X-Git-Url: https://git.openssl.org/gitweb/?p=openssl.git;a=blobdiff_plain;f=crypto%2Fec%2Fecp_smpl.c;h=bd9f7dfda784cbeca68f899a73a0ef006ab36b95;hp=de90f90aa10defb62c9f69cc5a889d3421fa2048;hb=1d97c8435171a7af575f73c526d79e1ef0ee5960;hpb=b6358c89a10128692875fb92921b663c4d079a1e

diff --git a/crypto/ec/ecp_smpl.c b/crypto/ec/ecp_smpl.c
index de90f90aa1..bd9f7dfda7 100644
--- a/crypto/ec/ecp_smpl.c
+++ b/crypto/ec/ecp_smpl.c
@@ -62,6 +62,8 @@
  * and contributed to the OpenSSL project.
  */
 
+
+
 #include <openssl/err.h>
 #include <openssl/symhacks.h>
 
@@ -70,6 +72,7 @@
 const EC_METHOD *EC_GFp_simple_method(void)
 	{
 	static const EC_METHOD ret = {
+		EC_FLAGS_DEFAULT_OCT,
 		NID_X9_62_prime_field,
 		ec_GFp_simple_group_init,
 		ec_GFp_simple_group_finish,
@@ -88,9 +91,7 @@ const EC_METHOD *EC_GFp_simple_method(void)
 		ec_GFp_simple_get_Jprojective_coordinates_GFp,
 		ec_GFp_simple_point_set_affine_coordinates,
 		ec_GFp_simple_point_get_affine_coordinates,
-		ec_GFp_simple_set_compressed_coordinates,
-		ec_GFp_simple_point2oct,
-		ec_GFp_simple_oct2point,
+		0,0,0,
 		ec_GFp_simple_add,
 		ec_GFp_simple_dbl,
 		ec_GFp_simple_invert,
@@ -129,9 +130,16 @@ const EC_METHOD *EC_GFp_simple_method(void)
 
 int ec_GFp_simple_group_init(EC_GROUP *group)
 	{
-	BN_init(&group->field);
-	BN_init(&group->a);
-	BN_init(&group->b);
+	group->field = BN_new();
+	group->a = BN_new();
+	group->b = BN_new();
+	if(!group->field || !group->a || !group->b)
+		{
+		if(!group->field) BN_free(group->field);
+		if(!group->a) BN_free(group->a);
+		if(!group->b) BN_free(group->b);
+		return 0;
+		}
 	group->a_is_minus3 = 0;
 	return 1;
 	}
@@ -139,25 +147,25 @@ int ec_GFp_simple_group_init(EC_GROUP *group)
 
 void ec_GFp_simple_group_finish(EC_GROUP *group)
 	{
-	BN_free(&group->field);
-	BN_free(&group->a);
-	BN_free(&group->b);
+	BN_free(group->field);
+	BN_free(group->a);
+	BN_free(group->b);
 	}
 
 
 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);
+	BN_clear_free(group->field);
+	BN_clear_free(group->a);
+	BN_clear_free(group->b);
 	}
 
 
 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;
+	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;
 
@@ -191,24 +199,24 @@ int ec_GFp_simple_group_set_curve(EC_GROUP *group,
 	if (tmp_a == NULL) goto err;
 
 	/* group->field */
-	if (!BN_copy(&group->field, p)) goto err;
-	BN_set_sign(&group->field, 0);
+	if (!BN_copy(group->field, p)) goto err;
+	BN_set_negative(group->field, 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; }	
+		{ if (!group->meth->field_encode(group, group->a, tmp_a, ctx)) goto err; }
 	else
-		if (!BN_copy(&group->a, tmp_a)) goto err;
+		if (!BN_copy(group->a, tmp_a)) goto err;
 	
 	/* group->b */
-	if (!BN_nnmod(&group->b, b, p, ctx)) goto err;
+	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;
+		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));
+	group->a_is_minus3 = (0 == BN_cmp(tmp_a, group->field));
 
 	ret = 1;
 
