EC_GROUP *EC_GROUP_new_curve_GFp(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
	{
	const EC_METHOD *meth;
	EC_GROUP *ret;

	meth = EC_GFp_nist_method();
	
	ret = EC_GROUP_new(meth);
	if (ret == NULL)
		return NULL;

	if (!EC_GROUP_set_curve_GFp(ret, p, a, b, ctx))
		{
		unsigned long err;
		  
		err = ERR_peek_last_error();

		if (!(ERR_GET_LIB(err) == ERR_LIB_EC &&
			((ERR_GET_REASON(err) == EC_R_NOT_A_NIST_PRIME) ||
			 (ERR_GET_REASON(err) == EC_R_NOT_A_SUPPORTED_NIST_PRIME))))
			{
			/* real error */
			
			EC_GROUP_clear_free(ret);
			return NULL;
			}
			
		
		/* not an actual error, we just cannot use EC_GFp_nist_method */

		ERR_clear_error();

		EC_GROUP_clear_free(ret);
		meth = EC_GFp_mont_method();

		ret = EC_GROUP_new(meth);
		if (ret == NULL)
			return NULL;

		if (!EC_GROUP_set_curve_GFp(ret, p, a, b, ctx))
			{
			EC_GROUP_clear_free(ret);
			return NULL;
			}
		}

	return ret;
	}
示例#2
0
EC_KEY *
EC_KEY_copy(EC_KEY * dest, const EC_KEY * src)
{
	EC_EXTRA_DATA *d;

	if (dest == NULL || src == NULL) {
		ECerr(EC_F_EC_KEY_COPY, ERR_R_PASSED_NULL_PARAMETER);
		return NULL;
	}
	/* copy the parameters */
	if (src->group) {
		const EC_METHOD *meth = EC_GROUP_method_of(src->group);
		/* clear the old group */
		EC_GROUP_free(dest->group);
		dest->group = EC_GROUP_new(meth);
		if (dest->group == NULL)
			return NULL;
		if (!EC_GROUP_copy(dest->group, src->group))
			return NULL;
	}
	/* copy the public key */
	if (src->pub_key && src->group) {
		EC_POINT_free(dest->pub_key);
		dest->pub_key = EC_POINT_new(src->group);
		if (dest->pub_key == NULL)
			return NULL;
		if (!EC_POINT_copy(dest->pub_key, src->pub_key))
			return NULL;
	}
	/* copy the private key */
	if (src->priv_key) {
		if (dest->priv_key == NULL) {
			dest->priv_key = BN_new();
			if (dest->priv_key == NULL)
				return NULL;
		}
		if (!BN_copy(dest->priv_key, src->priv_key))
			return NULL;
	}
	/* copy method/extra data */
	EC_EX_DATA_free_all_data(&dest->method_data);

	for (d = src->method_data; d != NULL; d = d->next) {
		void *t = d->dup_func(d->data);

		if (t == NULL)
			return 0;
		if (!EC_EX_DATA_set_data(&dest->method_data, t, d->dup_func,
		    d->free_func, d->clear_free_func))
			return 0;
	}

	/* copy the rest */
	dest->enc_flag = src->enc_flag;
	dest->conv_form = src->conv_form;
	dest->version = src->version;
	dest->flags = src->flags;

	return dest;
}
示例#3
0
EC_GROUP *EC_GROUP_new_curve_GFp(const BIGNUM *p, const BIGNUM *a,
                                 const BIGNUM *b, BN_CTX *ctx)
{
    const EC_METHOD *meth;
    EC_GROUP *ret;

#if defined(OPENSSL_BN_ASM_MONT)
    /*
     * This might appear controversial, but the fact is that generic
     * prime method was observed to deliver better performance even
     * for NIST primes on a range of platforms, e.g.: 60%-15%
     * improvement on IA-64, ~25% on ARM, 30%-90% on P4, 20%-25%
     * in 32-bit build and 35%--12% in 64-bit build on Core2...
     * Coefficients are relative to optimized bn_nist.c for most
     * intensive ECDSA verify and ECDH operations for 192- and 521-
     * bit keys respectively. Choice of these boundary values is
     * arguable, because the dependency of improvement coefficient
     * from key length is not a "monotone" curve. For example while
     * 571-bit result is 23% on ARM, 384-bit one is -1%. But it's
     * generally faster, sometimes "respectfully" faster, sometimes
     * "tolerably" slower... What effectively happens is that loop
     * with bn_mul_add_words is put against bn_mul_mont, and the
     * latter "wins" on short vectors. Correct solution should be
     * implementing dedicated NxN multiplication subroutines for
     * small N. But till it materializes, let's stick to generic
     * prime method...
     *                                              <appro>
     */
    meth = EC_GFp_mont_method();
#else
    if (BN_nist_mod_func(p))
        meth = EC_GFp_nist_method();
    else
        meth = EC_GFp_mont_method();
#endif

    ret = EC_GROUP_new(meth);
    if (ret == NULL)
        return NULL;

    if (!EC_GROUP_set_curve(ret, p, a, b, ctx)) {
        EC_GROUP_clear_free(ret);
        return NULL;
    }

    return ret;
}
示例#4
0
EC_GROUP *
EC_GROUP_new_curve_GF2m(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b,
    BN_CTX *ctx)
{
	const EC_METHOD *meth;
	EC_GROUP *ret;

	meth = EC_GF2m_simple_method();

	ret = EC_GROUP_new(meth);
	if (ret == NULL)
		return NULL;

	if (!EC_GROUP_set_curve_GF2m(ret, p, a, b, ctx)) {
		EC_GROUP_clear_free(ret);
		return NULL;
	}
	return ret;
}
示例#5
0
文件: ec_lib.c 项目: LucidOne/Rovio
EC_GROUP *EC_GROUP_dup(const EC_GROUP *a)
	{
	EC_GROUP *t = NULL;
	int ok = 0;

	if (a == NULL) return NULL;

	if ((t = EC_GROUP_new(a->meth)) == NULL) return(NULL);
	if (!EC_GROUP_copy(t, a)) goto err;

	ok = 1;

  err:	
	if (!ok)
		{
		if (t) EC_GROUP_free(t);
		return NULL;
		}
	else return t;
	}
示例#6
0
文件: ec_cvt.c 项目: Orav/kbengine
EC_GROUP *EC_GROUP_new_curve_GF2m(const BIGNUM *p, const BIGNUM *a,
                                  const BIGNUM *b, BN_CTX *ctx)
{
    const EC_METHOD *meth;
    EC_GROUP *ret;

# ifdef OPENSSL_FIPS
    if (FIPS_mode())
        return FIPS_ec_group_new_curve_gf2m(p, a, b, ctx);
# endif
    meth = EC_GF2m_simple_method();

    ret = EC_GROUP_new(meth);
    if (ret == NULL)
        return NULL;

    if (!EC_GROUP_set_curve_GF2m(ret, p, a, b, ctx)) {
        EC_GROUP_clear_free(ret);
        return NULL;
    }

    return ret;
}
示例#7
0
EC_KEY *EC_KEY_copy(EC_KEY *dest, const EC_KEY *src)
{
    if (dest == NULL || src == NULL) {
        ECerr(EC_F_EC_KEY_COPY, ERR_R_PASSED_NULL_PARAMETER);
        return NULL;
    }
    if (src->meth != dest->meth) {
        if (dest->meth->finish != NULL)
            dest->meth->finish(dest);
        if (dest->group && dest->group->meth->keyfinish)
            dest->group->meth->keyfinish(dest);
#ifndef OPENSSL_NO_ENGINE
        if (ENGINE_finish(dest->engine) == 0)
            return 0;
        dest->engine = NULL;
#endif
    }
    /* copy the parameters */
    if (src->group != NULL) {
        const EC_METHOD *meth = EC_GROUP_method_of(src->group);
        /* clear the old group */
        EC_GROUP_free(dest->group);
        dest->group = EC_GROUP_new(meth);
        if (dest->group == NULL)
            return NULL;
        if (!EC_GROUP_copy(dest->group, src->group))
            return NULL;

