

     if( ( ret = ecp_group_copy( &ctx->grp, &key->grp ) ) != 0 ||
         ( ret = mpi_copy( &ctx->d, &key->d ) ) != 0 ||
         ( ret = ecp_copy( &ctx->Q, &key->Q ) ) != 0 )
     {
         ecdsa_free( ctx );
     }

     return( ret );
 }

 /*
  * Initialize context
  */
 void ecdsa_init( ecdsa_context *ctx )
 {
     ecp_keypair_init( ctx );
 }

 /*
  * Free context
  */
 void ecdsa_free( ecdsa_context *ctx )
 {
     ecp_keypair_free( ctx );
 }

 #endif /* POLARSSL_ECDSA_C */
	/*
	* Elliptic curve DSA
	*
	* Copyright (C) 2006-2014, ARM Limited, All Rights Reserved
	*
	* This file is part of mbed TLS (https://tls.mbed.org)
	*
	* 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:
	*
	* SEC1 http://www.secg.org/index.php?action=secg,docs_secg
	*/

	#if !defined(POLARSSL_CONFIG_FILE)
	#include "mbedtls/config.h"
	#else
	#include POLARSSL_CONFIG_FILE
	#endif

	#if defined(POLARSSL_ECDSA_C)

	#include "mbedtls/ecdsa.h"
	#include "mbedtls/asn1write.h"

	#include <string.h>

	#if defined(POLARSSL_ECDSA_DETERMINISTIC)
	#include "mbedtls/hmac_drbg.h"
	#endif

	/*
	* Derive a suitable integer for group grp from a buffer of length len
	* SEC1 4.1.3 step 5 aka SEC1 4.1.4 step 3
	*/
	static int derive_mpi( const ecp_group grp, mpi x,
	const unsigned char *buf, size_t blen )
	{
	int ret;
	size_t n_size = ( grp->nbits + 7 ) / 8;
	size_t use_size = blen > n_size ? n_size : blen;

	MPI_CHK( mpi_read_binary( x, buf, use_size ) );
	if( use_size * 8 > grp->nbits )
	MPI_CHK( mpi_shift_r( x, use_size * 8 - grp->nbits ) );

	/* While at it, reduce modulo N */
	if( mpi_cmp_mpi( x, &grp->N ) >= 0 )
	MPI_CHK( mpi_sub_mpi( x, x, &grp->N ) );

	cleanup:
	return( ret );
	}

	/*
	* Compute ECDSA signature of a hashed message (SEC1 4.1.3)
	* Obviously, compared to SEC1 4.1.3, we skip step 4 (hash message)
	*/
	int ecdsa_sign( ecp_group grp, mpi r, mpi *s,
	const mpi d, const unsigned char buf, size_t blen,
	int (f_rng)(void , unsigned char , size_t), void p_rng )
	{
	int ret, key_tries, sign_tries, blind_tries;
	ecp_point R;
	mpi k, e, t;

	/* Fail cleanly on curves such as Curve25519 that can't be used for ECDSA */
	if( grp->N.p == NULL )
	return( POLARSSL_ERR_ECP_BAD_INPUT_DATA );

	ecp_point_init( &R );
	mpi_init( &k ); mpi_init( &e ); mpi_init( &t );

	sign_tries = 0;
	do
	{
	/*
	* Steps 1-3: generate a suitable ephemeral keypair
	* and set r = xR mod n
	*/
	key_tries = 0;
	do
	{
	MPI_CHK( ecp_gen_keypair( grp, &k, &R, f_rng, p_rng ) );
	MPI_CHK( mpi_mod_mpi( r, &R.X, &grp->N ) );

	if( key_tries++ > 10 )
	{
	ret = POLARSSL_ERR_ECP_RANDOM_FAILED;
	goto cleanup;
	}
	}
	while( mpi_cmp_int( r, 0 ) == 0 );

	/*
	* Step 5: derive MPI from hashed message
	*/
	MPI_CHK( derive_mpi( grp, &e, buf, blen ) );