@@ -227,7 +235,7 @@ int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, B
 	
 	if (p != NULL)
 		{
-		if (!BN_copy(p, &group->field)) return 0;
+		if (!BN_copy(p, group->field)) return 0;
 		}
 
 	if (a != NULL || b != NULL)
@@ -242,22 +250,22 @@ int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, B
 				}
 			if (a != NULL)
 				{
-				if (!group->meth->field_decode(group, a, &group->a, ctx)) goto err;
+				if (!group->meth->field_decode(group, a, group->a, ctx)) goto err;
 				}
 			if (b != NULL)
 				{
-				if (!group->meth->field_decode(group, b, &group->b, ctx)) goto err;
+				if (!group->meth->field_decode(group, b, group->b, ctx)) goto err;
 				}
 			}
 		else
 			{
 			if (a != NULL)
 				{
-				if (!BN_copy(a, &group->a)) goto err;
+				if (!BN_copy(a, group->a)) goto err;
 				}
 			if (b != NULL)
 				{
-				if (!BN_copy(b, &group->b)) goto err;
+				if (!BN_copy(b, group->b)) goto err;
 				}
 			}
 		}
@@ -273,7 +281,7 @@ int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, B
 
 int ec_GFp_simple_group_get_degree(const EC_GROUP *group)
 	{
-	return BN_num_bits(&group->field);
+	return BN_num_bits(group->field);
 	}
 
 
@@ -281,7 +289,7 @@ int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
 	{
 	int ret = 0;
 	BIGNUM *a,*b,*order,*tmp_1,*tmp_2;
-	const BIGNUM *p = &group->field;
+	const BIGNUM *p = group->field;
 	BN_CTX *new_ctx = NULL;
 
 	if (ctx == NULL)
@@ -303,18 +311,20 @@ int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
 
 	if (group->meth->field_decode)
 		{
-		if (!group->meth->field_decode(group, a, &group->a, ctx)) goto err;
-		if (!group->meth->field_decode(group, b, &group->b, ctx)) goto err;
+		if (!group->meth->field_decode(group, a, group->a, ctx)) goto err;
+		if (!group->meth->field_decode(group, b, group->b, ctx)) goto err;
 		}
 	else
 		{
-		if (!BN_copy(a, &group->a)) goto err;
-		if (!BN_copy(b, &group->b)) goto err;
+		if (!BN_copy(a, group->a)) goto err;
+		if (!BN_copy(b, group->b)) goto err;
 		}
 	
-	/* check the discriminant:
+	/*-
+	 * check the discriminant:
 	 * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p) 
-         * 0 =< a, b < p */
+         * 0 =< a, b < p 
+	 */
 	if (BN_is_zero(a))
 		{
 		if (BN_is_zero(b)) goto err;
@@ -336,7 +346,8 @@ int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
 	ret = 1;
 
 err:
-	BN_CTX_end(ctx);
+	if (ctx != NULL)
+		BN_CTX_end(ctx);
 	if (new_ctx != NULL)
 		BN_CTX_free(new_ctx);
 	return ret;
@@ -345,37 +356,44 @@ err:
 
 int ec_GFp_simple_point_init(EC_POINT *point)
 	{
-	BN_init(&point->X);
-	BN_init(&point->Y);
-	BN_init(&point->Z);
+	point->X = BN_new();
+	point->Y = BN_new();
+	point->Z = BN_new();
 	point->Z_is_one = 0;
 
+	if(!point->X || !point->Y || !point->Z)
+		{
+		if(point->X) BN_free(point->X);
+		if(point->Y) BN_free(point->Y);
+		if(point->Z) BN_free(point->Z);
+		return 0;
+		}
 	return 1;
 	}
 
 
 void ec_GFp_simple_point_finish(EC_POINT *point)
 	{
-	BN_free(&point->X);
-	BN_free(&point->Y);
-	BN_free(&point->Z);
+	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);
+	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;
+	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;
@@ -385,7 +403,7 @@ int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point)
 	{
 	point->Z_is_one = 0;
-	BN_zero(&point->Z);
+	BN_zero(point->Z);
 	return 1;
 	}
 