        /*  copy the public key */
        if (src->pub_key != NULL) {
            EC_POINT_free(dest->pub_key);
            dest->pub_key = EC_POINT_new(src->group);
            if (dest->pub_key == NULL)
                return NULL;
            if (!EC_POINT_copy(dest->pub_key, src->pub_key))
                return NULL;
        }
        /* copy the private key */
        if (src->priv_key != NULL) {
            if (dest->priv_key == NULL) {
                dest->priv_key = BN_new();
                if (dest->priv_key == NULL)
                    return NULL;
            }
            if (!BN_copy(dest->priv_key, src->priv_key))
                return NULL;
            if (src->group->meth->keycopy
                && src->group->meth->keycopy(dest, src) == 0)
                return NULL;
        }
    }


    /* copy the rest */
    dest->enc_flag = src->enc_flag;
    dest->conv_form = src->conv_form;
    dest->version = src->version;
    dest->flags = src->flags;
    if (!CRYPTO_dup_ex_data(CRYPTO_EX_INDEX_EC_KEY,
                            &dest->ex_data, &src->ex_data))
        return NULL;

    if (src->meth != dest->meth) {
#ifndef OPENSSL_NO_ENGINE
        if (src->engine != NULL && ENGINE_init(src->engine) == 0)
            return NULL;
        dest->engine = src->engine;
#endif
        dest->meth = src->meth;
    }

    if (src->meth->copy != NULL && src->meth->copy(dest, src) == 0)
        return NULL;

    return dest;
}
示例#8
0
文件: sm2test.c 项目: weicz/GmSSL
void  SM2PKE_test3()
{
	/* test3 params */
	const char *p = "8542D69E4C044F18E8B92435BF6FF7DE457283915C45517D722EDB8B08F1DFC3";
	const char *a = "787968B4FA32C3FD2417842E73BBFEFF2F3C848B6831D7E0EC65228B3937E498";
	const char *b = "63E4C6D3B23B0C849CF84241484BFE48F61D59A5B16BA06E6E12D1DA27C5249A";
	const char *xG = "421DEBD61B62EAB6746434EBC3CC315E32220B3BADD50BDC4C4E6C147FEDD43D";
	const char *yG = "0680512BCBB42C07D47349D2153B70C4E5D7FDFCBFA36EA1A85841B9E46E09A2";
	const char *n = "8542D69E4C044F18E8B92435BF6FF7DD297720630485628D5AE74EE7C32E79B7";
	const char *dB = "1649AB77A00637BD5E2EFE283FBF353534AA7F7CB89463F208DDBC2920BB0DA0";
	const char *xB = "435B39CCA8F3B508C1488AFC67BE491A0F7BA07E581A0E4849A5CF70628A7E0A";
	const char *yB = "75DDBA78F15FEECB4C7895E2C1CDF5FE01DEBB2CDBADF45399CCF77BBA076A42";
	
	BIGNUM *bn_p = BN_new();
	BN_hex2bn(&bn_p, p);
	BIGNUM *bn_a = BN_new();
	BN_hex2bn(&bn_a, a);
	BIGNUM *bn_b = BN_new();
	BN_hex2bn(&bn_b, b);
	BIGNUM *bn_xG = BN_new();
	BN_hex2bn(&bn_xG, xG);
	BIGNUM *bn_yG = BN_new();
	BN_hex2bn(&bn_yG, yG);
	BIGNUM *bn_n = BN_new();
	BN_hex2bn(&bn_n, n);
	BIGNUM *bn_dB = BN_new();
	BN_hex2bn(&bn_dB, dB);
	BIGNUM *bn_xB = BN_new();
	BN_hex2bn(&bn_xB, xB);
	BIGNUM *bn_yB = BN_new();
	BN_hex2bn(&bn_yB, yB);
	
	BN_CTX *bn_ctx = BN_CTX_new();
	EC_GROUP *ec_group = EC_GROUP_new(EC_GFp_mont_method());
	EC_GROUP_set_curve_GFp(ec_group, bn_p, bn_a, bn_b, bn_ctx);

	EC_POINT *G = EC_POINT_new(ec_group);
	EC_POINT_set_affine_coordinates_GFp(ec_group, G, bn_xG, bn_yG, bn_ctx);
	BIGNUM *bn_h = BN_new();	/* cofactor h = #E(Fp) / n */
	BN_div(bn_h, NULL, bn_p, bn_n, bn_ctx);
	EC_GROUP_set_generator(ec_group, G, bn_n, bn_h);
	
	EC_POINT *PB = EC_POINT_new(ec_group);
	EC_POINT_set_affine_coordinates_GFp(ec_group, PB, bn_xB, bn_yB, bn_ctx);
	EC_KEY *ec_key_B = EC_KEY_new();
	EC_KEY_set_group(ec_key_B, ec_group);
	EC_KEY_set_private_key(ec_key_B, bn_dB);
	EC_KEY_set_public_key(ec_key_B, PB);
	
	BN_free(bn_p);
	BN_free(bn_a);
	BN_free(bn_b);
	BN_free(bn_n);
	BN_free(bn_xG);
	BN_free(bn_yG);
	BN_free(bn_dB);
	BN_free(bn_xB);
	BN_free(bn_yB);
	BN_free(bn_h);
	BN_CTX_free(bn_ctx);
	EC_POINT_free(G);
	EC_POINT_free(PB);
	EC_GROUP_free(ec_group);

	char *M = "encryption standard";
	char *ctest = "04245C26FB68B1DDDDB12C4B6BF9F2B6D5FE60A383B0D18D1C4144ABF17F6252"
	"E776CB9264C2A7E88E52B19903FDC47378F605E36811F5C07423A24B84400F01"
	"B8650053A89B41C418B0C3AAD00D886C002864679C3D7360C30156FAB7C80A02"
	"76712DA9D8094A634B766D3A285E07480653426D";
	BIGNUM *ct = BN_new();
	BN_hex2bn(&ct, ctest);
	unsigned char ct2bin[116];
	BN_bn2bin(ct, ct2bin);
	BN_free(ct);

	int mlen = strlen(M);
	int c1len = PRIME_SIZE / 8 * 2 + 1;
	int clen = c1len + mlen + HASH_V / 8;
	
	unsigned char *C = malloc(sizeof(unsigned char) * clen);
	sm2_pke_encrypt(C, M, mlen, ec_key_B);	
	if (memcmp(C, ct2bin, clen) == 0)
		printf("sm2_pke_encrypt passed.\n");
	else 
		printf("sm2_pke_encrypt failed.\n");
	free(C);
	
	int m1len = clen - c1len - HASH_V / 8;
	unsigned char *M1bin = malloc(sizeof(unsigned char) * m1len);
	sm2_pke_decrypt((char *)ct2bin, M1bin, m1len, ec_key_B);	
	if (memcmp(M1bin, M, m1len) == 0)
		printf("sm2_pke_decrypt passed.\n");
	else 
		printf("sm2_pke_decrypt failed.\n");
	free(M1bin);

