Some actual method functions (not enough yet to use the EC library, though),

including EC arithmetics derived from Lenka Fibikova's code (with some
additional optimizations).

crypto/ec/ec.h

@@ -149,6 +149,7 @@ int EC_POINT_make_affine(const EC_GROUP *, const EC_POINT *, BN_CTX *);
 /* Error codes for the EC functions. */
 
 /* Function codes. */
+#define EC_F_EC_GFP_SIMPLE_GROUP_SET_GENERATOR		 117
 #define EC_F_EC_GROUP_CLEAR_FREE			 103
 #define EC_F_EC_GROUP_COPY				 102
 #define EC_F_EC_GROUP_FREE				 104

crypto/ec/ec_err.c

@@ -66,6 +66,7 @@
 #ifndef OPENSSL_NO_ERR
 static ERR_STRING_DATA EC_str_functs[]=
 	{
+{ERR_PACK(0,EC_F_EC_GFP_SIMPLE_GROUP_SET_GENERATOR,0),	"EC_GFP_SIMPLE_GROUP_SET_GENERATOR"},
 {ERR_PACK(0,EC_F_EC_GROUP_CLEAR_FREE,0),	"EC_GROUP_clear_free"},
 {ERR_PACK(0,EC_F_EC_GROUP_COPY,0),	"EC_GROUP_copy"},
 {ERR_PACK(0,EC_F_EC_GROUP_FREE,0),	"EC_GROUP_free"},

crypto/ec/ec_lcl.h

@@ -104,10 +104,10 @@ struct ec_method_st {
 
 	/* internal functions */
 
-	/* 'field_mult' and 'field_sqr' can be used by 'add' and 'dbl' so that
+	/* 'field_mul' and 'field_sqr' can be used by 'add' and 'dbl' so that
 	 * the same implementations of point operations can be used with different
 	 * optimized implementations of expensive field operations: */
-	int (*field_mult)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
+	int (*field_mul)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 	int (*field_sqr)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
 
 	int (*field_encode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); /* e.g. to Montgomery */
@@ -128,7 +128,6 @@ struct ec_group_st {
 	
 	BIGNUM field; /* Field specification.
 	               * For curves over GF(p), this is the modulus. */
-	void *field_data; /* method-specific (e.g., Montgomery structure) */
 
 	BIGNUM a, b; /* Curve coefficients.
 	              * (Here the assumption is that BIGNUMs can be used
@@ -141,6 +140,8 @@ struct ec_group_st {
 
 	EC_POINT *generator; /* optional */
 	BIGNUM order, cofactor;
+
+	void *field_data; /* method-specific (e.g., Montgomery structure) */
 } /* EC_GROUP */;
 
 
@@ -197,7 +198,7 @@ int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *
 int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
 int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
 int ec_GFp_simple_make_affine(const EC_GROUP *, const EC_POINT *, BN_CTX *);
-int ec_GFp_simple_field_mult(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
+int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
 
 
@@ -206,7 +207,8 @@ int ec_GFp_mont_group_init(EC_GROUP *);
 int ec_GFp_mont_group_set_curve_GFp(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 void ec_GFp_mont_group_finish(EC_GROUP *);
 void ec_GFp_mont_group_clear_finish(EC_GROUP *);
-int ec_GFp_mont_field_mult(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
+int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *);
+int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
 int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
 int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
@@ -217,7 +219,8 @@ int ec_GFp_recp_group_init(EC_GROUP *);
 int ec_GFp_recp_group_set_curve_GFp(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 void ec_GFp_recp_group_finish(EC_GROUP *);
 void ec_GFp_recp_group_clear_finish(EC_GROUP *);
-int ec_GFp_recp_field_mult(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
+int ec_GFp_recp_group_copy(EC_GROUP *, const EC_GROUP *);
+int ec_GFp_recp_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 int ec_GFp_recp_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
 int ec_GFp_recp_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
 int ec_GFp_recp_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
@@ -228,7 +231,8 @@ int ec_GFp_nist_group_init(EC_GROUP *);
 int ec_GFp_nist_group_set_curve_GFp(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 void ec_GFp_nist_group_finish(EC_GROUP *);
 void ec_GFp_nist_group_clear_finish(EC_GROUP *);
-int ec_GFp_nist_field_mult(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
+int ec_GFp_nist_group_copy(EC_GROUP *, const EC_GROUP *);
+int ec_GFp_nist_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 int ec_GFp_nist_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
 int ec_GFp_nist_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
 int ec_GFp_nist_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);