	/*
	* Generate a random value to blind inv_mod in next step,
	* avoiding a potential timing leak.
	*/
	blind_tries = 0;
	do
	{
	size_t n_size = ( grp->nbits + 7 ) / 8;
	MPI_CHK( mpi_fill_random( &t, n_size, f_rng, p_rng ) );
	MPI_CHK( mpi_shift_r( &t, 8 * n_size - grp->nbits ) );

	/* See ecp_gen_keypair() */
	if( ++blind_tries > 30 )
	return( POLARSSL_ERR_ECP_RANDOM_FAILED );
	}
	while( mpi_cmp_int( &t, 1 ) < 0 \|\|
	mpi_cmp_mpi( &t, &grp->N ) >= 0 );

	/*
	* Step 6: compute s = (e + r * d) / k = t (e + rd) / (kt) mod n
	*/
	MPI_CHK( mpi_mul_mpi( s, r, d ) );
	MPI_CHK( mpi_add_mpi( &e, &e, s ) );
	MPI_CHK( mpi_mul_mpi( &e, &e, &t ) );
	MPI_CHK( mpi_mul_mpi( &k, &k, &t ) );
	MPI_CHK( mpi_inv_mod( s, &k, &grp->N ) );
	MPI_CHK( mpi_mul_mpi( s, s, &e ) );
	MPI_CHK( mpi_mod_mpi( s, s, &grp->N ) );

	if( sign_tries++ > 10 )
	{
	ret = POLARSSL_ERR_ECP_RANDOM_FAILED;
	goto cleanup;
	}
	}
	while( mpi_cmp_int( s, 0 ) == 0 );

	cleanup:
	ecp_point_free( &R );
	mpi_free( &k ); mpi_free( &e ); mpi_free( &t );

	return( ret );
	}

	#if defined(POLARSSL_ECDSA_DETERMINISTIC)
	/*
	* Deterministic signature wrapper
	*/
	int ecdsa_sign_det( ecp_group grp, mpi r, mpi *s,
	const mpi d, const unsigned char buf, size_t blen,
	md_type_t md_alg )
	{
	int ret;
	hmac_drbg_context rng_ctx;
	unsigned char data[2 * POLARSSL_ECP_MAX_BYTES];
	size_t grp_len = ( grp->nbits + 7 ) / 8;
	const md_info_t *md_info;
	mpi h;

	if( ( md_info = md_info_from_type( md_alg ) ) == NULL )
	return( POLARSSL_ERR_ECP_BAD_INPUT_DATA );

	mpi_init( &h );
	memset( &rng_ctx, 0, sizeof( hmac_drbg_context ) );

	/* Use private key and message hash (reduced) to initialize HMAC_DRBG */
	MPI_CHK( mpi_write_binary( d, data, grp_len ) );
	MPI_CHK( derive_mpi( grp, &h, buf, blen ) );
	MPI_CHK( mpi_write_binary( &h, data + grp_len, grp_len ) );
	hmac_drbg_init_buf( &rng_ctx, md_info, data, 2 * grp_len );

	ret = ecdsa_sign( grp, r, s, d, buf, blen,
	hmac_drbg_random, &rng_ctx );

	cleanup:
	hmac_drbg_free( &rng_ctx );
	mpi_free( &h );

	return( ret );
	}
	#endif /* POLARSSL_ECDSA_DETERMINISTIC */

	/*
	* Verify ECDSA signature of hashed message (SEC1 4.1.4)
	* Obviously, compared to SEC1 4.1.3, we skip step 2 (hash message)
	*/
	int ecdsa_verify( ecp_group *grp,
	const unsigned char *buf, size_t blen,
	const ecp_point Q, const mpi r, const mpi *s)
	{
	int ret;
	mpi e, s_inv, u1, u2;
	ecp_point R, P;

	ecp_point_init( &R ); ecp_point_init( &P );
	mpi_init( &e ); mpi_init( &s_inv ); mpi_init( &u1 ); mpi_init( &u2 );