	EC_KEY_free(ec_key_B);
}
示例#9
0
static EC_GROUP *ec_group_new_from_data(const ec_list_element curve)
	{
	EC_GROUP *group=NULL;
	EC_POINT *P=NULL;
	BN_CTX	 *ctx=NULL;
	BIGNUM	 *p=NULL, *a=NULL, *b=NULL, *x=NULL, *y=NULL, *order=NULL;
	int	 ok=0;
	int	 seed_len,param_len;
	const EC_METHOD *meth;
	const EC_CURVE_DATA *data;
	const unsigned char *params;

	if ((ctx = BN_CTX_new()) == NULL)
		{
		ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_MALLOC_FAILURE);
		goto err;
		}

	data = curve.data;
	seed_len  = data->seed_len;
	param_len = data->param_len;
	params	  = (const unsigned char *)(data+1);	/* skip header */
	params	 += seed_len;				/* skip seed   */

	if (!(p = BN_bin2bn(params+0*param_len, param_len, NULL))
		|| !(a = BN_bin2bn(params+1*param_len, param_len, NULL))
		|| !(b = BN_bin2bn(params+2*param_len, param_len, NULL)))
		{
		ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_BN_LIB);
		goto err;
		}

	if (curve.meth != 0)
		{
		meth = curve.meth();
		if (((group = EC_GROUP_new(meth)) == NULL) ||
			(!(group->meth->group_set_curve(group, p, a, b, ctx))))
			{
			ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB);
			goto err;
			}
		}
	else if (data->field_type == NID_X9_62_prime_field)
		{
		if ((group = EC_GROUP_new_curve_GFp(p, a, b, ctx)) == NULL)
			{
			ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB);
			goto err;
			}
		}
#ifndef OPENSSL_NO_EC2M
	else	/* field_type == NID_X9_62_characteristic_two_field */
		{
		if ((group = EC_GROUP_new_curve_GF2m(p, a, b, ctx)) == NULL)
			{
			ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB);
			goto err;
			}
		}
#endif

	if ((P = EC_POINT_new(group)) == NULL)
		{
		ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB);
		goto err;
		}

	if (!(x = BN_bin2bn(params+3*param_len, param_len, NULL))
		|| !(y = BN_bin2bn(params+4*param_len, param_len, NULL)))
		{
		ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_BN_LIB);
		goto err;
		}
	if (!EC_POINT_set_affine_coordinates_GFp(group, P, x, y, ctx))
		{
		ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB);
		goto err;
		}
	if (!(order = BN_bin2bn(params+5*param_len, param_len, NULL))
		|| !BN_set_word(x, (BN_ULONG)data->cofactor))
		{
		ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_BN_LIB);
		goto err;
		}
	if (!EC_GROUP_set_generator(group, P, order, x))
		{
		ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB);
		goto err;
		}
	if (seed_len)
		{
		if (!EC_GROUP_set_seed(group, params-seed_len, seed_len))
			{
			ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB);
			goto err;
			}
		}
	ok=1;
err:
	if (!ok)
		{
		EC_GROUP_free(group);
		group = NULL;
		}
	if (P)
		EC_POINT_free(P);
	if (ctx)
		BN_CTX_free(ctx);
	if (p)
		BN_free(p);
	if (a)
		BN_free(a);
	if (b)
		BN_free(b);
	if (order)
		BN_free(order);
	if (x)
		BN_free(x);
	if (y)
		BN_free(y);
	return group;
	}
示例#10
0
int main()
{
    BIGNUM   *x, *y, *exp, *m, *order, *cof;
    BIGNUM   t, store[30];
    COMPLEX  *a, *b, *r;
    EC_POINT *point, *Q;
    int      i;

    x = BN_new();
    y = BN_new();
    order = BN_new();
    exp = BN_new();
    m = BN_new();

    a = COMP_new();
    b = COMP_new();
    r = COMP_new();
    for( i = 0; i < 30; i++ )
    	BN_init( &(store[i]) );

    if ( Context == NULL )
    	Context = BN_CTX_new();

    bi_init( &malloc );

    group = EC_GROUP_new( EC_GFp_simple_method() );
    if ( group == NULL )
    	goto err;

    if(!BN_set_word(m, 43l))
    	goto err;
    BN_set_word(x, 1l);
    BN_set_word(y, 0l);

    if ( !EC_GROUP_set_curve_GFp( group, m, x, y, Context) )
    	goto err;

    BN_set_word(x, 23l);
    BN_set_word(y, 8l);
    BN_set_word(order, 11l);

    point = EC_POINT_new( group );
    EC_POINT_set_affine_coordinates_GFp( group, point, x, y, Context );

    cof = BN_new();
    BN_set_word( cof, 4 );
    EC_GROUP_set_generator( group, point, order, cof );

    if ( EC_GROUP_check( group, Context ) )
    	printf(" group set is ok \n");

    TSS_DAA_ISSUER_KEY   issuer_key;
    TSS_DAA_ISSUER_PROOF issuer_proof;
    TSS_DAA_JOIN_issuer_setup(&issuer_key, &issuer_proof);


//    printf("\n");
//    BN_set_word(x, 41l);
//    BN_mod_inverse(x, x, m, Context);
//    BN_print_fp(stdout, x);
//
//    printf("\n");
//    BN_set_word(x, 11l);
//    BN_mod_inverse(x, x, m, Context);
//    BN_print_fp(stdout, x);

    char *str = "abcdefghijklmnop";
    Q = map_to_point( str );

    BN_set_word(x, 23l);
    BN_set_word(y, 8l);
    BN_set_word(order, 11l);

    Q = EC_POINT_new( group );
    EC_POINT_set_affine_coordinates_GFp( group, Q, x, y, Context );

    Tate( point, Q, order, 0,  store, a );
    printf("tate pair  t(p, Q) =:\n a.x: ");
    BN_print_fp(stdout, &a->x);
    printf("\na.y: ");
    BN_print_fp(stdout, &a->y);

    EC_POINT_dbl( group, point, point, Context);
    EC_POINT_get_affine_coordinates_GFp( group, point, x, y, Context);
    printf("2A.x =:\n");
    BN_print_fp(stdout, x);
    printf("2P.y= :\n");
    BN_print_fp(stdout, y);

    Tate( point, Q, order, 0,  store, a );
    printf("tate pair  t(2p, Q) =:\n a.x: ");
    BN_print_fp(stdout, &a->x);
    printf("\na.y: ");
    BN_print_fp(stdout, &a->y);

    BN_free( x );
    BN_free( y );
    BN_free( exp );
    BN_free( m );
    BN_free( order );
    BN_free( cof );

    COMP_free( a );
    COMP_free( b );
    COMP_free( r );

	return 0;
err:
	BN_free( &t );
	BN_free( x );
	BN_free( y );
	BN_free( exp );
	BN_free( m );
    BN_free( order );
    BN_free( cof );

	COMP_free( a );
	COMP_free( b );
	COMP_free( r );

	return 0;
}
void char2_field_tests()
	{	
	BN_CTX *ctx = NULL;
	BIGNUM *p, *a, *b;
	EC_GROUP *group;
	EC_GROUP *C2_K163 = NULL, *C2_K233 = NULL, *C2_K283 = NULL, *C2_K409 = NULL, *C2_K571 = NULL;
	EC_GROUP *C2_B163 = NULL, *C2_B233 = NULL, *C2_B283 = NULL, *C2_B409 = NULL, *C2_B571 = NULL;
	EC_POINT *P, *Q, *R;
	BIGNUM *x, *y, *z, *cof;
	unsigned char buf[100];
	size_t i, len;
	int k;
	