crypto/ec/ecp_mont.c

-/* TODO */
 /* crypto/ec/ecp_mont.c */
 /* ====================================================================
  * Copyright (c) 1998-2001 The OpenSSL Project.  All rights reserved.
@@ -64,7 +63,7 @@ const EC_METHOD *EC_GFp_mont_method(void)
 		ec_GFp_mont_group_set_curve_GFp,
 		ec_GFp_mont_group_finish,
 		ec_GFp_mont_group_clear_finish,
-		ec_GFp_simple_group_copy,
+		ec_GFp_mont_group_copy,
 		ec_GFp_simple_group_set_generator,
 		/* TODO: 'set' and 'get' functions for EC_GROUPs */
 		ec_GFp_simple_point_init,
@@ -79,10 +78,52 @@ const EC_METHOD *EC_GFp_mont_method(void)
 		ec_GFp_simple_is_at_infinity,
 		ec_GFp_simple_is_on_curve,
 		ec_GFp_simple_make_affine,
-		ec_GFp_mont_field_mult,
+		ec_GFp_mont_field_mul,
 		ec_GFp_mont_field_sqr,
 		ec_GFp_mont_field_encode,
 		ec_GFp_mont_field_decode };
 
 	return &ret;
 	}
+
+
+int ec_GFp_mont_group_init(EC_GROUP *group)
+	{
+	int ok;
+
+	ok = ec_GFp_simple_group_init(group);
+	group->field_data = NULL;
+	return ok;
+	}
+
+
+int ec_GFp_mont_group_set_curve_GFp(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
+/* TODO */
+
+
+void ec_GFp_mont_group_finish(EC_GROUP *group);
+/* TODO */
+
+
+void ec_GFp_mont_group_clear_finish(EC_GROUP *group);
+/* TODO */
+
+
+int ec_GFp_mont_group_copy(EC_GROUP *dest, const EC_GROUP *src);
+/* TODO */
+
+
+int ec_GFp_mont_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
+/* TODO */
+
+
+int ec_GFp_mont_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx);
+/* TODO */
+
+
+int ec_GFp_mont_field_encode(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx);
+/* TODO */
+
+
+int ec_GFp_mont_field_decode(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx);
+/* TODO */

crypto/ec/ecp_nist.c

-/* TODO */
 /* crypto/ec/ecp_nist.c */
 /* ====================================================================
  * Copyright (c) 1998-2001 The OpenSSL Project.  All rights reserved.
@@ -64,7 +63,7 @@ const EC_METHOD *EC_GFp_nist_method(void)
 		ec_GFp_nist_group_set_curve_GFp,
 		ec_GFp_nist_group_finish,
 		ec_GFp_nist_group_clear_finish,
-		ec_GFp_simple_group_copy,
+		ec_GFp_nist_group_copy,
 		ec_GFp_simple_group_set_generator,
 		/* TODO: 'set' and 'get' functions for EC_GROUPs */
 		ec_GFp_simple_point_init,
@@ -79,10 +78,52 @@ const EC_METHOD *EC_GFp_nist_method(void)
 		ec_GFp_simple_is_at_infinity,
 		ec_GFp_simple_is_on_curve,
 		ec_GFp_simple_make_affine,
-		ec_GFp_nist_field_mult,
+		ec_GFp_nist_field_mul,
 		ec_GFp_nist_field_sqr,
 		ec_GFp_nist_field_encode,
 		ec_GFp_nist_field_decode };
 
 	return &ret;
 	}
+
+
+int ec_GFp_nist_group_init(EC_GROUP *group)
+	{
+	int ok;
+
+	ok = ec_GFp_simple_group_init(group);
+	group->field_data = NULL;
+	return ok;
+	}
+
+
+int ec_GFp_nist_group_set_curve_GFp(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
+/* TODO */
+
+
+void ec_GFp_nist_group_finish(EC_GROUP *group);
+/* TODO */
+
+
+void ec_GFp_nist_group_clear_finish(EC_GROUP *group);
+/* TODO */
+
+
+int ec_GFp_nist_group_copy(EC_GROUP *dest, const EC_GROUP *src);
+/* TODO */
+
+
+int ec_GFp_nist_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
+/* TODO */
+
+
+int ec_GFp_nist_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx);
+/* TODO */
+
+
+int ec_GFp_nist_field_encode(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx);
+/* TODO */
+
+
+int ec_GFp_nist_field_decode(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx);
+/* TODO */