@@ -405,19 +423,19 @@ int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group, EC_POIN
 
 	if (x != NULL)
 		{
-		if (!BN_nnmod(&point->X, x, &group->field, ctx)) goto err;
+		if (!BN_nnmod(point->X, x, group->field, ctx)) goto err;
 		if (group->meth->field_encode)
 			{
-			if (!group->meth->field_encode(group, &point->X, &point->X, ctx)) goto err;
+			if (!group->meth->field_encode(group, point->X, point->X, ctx)) goto err;
 			}
 		}
 	
 	if (y != NULL)
 		{
-		if (!BN_nnmod(&point->Y, y, &group->field, ctx)) goto err;
+		if (!BN_nnmod(point->Y, y, group->field, ctx)) goto err;
 		if (group->meth->field_encode)
 			{
-			if (!group->meth->field_encode(group, &point->Y, &point->Y, ctx)) goto err;
+			if (!group->meth->field_encode(group, point->Y, point->Y, ctx)) goto err;
 			}
 		}
 	
@@ -425,17 +443,17 @@ int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group, EC_POIN
 		{
 		int Z_is_one;
 
-		if (!BN_nnmod(&point->Z, z, &group->field, ctx)) goto err;
-		Z_is_one = BN_is_one(&point->Z);
+		if (!BN_nnmod(point->Z, z, group->field, ctx)) goto err;
+		Z_is_one = BN_is_one(point->Z);
 		if (group->meth->field_encode)
 			{
 			if (Z_is_one && (group->meth->field_set_to_one != 0))
 				{
-				if (!group->meth->field_set_to_one(group, &point->Z, ctx)) goto err;
+				if (!group->meth->field_set_to_one(group, point->Z, ctx)) goto err;
 				}
 			else
 				{
-				if (!group->meth->field_encode(group, &point->Z, &point->Z, ctx)) goto err;
+				if (!group->meth->field_encode(group, point->Z, point->Z, ctx)) goto err;
 				}
 			}
 		point->Z_is_one = Z_is_one;
@@ -467,30 +485,30 @@ int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group, const E
 
 		if (x != NULL)
 			{
-			if (!group->meth->field_decode(group, x, &point->X, ctx)) goto err;
+			if (!group->meth->field_decode(group, x, point->X, ctx)) goto err;
 			}
 		if (y != NULL)
 			{
-			if (!group->meth->field_decode(group, y, &point->Y, ctx)) goto err;
+			if (!group->meth->field_decode(group, y, point->Y, ctx)) goto err;
 			}
 		if (z != NULL)
 			{
-			if (!group->meth->field_decode(group, z, &point->Z, ctx)) goto err;
+			if (!group->meth->field_decode(group, z, point->Z, ctx)) goto err;
 			}
 		}
 	else	
 		{
 		if (x != NULL)
 			{
-			if (!BN_copy(x, &point->X)) goto err;
+			if (!BN_copy(x, point->X)) goto err;
 			}
 		if (y != NULL)
 			{
-			if (!BN_copy(y, &point->Y)) goto err;
+			if (!BN_copy(y, point->Y)) goto err;
 			}
 		if (z != NULL)
 			{
-			if (!BN_copy(z, &point->Z)) goto err;
+			if (!BN_copy(z, point->Z)) goto err;
 			}
 		}
 	
@@ -549,12 +567,12 @@ int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_P
 	
 	if (group->meth->field_decode)
 		{
-		if (!group->meth->field_decode(group, Z, &point->Z, ctx)) goto err;
+		if (!group->meth->field_decode(group, Z, point->Z, ctx)) goto err;
 		Z_ = Z;
 		}
 	else
 		{
-		Z_ = &point->Z;
+		Z_ = point->Z;
 		}
 	