	/* Fail cleanly on curves such as Curve25519 that can't be used for ECDSA */
	if( grp->N.p == NULL )
	return( POLARSSL_ERR_ECP_BAD_INPUT_DATA );

	/*
	* Step 1: make sure r and s are in range 1..n-1
	*/
	if( mpi_cmp_int( r, 1 ) < 0 \|\| mpi_cmp_mpi( r, &grp->N ) >= 0 \|\|
	mpi_cmp_int( s, 1 ) < 0 \|\| mpi_cmp_mpi( s, &grp->N ) >= 0 )
	{
	ret = POLARSSL_ERR_ECP_VERIFY_FAILED;
	goto cleanup;
	}

	/*
	* Additional precaution: make sure Q is valid
	*/
	MPI_CHK( ecp_check_pubkey( grp, Q ) );

	/*
	* Step 3: derive MPI from hashed message
	*/
	MPI_CHK( derive_mpi( grp, &e, buf, blen ) );

	/*
	* Step 4: u1 = e / s mod n, u2 = r / s mod n
	*/
	MPI_CHK( mpi_inv_mod( &s_inv, s, &grp->N ) );

	MPI_CHK( mpi_mul_mpi( &u1, &e, &s_inv ) );
	MPI_CHK( mpi_mod_mpi( &u1, &u1, &grp->N ) );

	MPI_CHK( mpi_mul_mpi( &u2, r, &s_inv ) );
	MPI_CHK( mpi_mod_mpi( &u2, &u2, &grp->N ) );

	/*
	* Step 5: R = u1 G + u2 Q
	*
	* Since we're not using any secret data, no need to pass a RNG to
	* ecp_mul() for countermesures.
	*/
	MPI_CHK( ecp_mul( grp, &R, &u1, &grp->G, NULL, NULL ) );
	MPI_CHK( ecp_mul( grp, &P, &u2, Q, NULL, NULL ) );
	MPI_CHK( ecp_add( grp, &R, &R, &P ) );

	if( ecp_is_zero( &R ) )
	{
	ret = POLARSSL_ERR_ECP_VERIFY_FAILED;
	goto cleanup;
	}

	/*
	* Step 6: convert xR to an integer (no-op)
	* Step 7: reduce xR mod n (gives v)
	*/
	MPI_CHK( mpi_mod_mpi( &R.X, &R.X, &grp->N ) );

	/*
	* Step 8: check if v (that is, R.X) is equal to r
	*/
	if( mpi_cmp_mpi( &R.X, r ) != 0 )
	{
	ret = POLARSSL_ERR_ECP_VERIFY_FAILED;
	goto cleanup;
	}

	cleanup:
	ecp_point_free( &R ); ecp_point_free( &P );
	mpi_free( &e ); mpi_free( &s_inv ); mpi_free( &u1 ); mpi_free( &u2 );

	return( ret );
	}

	/*
	* Convert a signature (given by context) to ASN.1
	*/
	static int ecdsa_signature_to_asn1( const mpi r, const mpi s,
	unsigned char sig, size_t slen )
	{
	int ret;
	unsigned char buf[POLARSSL_ECDSA_MAX_LEN];
	unsigned char *p = buf + sizeof( buf );
	size_t len = 0;

	ASN1_CHK_ADD( len, asn1_write_mpi( &p, buf, s ) );
	ASN1_CHK_ADD( len, asn1_write_mpi( &p, buf, r ) );

	ASN1_CHK_ADD( len, asn1_write_len( &p, buf, len ) );
	ASN1_CHK_ADD( len, asn1_write_tag( &p, buf,
	ASN1_CONSTRUCTED \| ASN1_SEQUENCE ) );

	memcpy( sig, p, len );
	*slen = len;

	return( 0 );
	}

	/*
	* Compute and write signature
	*/
	int ecdsa_write_signature( ecdsa_context *ctx, md_type_t md_alg,
	const unsigned char *hash, size_t hlen,
	unsigned char sig, size_t slen,
	int (f_rng)(void , unsigned char *, size_t),
	void *p_rng )
	{
	int ret;
	mpi r, s;

	mpi_init( &r );
	mpi_init( &s );