crypto/ec/ecp_recp.c

-/* TODO */
 /* crypto/ec/ecp_recp.c */
 /* ====================================================================
  * Copyright (c) 1998-2001 The OpenSSL Project.  All rights reserved.
@@ -64,7 +63,7 @@ const EC_METHOD *EC_GFp_recp_method(void)
 		ec_GFp_recp_group_set_curve_GFp,
 		ec_GFp_recp_group_finish,
 		ec_GFp_recp_group_clear_finish,
-		ec_GFp_simple_group_copy,
+		ec_GFp_recp_group_copy,
 		ec_GFp_simple_group_set_generator,
 		/* TODO: 'set' and 'get' functions for EC_GROUPs */
 		ec_GFp_simple_point_init,
@@ -79,10 +78,52 @@ const EC_METHOD *EC_GFp_recp_method(void)
 		ec_GFp_simple_is_at_infinity,
 		ec_GFp_simple_is_on_curve,
 		ec_GFp_simple_make_affine,
-		ec_GFp_recp_field_mult,
+		ec_GFp_recp_field_mul,
 		ec_GFp_recp_field_sqr,
 		ec_GFp_recp_field_encode,
 		ec_GFp_recp_field_decode };
 
 	return &ret;
 	}
+
+
+int ec_GFp_recp_group_init(EC_GROUP *group)
+	{
+	int ok;
+
+	ok = ec_GFp_simple_group_init(group);
+	group->field_data = NULL;
+	return ok;
+	}
+
+
+int ec_GFp_recp_group_set_curve_GFp(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
+/* TODO */
+
+
+void ec_GFp_recp_group_finish(EC_GROUP *group);
+/* TODO */
+
+
+void ec_GFp_recp_group_clear_finish(EC_GROUP *group);
+/* TODO */
+
+
+int ec_GFp_recp_group_copy(EC_GROUP *dest, const EC_GROUP *src);
+/* TODO */
+
+
+int ec_GFp_recp_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
+/* TODO */
+
+
+int ec_GFp_recp_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx);
+/* TODO */
+
+
+int ec_GFp_recp_field_encode(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx);
+/* TODO */
+
+
+int ec_GFp_recp_field_decode(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx);
+/* TODO */

crypto/ec/ecp_smpl.c

-/* TODO */
 /* crypto/ec/ecp_smpl.c */
+/* Includes code written by Lenka Fibikova <fibikova@exp-math.uni-essen.de>
+ * for the OpenSSL project. */
 /* ====================================================================
  * Copyright (c) 1998-2001 The OpenSSL Project.  All rights reserved.
  *
@@ -54,6 +55,8 @@
  *
  */
 
+#include <openssl/err.h>
+
 #include "ec_lcl.h"
 
 
@@ -79,10 +82,516 @@ const EC_METHOD *EC_GFp_simple_method(void)
 		ec_GFp_simple_is_at_infinity,
 		ec_GFp_simple_is_on_curve,
 		ec_GFp_simple_make_affine,
-		ec_GFp_simple_field_mult,
+		ec_GFp_simple_field_mul,
 		ec_GFp_simple_field_sqr,
 		0 /* field_encode */,
 		0 /* field_decode */ };
 