#if 1 /* optional */
	ctx = BN_CTX_new();
	if (!ctx) ABORT;
#endif

	p = BN_new();
	a = BN_new();
	b = BN_new();
	if (!p || !a || !b) ABORT;

	if (!BN_hex2bn(&p, "13")) ABORT;
	if (!BN_hex2bn(&a, "3")) ABORT;
	if (!BN_hex2bn(&b, "1")) ABORT;
	
	group = EC_GROUP_new(EC_GF2m_simple_method()); /* applications should use EC_GROUP_new_curve_GF2m
	                                                * so that the library gets to choose the EC_METHOD */
	if (!group) ABORT;
	if (!EC_GROUP_set_curve_GF2m(group, p, a, b, ctx)) ABORT;

	{
		EC_GROUP *tmp;
		tmp = EC_GROUP_new(EC_GROUP_method_of(group));
		if (!tmp) ABORT;
		if (!EC_GROUP_copy(tmp, group)) ABORT;
		EC_GROUP_free(group);
		group = tmp;
	}
	
	if (!EC_GROUP_get_curve_GF2m(group, p, a, b, ctx)) ABORT;

	fprintf(stdout, "Curve defined by Weierstrass equation\n     y^2 + x*y = x^3 + a*x^2 + b  (mod 0x");
	BN_print_fp(stdout, p);
	fprintf(stdout, ")\n     a = 0x");
	BN_print_fp(stdout, a);
	fprintf(stdout, "\n     b = 0x");
	BN_print_fp(stdout, b);
	fprintf(stdout, "\n(0x... means binary polynomial)\n");

	P = EC_POINT_new(group);
	Q = EC_POINT_new(group);
	R = EC_POINT_new(group);
	if (!P || !Q || !R) ABORT;
	
	if (!EC_POINT_set_to_infinity(group, P)) ABORT;
	if (!EC_POINT_is_at_infinity(group, P)) ABORT;

	buf[0] = 0;
	if (!EC_POINT_oct2point(group, Q, buf, 1, ctx)) ABORT;

	if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
	if (!EC_POINT_is_at_infinity(group, P)) ABORT;

	x = BN_new();
	y = BN_new();
	z = BN_new();
	cof = BN_new();
	if (!x || !y || !z || !cof) ABORT;

	if (!BN_hex2bn(&x, "6")) ABORT;
/* Change test based on whether binary point compression is enabled or not. */
#ifdef OPENSSL_EC_BIN_PT_COMP
	if (!EC_POINT_set_compressed_coordinates_GF2m(group, Q, x, 1, ctx)) ABORT;
#else
	if (!BN_hex2bn(&y, "8")) ABORT;
	if (!EC_POINT_set_affine_coordinates_GF2m(group, Q, x, y, ctx)) ABORT;
#endif
	if (!EC_POINT_is_on_curve(group, Q, ctx))
		{
/* Change test based on whether binary point compression is enabled or not. */
#ifdef OPENSSL_EC_BIN_PT_COMP
		if (!EC_POINT_get_affine_coordinates_GF2m(group, Q, x, y, ctx)) ABORT;
#endif
		fprintf(stderr, "Point is not on curve: x = 0x");
		BN_print_fp(stderr, x);
		fprintf(stderr, ", y = 0x");
		BN_print_fp(stderr, y);
		fprintf(stderr, "\n");
		ABORT;
		}

	fprintf(stdout, "A cyclic subgroup:\n");
	k = 100;
	do
		{
		if (k-- == 0) ABORT;

		if (EC_POINT_is_at_infinity(group, P))
			fprintf(stdout, "     point at infinity\n");
		else
			{
			if (!EC_POINT_get_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT;

			fprintf(stdout, "     x = 0x");
			BN_print_fp(stdout, x);
			fprintf(stdout, ", y = 0x");
			BN_print_fp(stdout, y);
			fprintf(stdout, "\n");
			}
		
		if (!EC_POINT_copy(R, P)) ABORT;
		if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
		}
	while (!EC_POINT_is_at_infinity(group, P));

	if (!EC_POINT_add(group, P, Q, R, ctx)) ABORT;
	if (!EC_POINT_is_at_infinity(group, P)) ABORT;

/* Change test based on whether binary point compression is enabled or not. */
#ifdef OPENSSL_EC_BIN_PT_COMP
	len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf, sizeof buf, ctx);
	if (len == 0) ABORT;
	if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
	if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
	fprintf(stdout, "Generator as octet string, compressed form:\n     ");
	for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
#endif
	
	len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, sizeof buf, ctx);
	if (len == 0) ABORT;
	if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
	if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
	fprintf(stdout, "\nGenerator as octet string, uncompressed form:\n     ");
	for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
	
/* Change test based on whether binary point compression is enabled or not. */
#ifdef OPENSSL_EC_BIN_PT_COMP
	len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf, ctx);
	if (len == 0) ABORT;
	if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
	if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
	fprintf(stdout, "\nGenerator as octet string, hybrid form:\n     ");
	for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
#endif

	fprintf(stdout, "\n");
	
	if (!EC_POINT_invert(group, P, ctx)) ABORT;
	if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;


	/* Curve K-163 (FIPS PUB 186-2, App. 6) */
	CHAR2_CURVE_TEST
		(
		"NIST curve K-163",
		"0800000000000000000000000000000000000000C9",
		"1",
		"1",
		"02FE13C0537BBC11ACAA07D793DE4E6D5E5C94EEE8",
		"0289070FB05D38FF58321F2E800536D538CCDAA3D9",
		1,
		"04000000000000000000020108A2E0CC0D99F8A5EF",
		"2",
		163,
		C2_K163
		);

	/* Curve B-163 (FIPS PUB 186-2, App. 6) */
	CHAR2_CURVE_TEST
		(
		"NIST curve B-163",
		"0800000000000000000000000000000000000000C9",
		"1",
		"020A601907B8C953CA1481EB10512F78744A3205FD",
		"03F0EBA16286A2D57EA0991168D4994637E8343E36",
		"00D51FBC6C71A0094FA2CDD545B11C5C0C797324F1",
		1,
		"040000000000000000000292FE77E70C12A4234C33",
		"2",
		163,
		C2_B163
		);

	/* Curve K-233 (FIPS PUB 186-2, App. 6) */
	CHAR2_CURVE_TEST
		(
		"NIST curve K-233",
		"020000000000000000000000000000000000000004000000000000000001",
		"0",
		"1",
		"017232BA853A7E731AF129F22FF4149563A419C26BF50A4C9D6EEFAD6126",
		"01DB537DECE819B7F70F555A67C427A8CD9BF18AEB9B56E0C11056FAE6A3",
		0,
		"008000000000000000000000000000069D5BB915BCD46EFB1AD5F173ABDF",
		"4",
		233,
		C2_K233
		);

	/* Curve B-233 (FIPS PUB 186-2, App. 6) */
	CHAR2_CURVE_TEST
		(
		"NIST curve B-233",
		"020000000000000000000000000000000000000004000000000000000001",
		"000000000000000000000000000000000000000000000000000000000001",
		"0066647EDE6C332C7F8C0923BB58213B333B20E9CE4281FE115F7D8F90AD",
		"00FAC9DFCBAC8313BB2139F1BB755FEF65BC391F8B36F8F8EB7371FD558B",
		"01006A08A41903350678E58528BEBF8A0BEFF867A7CA36716F7E01F81052",
		1,
		"01000000000000000000000000000013E974E72F8A6922031D2603CFE0D7",
		"2",
		233,
		C2_B233
		);