	#if defined(POLARSSL_ECDSA_DETERMINISTIC)
	(void) f_rng;
	(void) p_rng;

	MPI_CHK( ecdsa_sign_det( &ctx->grp, &r, &s, &ctx->d,
	hash, hlen, md_alg ) );
	#else
	(void) md_alg;

	MPI_CHK( ecdsa_sign( &ctx->grp, &r, &s, &ctx->d,
	hash, hlen, f_rng, p_rng ) );
	#endif

	MPI_CHK( ecdsa_signature_to_asn1( &r, &s, sig, slen ) );

	cleanup:
	mpi_free( &r );
	mpi_free( &s );

	return( ret );
	}

	#if ! defined(POLARSSL_DEPRECATED_REMOVED)
	int ecdsa_write_signature_det( ecdsa_context *ctx,
	const unsigned char *hash, size_t hlen,
	unsigned char sig, size_t slen,
	md_type_t md_alg )
	{
	return( ecdsa_write_signature( ctx, md_alg, hash, hlen, sig, slen,
	NULL, NULL ) );
	}
	#endif

	/*
	* Read and check signature
	*/
	int ecdsa_read_signature( ecdsa_context *ctx,
	const unsigned char *hash, size_t hlen,
	const unsigned char *sig, size_t slen )
	{
	int ret;
	unsigned char p = (unsigned char ) sig;
	const unsigned char *end = sig + slen;
	size_t len;
	mpi r, s;

	mpi_init( &r );
	mpi_init( &s );

	if( ( ret = asn1_get_tag( &p, end, &len,
	ASN1_CONSTRUCTED \| ASN1_SEQUENCE ) ) != 0 )
	{
	ret += POLARSSL_ERR_ECP_BAD_INPUT_DATA;
	goto cleanup;
	}

	if( p + len != end )
	{
	ret = POLARSSL_ERR_ECP_BAD_INPUT_DATA +
	POLARSSL_ERR_ASN1_LENGTH_MISMATCH;
	goto cleanup;
	}

	if( ( ret = asn1_get_mpi( &p, end, &r ) ) != 0 \|\|
	( ret = asn1_get_mpi( &p, end, &s ) ) != 0 )
	{
	ret += POLARSSL_ERR_ECP_BAD_INPUT_DATA;
	goto cleanup;
	}

	if( ( ret = ecdsa_verify( &ctx->grp, hash, hlen,
	&ctx->Q, &r, &s ) ) != 0 )
	goto cleanup;

	if( p != end )
	ret = POLARSSL_ERR_ECP_SIG_LEN_MISMATCH;

	cleanup:
	mpi_free( &r );
	mpi_free( &s );

	return( ret );
	}

	/*
	* Generate key pair
	*/
	int ecdsa_genkey( ecdsa_context *ctx, ecp_group_id gid,
	int (f_rng)(void , unsigned char , size_t), void p_rng )
	{
	return( ecp_use_known_dp( &ctx->grp, gid ) \|\|
	ecp_gen_keypair( &ctx->grp, &ctx->d, &ctx->Q, f_rng, p_rng ) );
	}

	/*
	* Set context from an ecp_keypair
	*/
	int ecdsa_from_keypair( ecdsa_context ctx, const ecp_keypair key )
	{
	int ret;

	if( ( ret = ecp_group_copy( &ctx->grp, &key->grp ) ) != 0 \|\|
	( ret = mpi_copy( &ctx->d, &key->d ) ) != 0 \|\|
	( ret = ecp_copy( &ctx->Q, &key->Q ) ) != 0 )
	{
	ecdsa_free( ctx );
	}

	return( ret );
	}

	/*
	* Initialize context
	*/
	void ecdsa_init( ecdsa_context *ctx )
	{
	ecp_keypair_init( ctx );
	}

	/*
	* Free context
	*/
	void ecdsa_free( ecdsa_context *ctx )
	{
	ecp_keypair_free( ctx );
	}

	#endif /* POLARSSL_ECDSA_C */