 	return &ret;
 	}
+
+
+int ec_GFp_simple_group_init(EC_GROUP *group)
+	{
+	BN_init(&group->field);
+	BN_init(&group->a);
+	BN_init(&group->b);
+	group->a_is_minus3 = 0;
+	group->generator = NULL;
+	BN_init(&group->order);
+	BN_init(&group->cofactor);
+	return 1;
+	}
+
+
+int ec_GFp_simple_group_set_curve_GFp(EC_GROUP *group,
+	const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
+	{
+	int ret = 0;
+	BN_CTX *new_ctx = NULL;
+	BIGNUM *tmp_a;
+	
+	if (ctx == NULL)
+		{
+		ctx = new_ctx = BN_CTX_new();
+		if (ctx == NULL)
+			return 0;
+		}
+	BN_CTX_start(ctx);
+
+	tmp_a = BN_CTX_get(ctx);
+	if (tmp_a == NULL) goto err;
+
+	/* group->field */
+	if (!BN_copy(&group->field, p)) goto err;
+	group->field.neg = 0;
+
+	/* group->a */
+	if (!BN_nnmod(tmp_a, a, p, ctx)) goto err;
+	if (group->meth->field_encode)
+		{ if (!group->meth->field_encode(group, &group->a, tmp_a, ctx)) goto err; }	
+	else
+		if (!BN_copy(&group->a, tmp_a)) goto err;
+	
+	/* group->b */
+	if (!BN_nnmod(&group->b, b, p, ctx)) goto err;
+	if (group->meth->field_encode)
+		if (!group->meth->field_encode(group, &group->b, &group->b, ctx)) goto err;
+	
+	/* group->a_is_minus3 */
+	if (!BN_add_word(tmp_a, 3)) goto err;
+	group->a_is_minus3 = (0 == BN_cmp(tmp_a, &group->field));
+
+	ret = 1;
+
+ err:
+	BN_CTX_end(ctx);
+	if (new_ctx != NULL)
+		BN_CTX_free(new_ctx);
+	return ret;
+	}
+
+
+void ec_GFp_simple_group_finish(EC_GROUP *group)
+	{
+	BN_free(&group->field);
+	BN_free(&group->a);
+	BN_free(&group->b);
+	if (group->generator != NULL)
+		EC_POINT_free(group->generator);
+	BN_free(&group->order);
+	BN_free(&group->cofactor);
+	}
+
+
+void ec_GFp_simple_group_clear_finish(EC_GROUP *group)
+	{
+	BN_clear_free(&group->field);
+	BN_clear_free(&group->a);
+	BN_clear_free(&group->b);
+	if (group->generator != NULL)
+		{
+		EC_POINT_clear_free(group->generator);
+		group->generator = NULL;
+		}
+	BN_clear_free(&group->order);
+	BN_clear_free(&group->cofactor);
+	}
+
+
+int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
+	{
+	if (!BN_copy(&dest->field, &src->field)) return 0;
+	if (!BN_copy(&dest->a, &src->a)) return 0;
+	if (!BN_copy(&dest->b, &src->b)) return 0;
+
+	dest->a_is_minus3 = src->a_is_minus3;
+
+	if (src->generator != NULL)
+		{
+		if (dest->generator == NULL)
+			{
+			dest->generator = EC_POINT_new(dest);
+			if (dest->generator == NULL) return 0;
+			}
+		if (!EC_POINT_copy(dest->generator, src->generator)) return 0;
+		}
+	else
+		{
+		/* src->generator == NULL */
+		if (dest->generator != NULL)
+			{
+			EC_POINT_clear_free(dest->generator);
+			dest->generator = NULL;
+			}
+		}
+
+	if (!BN_copy(&dest->order, &src->order)) return 0;
+	if (!BN_copy(&dest->cofactor, &src->cofactor)) return 0;
+
+	return 1;
+	}
+
+
+int ec_GFp_simple_group_set_generator(EC_GROUP *group, const EC_POINT *generator,
+	const BIGNUM *order, const BIGNUM *cofactor)
+	{
+	if (generator)
+		{
+		ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_GENERATOR, ERR_R_PASSED_NULL_PARAMETER);
+		return 0   ;
+		}
+