	/* Curve K-283 (FIPS PUB 186-2, App. 6) */
	CHAR2_CURVE_TEST
		(
		"NIST curve K-283",
		"0800000000000000000000000000000000000000000000000000000000000000000010A1",
		"0",
		"1",
		"0503213F78CA44883F1A3B8162F188E553CD265F23C1567A16876913B0C2AC2458492836",
		"01CCDA380F1C9E318D90F95D07E5426FE87E45C0E8184698E45962364E34116177DD2259",
		0,
		"01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE9AE2ED07577265DFF7F94451E061E163C61",
		"4",
		283,
		C2_K283
		);

	/* Curve B-283 (FIPS PUB 186-2, App. 6) */
	CHAR2_CURVE_TEST
		(
		"NIST curve B-283",
		"0800000000000000000000000000000000000000000000000000000000000000000010A1",
		"000000000000000000000000000000000000000000000000000000000000000000000001",
		"027B680AC8B8596DA5A4AF8A19A0303FCA97FD7645309FA2A581485AF6263E313B79A2F5",
		"05F939258DB7DD90E1934F8C70B0DFEC2EED25B8557EAC9C80E2E198F8CDBECD86B12053",
		"03676854FE24141CB98FE6D4B20D02B4516FF702350EDDB0826779C813F0DF45BE8112F4",
		1,
		"03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEF90399660FC938A90165B042A7CEFADB307",
		"2",
		283,
		C2_B283
		);

	/* Curve K-409 (FIPS PUB 186-2, App. 6) */
	CHAR2_CURVE_TEST
		(
		"NIST curve K-409",
		"02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001",
		"0",
		"1",
		"0060F05F658F49C1AD3AB1890F7184210EFD0987E307C84C27ACCFB8F9F67CC2C460189EB5AAAA62EE222EB1B35540CFE9023746",
		"01E369050B7C4E42ACBA1DACBF04299C3460782F918EA427E6325165E9EA10E3DA5F6C42E9C55215AA9CA27A5863EC48D8E0286B",
		1,
		"007FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE5F83B2D4EA20400EC4557D5ED3E3E7CA5B4B5C83B8E01E5FCF",
		"4",
		409,
		C2_K409
		);

	/* Curve B-409 (FIPS PUB 186-2, App. 6) */
	CHAR2_CURVE_TEST
		(
		"NIST curve B-409",
		"02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001",
		"00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
		"0021A5C2C8EE9FEB5C4B9A753B7B476B7FD6422EF1F3DD674761FA99D6AC27C8A9A197B272822F6CD57A55AA4F50AE317B13545F",
		"015D4860D088DDB3496B0C6064756260441CDE4AF1771D4DB01FFE5B34E59703DC255A868A1180515603AEAB60794E54BB7996A7",
		"0061B1CFAB6BE5F32BBFA78324ED106A7636B9C5A7BD198D0158AA4F5488D08F38514F1FDF4B4F40D2181B3681C364BA0273C706",
		1,
		"010000000000000000000000000000000000000000000000000001E2AAD6A612F33307BE5FA47C3C9E052F838164CD37D9A21173",
		"2",
		409,
		C2_B409
		);

	/* Curve K-571 (FIPS PUB 186-2, App. 6) */
	CHAR2_CURVE_TEST
		(
		"NIST curve K-571",
		"80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425",
		"0",
		"1",
		"026EB7A859923FBC82189631F8103FE4AC9CA2970012D5D46024804801841CA44370958493B205E647DA304DB4CEB08CBBD1BA39494776FB988B47174DCA88C7E2945283A01C8972",
		"0349DC807F4FBF374F4AEADE3BCA95314DD58CEC9F307A54FFC61EFC006D8A2C9D4979C0AC44AEA74FBEBBB9F772AEDCB620B01A7BA7AF1B320430C8591984F601CD4C143EF1C7A3",
		0,
		"020000000000000000000000000000000000000000000000000000000000000000000000131850E1F19A63E4B391A8DB917F4138B630D84BE5D639381E91DEB45CFE778F637C1001",
		"4",
		571,
		C2_K571
		);

	/* Curve B-571 (FIPS PUB 186-2, App. 6) */
	CHAR2_CURVE_TEST
		(
		"NIST curve B-571",
		"80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425",
		"000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
		"02F40E7E2221F295DE297117B7F3D62F5C6A97FFCB8CEFF1CD6BA8CE4A9A18AD84FFABBD8EFA59332BE7AD6756A66E294AFD185A78FF12AA520E4DE739BACA0C7FFEFF7F2955727A",
		"0303001D34B856296C16C0D40D3CD7750A93D1D2955FA80AA5F40FC8DB7B2ABDBDE53950F4C0D293CDD711A35B67FB1499AE60038614F1394ABFA3B4C850D927E1E7769C8EEC2D19",
		"037BF27342DA639B6DCCFFFEB73D69D78C6C27A6009CBBCA1980F8533921E8A684423E43BAB08A576291AF8F461BB2A8B3531D2F0485C19B16E2F1516E23DD3C1A4827AF1B8AC15B",
		1,
		"03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE661CE18FF55987308059B186823851EC7DD9CA1161DE93D5174D66E8382E9BB2FE84E47",
		"2",
		571,
		C2_B571
		);

	/* more tests using the last curve */

	if (!EC_POINT_copy(Q, P)) ABORT;
	if (EC_POINT_is_at_infinity(group, Q)) ABORT;
	if (!EC_POINT_dbl(group, P, P, ctx)) ABORT;
	if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
	if (!EC_POINT_invert(group, Q, ctx)) ABORT; /* P = -2Q */

	if (!EC_POINT_add(group, R, P, Q, ctx)) ABORT;
	if (!EC_POINT_add(group, R, R, Q, ctx)) ABORT;
	if (!EC_POINT_is_at_infinity(group, R)) ABORT; /* R = P + 2Q */

	{
		const EC_POINT *points[3];
		const BIGNUM *scalars[3];
	
		if (EC_POINT_is_at_infinity(group, Q)) ABORT;
		points[0] = Q;
		points[1] = Q;
		points[2] = Q;

		if (!BN_add(y, z, BN_value_one())) ABORT;
		if (BN_is_odd(y)) ABORT;
		if (!BN_rshift1(y, y)) ABORT;
		scalars[0] = y; /* (group order + 1)/2,  so  y*Q + y*Q = Q */
		scalars[1] = y;

		fprintf(stdout, "combined multiplication ...");
		fflush(stdout);