+	if (group->generator == NULL)
+		{
+		group->generator = EC_POINT_new(group);
+		if (group->generator == NULL) return 0;
+		}
+	if (!EC_POINT_copy(group->generator, generator)) return 0;
+
+	if (order != NULL)
+		{ if (!BN_copy(&group->order, order)) return 0; }	
+	else
+		{ if (!BN_zero(&group->order)) return 0; }	
+
+	if (cofactor != NULL)
+		{ if (!BN_copy(&group->cofactor, cofactor)) return 0; }	
+	else
+		{ if (!BN_zero(&group->cofactor)) return 0; }	
+
+	return 1;
+	}
+
+
+/* TODO: 'set' and 'get' functions for EC_GROUPs */
+
+
+int ec_GFp_simple_point_init(EC_POINT *point)
+	{
+	BN_init(&point->X);
+	BN_init(&point->Y);
+	BN_init(&point->Z);
+	point->Z_is_one = 0;
+
+	return 1;
+	}
+
+
+void ec_GFp_simple_point_finish(EC_POINT *point)
+	{
+	BN_free(&point->X);
+	BN_free(&point->Y);
+	BN_free(&point->Z);
+	}
+
+
+void ec_GFp_simple_point_clear_finish(EC_POINT *point)
+	{
+	BN_clear_free(&point->X);
+	BN_clear_free(&point->Y);
+	BN_clear_free(&point->Z);
+	point->Z_is_one = 0;
+	}
+
+
+int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
+	{
+	if (!BN_copy(&dest->X, &src->X)) return 0;
+	if (!BN_copy(&dest->Y, &src->Y)) return 0;
+	if (!BN_copy(&dest->Z, &src->Z)) return 0;
+	dest->Z_is_one = src->Z_is_one;
+
+	return 1;
+	}
+
+
+/* TODO: 'set' and 'get' functions for EC_POINTs */
+
+
+size_t ec_GFp_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form,
+	unsigned char *buf, size_t len, BN_CTX *ctx);
+/* TODO */
+
+
+int ec_GFp_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
+	const unsigned char *buf, size_t len, BN_CTX *);
+/* TODO */
+
+
+int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
+	{
+	int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
+	int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
+	const BIGNUM *p;
+	BN_CTX *new_ctx = NULL;
+	BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6;
+	int ret = 0;
+	
+	if (a == b)
+		return EC_POINT_dbl(group, r, a, ctx);
+	if (EC_POINT_is_at_infinity(group, a))
+		return EC_POINT_copy(r, b);
+	if (EC_POINT_is_at_infinity(group, b))
+		return EC_POINT_copy(r, a);
+	
+	field_mul = group->meth->field_mul;
+	field_sqr = group->meth->field_sqr;
+	p = &group->field;
+
+	if (ctx == NULL)
+		{
+		ctx = new_ctx = BN_CTX_new();
+		if (ctx == NULL)
+			return 0;
+		}
+	BN_CTX_start(ctx);
+
+	n0 = BN_CTX_get(ctx);
+	n1 = BN_CTX_get(ctx);
+	n2 = BN_CTX_get(ctx);
+	n3 = BN_CTX_get(ctx);
+	n4 = BN_CTX_get(ctx);
+	n5 = BN_CTX_get(ctx);
+	n6 = BN_CTX_get(ctx);
+	if (n6 == NULL) goto end;
+
+	/* n1, n2 */
+	if (b->Z_is_one)
+		{
+		if (!BN_copy(n1, &a->X)) goto end;
+		if (!BN_copy(n2, &a->Y)) goto end;
+		/* n1 = X_a */
+		/* n2 = Y_a */
+		}
+	else
+		{
+		if (!field_sqr(group, n0, &b->Z, ctx)) goto end;
+		if (!field_mul(group, n1, &a->X, n0, ctx)) goto end;
+		/* n1 = X_a * Z_b^2 */
+
+		if (!field_mul(group, n0, n0, &b->Z, ctx)) goto end;
+		if (!field_mul(group, n2, &a->Y, n0, ctx)) goto end;
+		/* n2 = Y_a * Z_b^3 */
+		}
+
+	/* n3, n4 */
+	if (a->Z_is_one)
+		{
+		if (!BN_copy(n3, &b->X)) goto end;
+		if (!BN_copy(n4, &b->Y)) goto end;
+		/* n3 = X_b */
+		/* n4 = Y_b */
+		}
+	else
+		{
+		if (!field_sqr(group, n0, &a->Z, ctx)) goto end;
+		if (!field_mul(group, n3, &b->X, n0, ctx)) goto end;
+		/* n3 = X_b * Z_a^2 */
+
+		if (!field_mul(group, n0, n0, &a->Z, ctx)) goto end;
+		if (!field_mul(group, n4, &b->Y, n0, ctx)) goto end;
+		/* n4 = Y_b * Z_a^3 */
+		}
+
+	/* n5, n6 */
+	if (!BN_mod_sub_quick(n5, n1, n3, p)) goto end;
+	if (!BN_mod_sub_quick(n6, n2, n4, p)) goto end;
+	/* n5 = n1 - n3 */
+	/* n6 = n2 - n4 */
+
+	if (BN_is_zero(n5))
+		{
+		if (BN_is_zero(n6))
+			{
+			/* a is the same point as b */
+			BN_CTX_end(ctx);
+			ctx = NULL;
+			ret = EC_POINT_dbl(group, r, a, ctx);
+			goto end;
+			}
+		else
+			{
+			/* a is the inverse of b */
+			if (!BN_zero(&r->Z)) goto end;
+			r->Z_is_one = 0;
+			ret = 1;
+			goto end;
+			}
+		}
+
+	/* 'n7', 'n8' */
+	if (!BN_mod_add_quick(n1, n1, n3, p)) goto end;
+	if (!BN_mod_add_quick(n2, n2, n4, p)) goto end;
+	/* 'n7' = n1 + n3 */
+	/* 'n8' = n2 + n4 */
+
+	/* Z_r */
+	if (a->Z_is_one && b->Z_is_one)
+		{
+		if (!BN_copy(&r->Z, n5)) goto end;
+		}
+	else
+		{
+		if (a->Z_is_one)
+			{ if (!BN_copy(n0, &b->Z)) goto end; }
+		else if (b->Z_is_one)
+			{ if (!BN_copy(n0, &a->Z)) goto end; }
+		else
+			{ if (!field_mul(group, n0, &a->Z, &b->Z, ctx)) goto end; }
+		if (!field_mul(group, &r->Z, n0, n5, ctx)) goto end;
+		}
+	r->Z_is_one = 0;
+	/* Z_r = Z_a * Z_b * n5 */
+
+	/* X_r */
+	if (!field_sqr(group, n0, n6, ctx)) goto end;
+	if (!field_sqr(group, n4, n5, ctx)) goto end;
+	if (!field_mul(group, n3, n1, n4, ctx)) goto end;
+	if (!BN_mod_sub_quick(&r->X, n0, n3, p)) goto end;
+	/* X_r = n6^2 - n5^2 * 'n7' */
+	
+	/* 'n9' */
+	if (!BN_mod_lshift1_quick(n0, &r->X, p)) goto end;
+	if (!BN_mod_sub_quick(n0, n3, n0, p)) goto end;
+	/* n9 = n5^2 * 'n7' - 2 * X_r */
+
+	/* Y_r */
+	if (!field_mul(group, n0, n0, n6, ctx)) goto end;
+	if (!field_mul(group, n5, n4, n5, ctx)) goto end; /* now n5 is n5^3 */
+	if (!field_mul(group, n1, n2, n5, ctx)) goto end;
+	if (!BN_mod_sub_quick(n0, n0, n1, p)) goto end;
+	if (BN_is_odd(n0))
+		if (!BN_add(n0, n0, p)) goto end;
+	/* now  0 <= n0 < 2*p,  and n0 is even */
+	if (!BN_rshift1(&r->Y, n0)) goto end;
+	/* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */
+
+	ret = 1;
+
+ end:
+	if (ctx) /* otherwise we already called BN_CTX_end */
+		BN_CTX_end(ctx);
+	if (new_ctx != NULL)
+		BN_CTX_free(new_ctx);
+	return ret;
+	}
+
+
+int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx)
+	{
+	int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
+	int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
+	const BIGNUM *p;
+	BN_CTX *new_ctx = NULL;
+	BIGNUM *n0, *n1, *n2, *n3;
+	int ret = 0;
+	
+	if (EC_POINT_is_at_infinity(group, a))
+		{
+		if (!BN_zero(&r->Z)) return 0;
+		r->Z_is_one = 0;
+		return 1;
+		}
+
+	field_mul = group->meth->field_mul;
+	field_sqr = group->meth->field_sqr;
+	p = &group->field;
+
+	if (ctx == NULL)
+		{
+		ctx = new_ctx = BN_CTX_new();