		/* z is still the group order */
		if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
		if (!EC_POINTs_mul(group, R, z, 2, points, scalars, ctx)) ABORT;
		if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
		if (0 != EC_POINT_cmp(group, R, Q, ctx)) ABORT;

		fprintf(stdout, ".");
		fflush(stdout);

		if (!BN_pseudo_rand(y, BN_num_bits(y), 0, 0)) ABORT;
		if (!BN_add(z, z, y)) ABORT;
		BN_set_negative(z, 1);
		scalars[0] = y;
		scalars[1] = z; /* z = -(order + y) */

		if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
		if (!EC_POINT_is_at_infinity(group, P)) ABORT;

		fprintf(stdout, ".");
		fflush(stdout);

		if (!BN_pseudo_rand(x, BN_num_bits(y) - 1, 0, 0)) ABORT;
		if (!BN_add(z, x, y)) ABORT;
		BN_set_negative(z, 1);
		scalars[0] = x;
		scalars[1] = y;
		scalars[2] = z; /* z = -(x+y) */

		if (!EC_POINTs_mul(group, P, NULL, 3, points, scalars, ctx)) ABORT;
		if (!EC_POINT_is_at_infinity(group, P)) ABORT;

		fprintf(stdout, " ok\n\n");
	}


#if 0
	timings(C2_K163, TIMING_BASE_PT, ctx);
	timings(C2_K163, TIMING_RAND_PT, ctx);
	timings(C2_K163, TIMING_SIMUL, ctx);
	timings(C2_B163, TIMING_BASE_PT, ctx);
	timings(C2_B163, TIMING_RAND_PT, ctx);
	timings(C2_B163, TIMING_SIMUL, ctx);
	timings(C2_K233, TIMING_BASE_PT, ctx);
	timings(C2_K233, TIMING_RAND_PT, ctx);
	timings(C2_K233, TIMING_SIMUL, ctx);
	timings(C2_B233, TIMING_BASE_PT, ctx);
	timings(C2_B233, TIMING_RAND_PT, ctx);
	timings(C2_B233, TIMING_SIMUL, ctx);
	timings(C2_K283, TIMING_BASE_PT, ctx);
	timings(C2_K283, TIMING_RAND_PT, ctx);
	timings(C2_K283, TIMING_SIMUL, ctx);
	timings(C2_B283, TIMING_BASE_PT, ctx);
	timings(C2_B283, TIMING_RAND_PT, ctx);
	timings(C2_B283, TIMING_SIMUL, ctx);
	timings(C2_K409, TIMING_BASE_PT, ctx);
	timings(C2_K409, TIMING_RAND_PT, ctx);
	timings(C2_K409, TIMING_SIMUL, ctx);
	timings(C2_B409, TIMING_BASE_PT, ctx);
	timings(C2_B409, TIMING_RAND_PT, ctx);
	timings(C2_B409, TIMING_SIMUL, ctx);
	timings(C2_K571, TIMING_BASE_PT, ctx);
	timings(C2_K571, TIMING_RAND_PT, ctx);
	timings(C2_K571, TIMING_SIMUL, ctx);
	timings(C2_B571, TIMING_BASE_PT, ctx);
	timings(C2_B571, TIMING_RAND_PT, ctx);
	timings(C2_B571, TIMING_SIMUL, ctx);
#endif


	if (ctx)
		BN_CTX_free(ctx);
	BN_free(p); BN_free(a);	BN_free(b);
	EC_GROUP_free(group);
	EC_POINT_free(P);
	EC_POINT_free(Q);
	EC_POINT_free(R);
	BN_free(x); BN_free(y); BN_free(z); BN_free(cof);

	if (C2_K163) EC_GROUP_free(C2_K163);
	if (C2_B163) EC_GROUP_free(C2_B163);
	if (C2_K233) EC_GROUP_free(C2_K233);
	if (C2_B233) EC_GROUP_free(C2_B233);
	if (C2_K283) EC_GROUP_free(C2_K283);
	if (C2_B283) EC_GROUP_free(C2_B283);
	if (C2_K409) EC_GROUP_free(C2_K409);
	if (C2_B409) EC_GROUP_free(C2_B409);
	if (C2_K571) EC_GROUP_free(C2_K571);
	if (C2_B571) EC_GROUP_free(C2_B571);

	}
void prime_field_tests()
	{	
	BN_CTX *ctx = NULL;
	BIGNUM *p, *a, *b;
	EC_GROUP *group;
	EC_GROUP *P_160 = NULL, *P_192 = NULL, *P_224 = NULL, *P_256 = NULL, *P_384 = NULL, *P_521 = NULL;
	EC_POINT *P, *Q, *R;
	BIGNUM *x, *y, *z;
	unsigned char buf[100];
	size_t i, len;
	int k;
	
#if 1 /* optional */
	ctx = BN_CTX_new();
	if (!ctx) ABORT;
#endif

	p = BN_new();
	a = BN_new();
	b = BN_new();
	if (!p || !a || !b) ABORT;

	if (!BN_hex2bn(&p, "17")) ABORT;
	if (!BN_hex2bn(&a, "1")) ABORT;
	if (!BN_hex2bn(&b, "1")) ABORT;
	
	group = EC_GROUP_new(EC_GFp_mont_method()); /* applications should use EC_GROUP_new_curve_GFp
	                                             * so that the library gets to choose the EC_METHOD */
	if (!group) ABORT;

	if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;

	{
		EC_GROUP *tmp;
		tmp = EC_GROUP_new(EC_GROUP_method_of(group));
		if (!tmp) ABORT;
		if (!EC_GROUP_copy(tmp, group)) ABORT;
		EC_GROUP_free(group);
		group = tmp;
	}
	
	if (!EC_GROUP_get_curve_GFp(group, p, a, b, ctx)) ABORT;

	fprintf(stdout, "Curve defined by Weierstrass equation\n     y^2 = x^3 + a*x + b  (mod 0x");
	BN_print_fp(stdout, p);
	fprintf(stdout, ")\n     a = 0x");
	BN_print_fp(stdout, a);
	fprintf(stdout, "\n     b = 0x");
	BN_print_fp(stdout, b);
	fprintf(stdout, "\n");

	P = EC_POINT_new(group);
	Q = EC_POINT_new(group);
	R = EC_POINT_new(group);
	if (!P || !Q || !R) ABORT;
	
	if (!EC_POINT_set_to_infinity(group, P)) ABORT;
	if (!EC_POINT_is_at_infinity(group, P)) ABORT;

	buf[0] = 0;
	if (!EC_POINT_oct2point(group, Q, buf, 1, ctx)) ABORT;

	if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
	if (!EC_POINT_is_at_infinity(group, P)) ABORT;

	x = BN_new();
	y = BN_new();
	z = BN_new();
	if (!x || !y || !z) ABORT;

	if (!BN_hex2bn(&x, "D")) ABORT;
	if (!EC_POINT_set_compressed_coordinates_GFp(group, Q, x, 1, ctx)) ABORT;
	if (!EC_POINT_is_on_curve(group, Q, ctx))
		{
		if (!EC_POINT_get_affine_coordinates_GFp(group, Q, x, y, ctx)) ABORT;
		fprintf(stderr, "Point is not on curve: x = 0x");
		BN_print_fp(stderr, x);
		fprintf(stderr, ", y = 0x");
		BN_print_fp(stderr, y);
		fprintf(stderr, "\n");
		ABORT;
		}

	fprintf(stdout, "A cyclic subgroup:\n");
	k = 100;
	do
		{
		if (k-- == 0) ABORT;

		if (EC_POINT_is_at_infinity(group, P))
			fprintf(stdout, "     point at infinity\n");
		else
			{
			if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;

			fprintf(stdout, "     x = 0x");
			BN_print_fp(stdout, x);
			fprintf(stdout, ", y = 0x");
			BN_print_fp(stdout, y);
			fprintf(stdout, "\n");
			}
		
		if (!EC_POINT_copy(R, P)) ABORT;
		if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;

#if 0 /* optional */
		{
			EC_POINT *points[3];
		
			points[0] = R;
			points[1] = Q;
			points[2] = P;
			if (!EC_POINTs_make_affine(group, 2, points, ctx)) ABORT;
		}
#endif