+		if (ctx == NULL)
+			return 0;
+		}
+	BN_CTX_start(ctx);
+
+	n0 = BN_CTX_get(ctx);
+	n1 = BN_CTX_get(ctx);
+	n2 = BN_CTX_get(ctx);
+	n3 = BN_CTX_get(ctx);
+	if (n3 == NULL) goto err;
+
+	/* TODO: optimization for group->a_is_minus3 */
+
+	/* n1 */
+	if (a->Z_is_one)
+		{
+		if (!field_sqr(group, n0, &a->X, ctx)) goto err;
+		if (!BN_mod_lshift1_quick(n1, n0, p)) goto err;
+		if (!BN_mod_add_quick(n0, n0, n1, p)) goto err;
+		if (!BN_mod_add_quick(n1, n0, &group->a, p)) goto err;
+		/* n1 = 3 * X_a^2 + a_curve */
+		}
+	else if (group->a_is_minus3)
+		{
+		if (!field_sqr(group, n1, &a->Z, ctx)) goto err;
+		if (!BN_mod_add_quick(n0, &a->X, n1, p)) goto err;
+		if (!BN_mod_sub_quick(n2, &a->X, n1, p)) goto err;
+		if (!field_mul(group, n1, n0, n2, ctx)) goto err;
+		if (!BN_mod_lshift1_quick(n0, n1, p)) goto err;
+		if (!BN_mod_add_quick(n1, n0, n1, p)) goto err;
+		/* n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2)
+		 *    = 3 * X_a^2 - 3 * Z_a^4 */
+		}
+	else
+		{
+		if (!field_sqr(group, n0, &a->X, ctx)) goto err;
+		if (!BN_mod_lshift1_quick(n1, n0, p)) goto err;
+		if (!BN_mod_add_quick(n0, n0, n1, p)) goto err;
+		if (!field_sqr(group, n1, &a->Z, ctx)) goto err;
+		if (!field_sqr(group, n1, n1, ctx)) goto err;
+		if (!field_mul(group, n1, n1, &group->a, ctx)) goto err;
+		if (!BN_mod_add_quick(n1, n1, n0, p)) goto err;
+		/* n1 = 3 * X_a^2 + a_curve * Z_a^4 */
+		}
+
+	/* Z_r */
+	if (a->Z_is_one)
+		{
+		if (!BN_copy(n0, &a->Y)) goto err;
+		}
+	else
+		{
+		if (!field_mul(group, n0, &a->Y, &a->Z, ctx)) goto err;
+		}
+	if (!BN_mod_lshift1_quick(&r->Z, n0, p)) goto err;
+	r->Z_is_one = 0;
+	/* Z_r = 2 * Y_a * Z_a */
+
+	/* n2 */
+	if (!field_sqr(group, n3, &a->Y, ctx)) goto err;
+	if (!field_mul(group, n2, &a->X, n3, ctx)) goto err;
+	if (!BN_mod_lshift_quick(n2, n2, 2, p)) goto err;
+	/* n2 = 4 * X_a * Y_a^2 */
+
+	/* X_r */
+	if (!BN_mod_lshift1_quick(n0, n2, p)) goto err;
+	if (!field_sqr(group, &r->X, n1, ctx)) goto err;
+	if (!BN_mod_sub_quick(&r->X, &r->X, n0, p)) goto err;
+	/* X_r = n1^2 - 2 * n2 */
+	
+	/* n3 */
+	if (!field_sqr(group, n0, n3, ctx)) goto err;
+	if (!BN_mod_lshift_quick(n3, n0, 3, p)) goto err;
+	/* n3 = 8 * Y_a^4 */
+	
+	/* Y_r */
+	if (!BN_mod_sub_quick(n0, n2, &r->X, p)) goto err;
+	if (!field_mul(group, n0, n1, n0, ctx)) goto err;
+	if (!BN_mod_sub_quick(&r->Y, n0, n3, p)) goto err;
+	/* Y_r = n1 * (n2 - X_r) - n3 */
+
+	ret = 1;
+
+ err:
+	BN_CTX_end(ctx);
+	if (new_ctx != NULL)
+		BN_CTX_free(new_ctx);
+	return ret;
+	}
+
+
+int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
+	{
+	return BN_is_zero(&point->Z);
+	}
+
+
+int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx);
+/* TODO */
+
+
+int ec_GFp_simple_make_affine(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx);
+/* TODO */
+
+
+int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
+	{
+	return BN_mod_mul(r, a, b, &group->field, ctx);
+	}
+
+
+int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
+	{
+	return BN_mod_sqr(r, a, &group->field, ctx);
+	}