		}
	while (!EC_POINT_is_at_infinity(group, P));

	if (!EC_POINT_add(group, P, Q, R, ctx)) ABORT;
	if (!EC_POINT_is_at_infinity(group, P)) ABORT;

	len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf, sizeof buf, ctx);
	if (len == 0) ABORT;
	if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
	if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
	fprintf(stdout, "Generator as octect string, compressed form:\n     ");
	for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
	
	len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, sizeof buf, ctx);
	if (len == 0) ABORT;
	if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
	if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
	fprintf(stdout, "\nGenerator as octect string, uncompressed form:\n     ");
	for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
	
	len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf, ctx);
	if (len == 0) ABORT;
	if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
	if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
	fprintf(stdout, "\nGenerator as octect string, hybrid form:\n     ");
	for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
	
	if (!EC_POINT_get_Jprojective_coordinates_GFp(group, R, x, y, z, ctx)) ABORT;
	fprintf(stdout, "\nA representation of the inverse of that generator in\nJacobian projective coordinates:\n     X = 0x");
	BN_print_fp(stdout, x);
	fprintf(stdout, ", Y = 0x");
	BN_print_fp(stdout, y);
	fprintf(stdout, ", Z = 0x");
	BN_print_fp(stdout, z);
	fprintf(stdout, "\n");

	if (!EC_POINT_invert(group, P, ctx)) ABORT;
	if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;


	/* Curve secp160r1 (Certicom Research SEC 2 Version 1.0, section 2.4.2, 2000)
	 * -- not a NIST curve, but commonly used */
	
	if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF")) ABORT;
	if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
	if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC")) ABORT;
	if (!BN_hex2bn(&b, "1C97BEFC54BD7A8B65ACF89F81D4D4ADC565FA45")) ABORT;
	if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;

	if (!BN_hex2bn(&x, "4A96B5688EF573284664698968C38BB913CBFC82")) ABORT;
	if (!BN_hex2bn(&y, "23a628553168947d59dcc912042351377ac5fb32")) ABORT;
	if (!EC_POINT_set_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
	if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
	if (!BN_hex2bn(&z, "0100000000000000000001F4C8F927AED3CA752257")) ABORT;
	if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;

	if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
	fprintf(stdout, "\nSEC2 curve secp160r1 -- Generator:\n     x = 0x");
	BN_print_fp(stdout, x);
	fprintf(stdout, "\n     y = 0x");
	BN_print_fp(stdout, y);
	fprintf(stdout, "\n");
	/* G_y value taken from the standard: */
	if (!BN_hex2bn(&z, "23a628553168947d59dcc912042351377ac5fb32")) ABORT;
	if (0 != BN_cmp(y, z)) ABORT;

	fprintf(stdout, "verify degree ...");
	if (EC_GROUP_get_degree(group) != 160) ABORT;
	fprintf(stdout, " ok\n");
	
	fprintf(stdout, "verify group order ...");
	fflush(stdout);
	if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
	if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
	if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
	fprintf(stdout, ".");
	fflush(stdout);
	if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
	if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
	if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
	fprintf(stdout, " ok\n");

	if (!(P_160 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
	if (!EC_GROUP_copy(P_160, group)) ABORT;


	/* Curve P-192 (FIPS PUB 186-2, App. 6) */
	
	if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF")) ABORT;
	if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
	if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC")) ABORT;
	if (!BN_hex2bn(&b, "64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1")) ABORT;
	if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;

	if (!BN_hex2bn(&x, "188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012")) ABORT;
	if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT;
	if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
	if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831")) ABORT;
	if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;

	if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
	fprintf(stdout, "\nNIST curve P-192 -- Generator:\n     x = 0x");
	BN_print_fp(stdout, x);
	fprintf(stdout, "\n     y = 0x");
	BN_print_fp(stdout, y);
	fprintf(stdout, "\n");
	/* G_y value taken from the standard: */
	if (!BN_hex2bn(&z, "07192B95FFC8DA78631011ED6B24CDD573F977A11E794811")) ABORT;
	if (0 != BN_cmp(y, z)) ABORT;

	fprintf(stdout, "verify degree ...");
	if (EC_GROUP_get_degree(group) != 192) ABORT;
	fprintf(stdout, " ok\n");
	
	fprintf(stdout, "verify group order ...");
	fflush(stdout);
	if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
	if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
	if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
	fprintf(stdout, ".");
	fflush(stdout);
#if 0
	if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
#endif
	if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
	if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
	fprintf(stdout, " ok\n");

	if (!(P_192 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
	if (!EC_GROUP_copy(P_192, group)) ABORT;


	/* Curve P-224 (FIPS PUB 186-2, App. 6) */
	
	if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001")) ABORT;
	if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
	if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE")) ABORT;
	if (!BN_hex2bn(&b, "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4")) ABORT;
	if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;

	if (!BN_hex2bn(&x, "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21")) ABORT;
	if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx)) ABORT;
	if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
	if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D")) ABORT;
	if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;

	if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
	fprintf(stdout, "\nNIST curve P-224 -- Generator:\n     x = 0x");
	BN_print_fp(stdout, x);
	fprintf(stdout, "\n     y = 0x");
	BN_print_fp(stdout, y);
	fprintf(stdout, "\n");
	/* G_y value taken from the standard: */
	if (!BN_hex2bn(&z, "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34")) ABORT;
	if (0 != BN_cmp(y, z)) ABORT;
	
	fprintf(stdout, "verify degree ...");
	if (EC_GROUP_get_degree(group) != 224) ABORT;
	fprintf(stdout, " ok\n");
	
	fprintf(stdout, "verify group order ...");
	fflush(stdout);
	if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
	if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
	if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
	fprintf(stdout, ".");
	fflush(stdout);
#if 0
	if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
#endif
	if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
	if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
	fprintf(stdout, " ok\n");

	if (!(P_224 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
	if (!EC_GROUP_copy(P_224, group)) ABORT;


	/* Curve P-256 (FIPS PUB 186-2, App. 6) */
	
	if (!BN_hex2bn(&p, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF")) ABORT;
	if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
	if (!BN_hex2bn(&a, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC")) ABORT;
	if (!BN_hex2bn(&b, "5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B")) ABORT;
	if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;

	if (!BN_hex2bn(&x, "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296")) ABORT;
	if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT;
	if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
	if (!BN_hex2bn(&z, "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E"
		"84F3B9CAC2FC632551")) ABORT;
	if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;

	if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
	fprintf(stdout, "\nNIST curve P-256 -- Generator:\n     x = 0x");
	BN_print_fp(stdout, x);
	fprintf(stdout, "\n     y = 0x");
	BN_print_fp(stdout, y);
	fprintf(stdout, "\n");
	/* G_y value taken from the standard: */
	if (!BN_hex2bn(&z, "4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5")) ABORT;
	if (0 != BN_cmp(y, z)) ABORT;
	
	fprintf(stdout, "verify degree ...");
	if (EC_GROUP_get_degree(group) != 256) ABORT;
	fprintf(stdout, " ok\n");
	
	fprintf(stdout, "verify group order ...");
	fflush(stdout);
	if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
	if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
	if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
	fprintf(stdout, ".");
	fflush(stdout);
#if 0
	if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
#endif
	if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
	if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
	fprintf(stdout, " ok\n");

	if (!(P_256 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
	if (!EC_GROUP_copy(P_256, group)) ABORT;


	/* Curve P-384 (FIPS PUB 186-2, App. 6) */
	
	if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
		"FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF")) ABORT;
	if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
	if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
		"FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC")) ABORT;
	if (!BN_hex2bn(&b, "B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141"
		"120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF")) ABORT;
	if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;

	if (!BN_hex2bn(&x, "AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B"
		"9859F741E082542A385502F25DBF55296C3A545E3872760AB7")) ABORT;
	if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT;
	if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
	if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
		"FFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973")) ABORT;
	if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;

	if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
	fprintf(stdout, "\nNIST curve P-384 -- Generator:\n     x = 0x");
	BN_print_fp(stdout, x);
	fprintf(stdout, "\n     y = 0x");
	BN_print_fp(stdout, y);
	fprintf(stdout, "\n");
	/* G_y value taken from the standard: */
	if (!BN_hex2bn(&z, "3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A14"
		"7CE9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F")) ABORT;
	if (0 != BN_cmp(y, z)) ABORT;
	
	fprintf(stdout, "verify degree ...");
	if (EC_GROUP_get_degree(group) != 384) ABORT;
	fprintf(stdout, " ok\n");
	
	fprintf(stdout, "verify group order ...");
	fflush(stdout);
	if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
	if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
	if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
	fprintf(stdout, ".");
	fflush(stdout);
#if 0
	if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
#endif
	if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
	if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
	fprintf(stdout, " ok\n");

	if (!(P_384 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
	if (!EC_GROUP_copy(P_384, group)) ABORT;


	/* Curve P-521 (FIPS PUB 186-2, App. 6) */
	
	if (!BN_hex2bn(&p, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
		"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
		"FFFFFFFFFFFFFFFFFFFFFFFFFFFF")) ABORT;
	if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
	if (!BN_hex2bn(&a, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
		"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
		"FFFFFFFFFFFFFFFFFFFFFFFFFFFC")) ABORT;
	if (!BN_hex2bn(&b, "051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B"
		"315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573"
		"DF883D2C34F1EF451FD46B503F00")) ABORT;
	if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;

	if (!BN_hex2bn(&x, "C6858E06B70404E9CD9E3ECB662395B4429C648139053F"
		"B521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B"
		"3C1856A429BF97E7E31C2E5BD66")) ABORT;
	if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx)) ABORT;
	if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
	if (!BN_hex2bn(&z, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
		"FFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5"
		"C9B8899C47AEBB6FB71E91386409")) ABORT;
	if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;

	if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
	fprintf(stdout, "\nNIST curve P-521 -- Generator:\n     x = 0x");
	BN_print_fp(stdout, x);
	fprintf(stdout, "\n     y = 0x");
	BN_print_fp(stdout, y);
	fprintf(stdout, "\n");
	/* G_y value taken from the standard: */
	if (!BN_hex2bn(&z, "11839296A789A3BC0045C8A5FB42C7D1BD998F54449579"
		"B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C"
		"7086A272C24088BE94769FD16650")) ABORT;
	if (0 != BN_cmp(y, z)) ABORT;
	
	fprintf(stdout, "verify degree ...");
	if (EC_GROUP_get_degree(group) != 521) ABORT;
	fprintf(stdout, " ok\n");
	
	fprintf(stdout, "verify group order ...");
	fflush(stdout);
	if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
	if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
	if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
	fprintf(stdout, ".");
	fflush(stdout);
#if 0
	if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
#endif
	if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
	if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
	fprintf(stdout, " ok\n");

	if (!(P_521 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
	if (!EC_GROUP_copy(P_521, group)) ABORT;


	/* more tests using the last curve */

	if (!EC_POINT_copy(Q, P)) ABORT;
	if (EC_POINT_is_at_infinity(group, Q)) ABORT;
	if (!EC_POINT_dbl(group, P, P, ctx)) ABORT;
	if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
	if (!EC_POINT_invert(group, Q, ctx)) ABORT; /* P = -2Q */

	if (!EC_POINT_add(group, R, P, Q, ctx)) ABORT;
	if (!EC_POINT_add(group, R, R, Q, ctx)) ABORT;
	if (!EC_POINT_is_at_infinity(group, R)) ABORT; /* R = P + 2Q */

	{
		const EC_POINT *points[3];
		const BIGNUM *scalars[3];
	
		if (EC_POINT_is_at_infinity(group, Q)) ABORT;
		points[0] = Q;
		points[1] = Q;
		points[2] = Q;

		if (!BN_add(y, z, BN_value_one())) ABORT;
		if (BN_is_odd(y)) ABORT;
		if (!BN_rshift1(y, y)) ABORT;
		scalars[0] = y; /* (group order + 1)/2,  so  y*Q + y*Q = Q */
		scalars[1] = y;

		fprintf(stdout, "combined multiplication ...");
		fflush(stdout);

		/* z is still the group order */
		if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
		if (!EC_POINTs_mul(group, R, z, 2, points, scalars, ctx)) ABORT;
		if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
		if (0 != EC_POINT_cmp(group, R, Q, ctx)) ABORT;

		fprintf(stdout, ".");
		fflush(stdout);

		if (!BN_pseudo_rand(y, BN_num_bits(y), 0, 0)) ABORT;
		if (!BN_add(z, z, y)) ABORT;
		BN_set_negative(z, 1);
		scalars[0] = y;
		scalars[1] = z; /* z = -(order + y) */

		if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
		if (!EC_POINT_is_at_infinity(group, P)) ABORT;

		fprintf(stdout, ".");
		fflush(stdout);

		if (!BN_pseudo_rand(x, BN_num_bits(y) - 1, 0, 0)) ABORT;
		if (!BN_add(z, x, y)) ABORT;
		BN_set_negative(z, 1);
		scalars[0] = x;
		scalars[1] = y;
		scalars[2] = z; /* z = -(x+y) */

		if (!EC_POINTs_mul(group, P, NULL, 3, points, scalars, ctx)) ABORT;
		if (!EC_POINT_is_at_infinity(group, P)) ABORT;

		fprintf(stdout, " ok\n\n");
	}


#if 0
	timings(P_160, TIMING_BASE_PT, ctx);
	timings(P_160, TIMING_RAND_PT, ctx);
	timings(P_160, TIMING_SIMUL, ctx);
	timings(P_192, TIMING_BASE_PT, ctx);
	timings(P_192, TIMING_RAND_PT, ctx);
	timings(P_192, TIMING_SIMUL, ctx);
	timings(P_224, TIMING_BASE_PT, ctx);
	timings(P_224, TIMING_RAND_PT, ctx);
	timings(P_224, TIMING_SIMUL, ctx);
	timings(P_256, TIMING_BASE_PT, ctx);
	timings(P_256, TIMING_RAND_PT, ctx);
	timings(P_256, TIMING_SIMUL, ctx);
	timings(P_384, TIMING_BASE_PT, ctx);
	timings(P_384, TIMING_RAND_PT, ctx);
	timings(P_384, TIMING_SIMUL, ctx);
	timings(P_521, TIMING_BASE_PT, ctx);
	timings(P_521, TIMING_RAND_PT, ctx);
	timings(P_521, TIMING_SIMUL, ctx);
#endif


	if (ctx)
		BN_CTX_free(ctx);
	BN_free(p); BN_free(a);	BN_free(b);
	EC_GROUP_free(group);
	EC_POINT_free(P);
	EC_POINT_free(Q);
	EC_POINT_free(R);
	BN_free(x); BN_free(y); BN_free(z);

	if (P_160) EC_GROUP_free(P_160);
	if (P_192) EC_GROUP_free(P_192);
	if (P_224) EC_GROUP_free(P_224);
	if (P_256) EC_GROUP_free(P_256);
	if (P_384) EC_GROUP_free(P_384);
	if (P_521) EC_GROUP_free(P_521);

	}