 	if (BN_is_one(Z_))
@@ -563,28 +581,28 @@ int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_P
 			{
 			if (x != NULL)
 				{
-				if (!group->meth->field_decode(group, x, &point->X, ctx)) goto err;
+				if (!group->meth->field_decode(group, x, point->X, ctx)) goto err;
 				}
 			if (y != NULL)
 				{
-				if (!group->meth->field_decode(group, y, &point->Y, ctx)) goto err;
+				if (!group->meth->field_decode(group, y, point->Y, ctx)) goto err;
 				}
 			}
 		else
 			{
 			if (x != NULL)
 				{
-				if (!BN_copy(x, &point->X)) goto err;
+				if (!BN_copy(x, point->X)) goto err;
 				}
 			if (y != NULL)
 				{
-				if (!BN_copy(y, &point->Y)) goto err;
+				if (!BN_copy(y, point->Y)) goto err;
 				}
 			}
 		}
 	else
 		{
-		if (!BN_mod_inverse(Z_1, Z_, &group->field, ctx))
+		if (!BN_mod_inverse(Z_1, Z_, group->field, ctx))
 			{
 			ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_BN_LIB);
 			goto err;
@@ -597,13 +615,13 @@ int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_P
 			}
 		else
 			{
-			if (!BN_mod_sqr(Z_2, Z_1, &group->field, ctx)) goto err;
+			if (!BN_mod_sqr(Z_2, Z_1, group->field, ctx)) goto err;
 			}
 	
 		if (x != NULL)
 			{
 			/* in the Montgomery case, field_mul will cancel out Montgomery factor in X: */
-			if (!group->meth->field_mul(group, x, &point->X, Z_2, ctx)) goto err;
+			if (!group->meth->field_mul(group, x, point->X, Z_2, ctx)) goto err;
 			}
 
 		if (y != NULL)
@@ -615,11 +633,11 @@ int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_P
 				}
 			else
 				{
-				if (!BN_mod_mul(Z_3, Z_2, Z_1, &group->field, ctx)) goto err;
+				if (!BN_mod_mul(Z_3, Z_2, Z_1, group->field, ctx)) goto err;
 				}
 
 			/* in the Montgomery case, field_mul will cancel out Montgomery factor in Y: */
-			if (!group->meth->field_mul(group, y, &point->Y, Z_3, ctx)) goto err;
+			if (!group->meth->field_mul(group, y, point->Y, Z_3, ctx)) goto err;
 			}
 		}
 
@@ -632,369 +650,6 @@ int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_P
 	return ret;
 	}
 
-
-int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *point,
-	const BIGNUM *x_, int y_bit, BN_CTX *ctx)
-	{
-	BN_CTX *new_ctx = NULL;
-	BIGNUM *tmp1, *tmp2, *x, *y;
-	int ret = 0;
-
-	if (ctx == NULL)
-		{
-		ctx = new_ctx = BN_CTX_new();
-		if (ctx == NULL)
-			return 0;
-		}
-
-	y_bit = (y_bit != 0);
-
-	BN_CTX_start(ctx);
-	tmp1 = BN_CTX_get(ctx);
-	tmp2 = BN_CTX_get(ctx);
-	x = BN_CTX_get(ctx);
-	y = BN_CTX_get(ctx);
-	if (y == NULL) goto err;
-
-	/* Recover y.  We have a Weierstrass equation
-	 *     y^2 = x^3 + a*x + b,
-	 * so  y  is one of the square roots of  x^3 + a*x + b.
-	 */
-
-	/* tmp1 := x^3 */
-	if (!BN_nnmod(x, x_, &group->field,ctx)) goto err;
-	if (group->meth->field_decode == 0)
-		{
-		/* field_{sqr,mul} work on standard representation */
-		if (!group->meth->field_sqr(group, tmp2, x_, ctx)) goto err;
-		if (!group->meth->field_mul(group, tmp1, tmp2, x_, ctx)) goto err;
-		}
-	else
-		{
-		if (!BN_mod_sqr(tmp2, x_, &group->field, ctx)) goto err;
-		if (!BN_mod_mul(tmp1, tmp2, x_, &group->field, ctx)) goto err;
-		}
-	
-	/* tmp1 := tmp1 + a*x */
-	if (group->a_is_minus3)
-		{
-		if (!BN_mod_lshift1_quick(tmp2, x, &group->field)) goto err;
-		if (!BN_mod_add_quick(tmp2, tmp2, x, &group->field)) goto err;
-		if (!BN_mod_sub_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
-		}
-	else
-		{
-		if (group->meth->field_decode)
-			{
-			if (!group->meth->field_decode(group, tmp2, &group->a, ctx)) goto err;
-			if (!BN_mod_mul(tmp2, tmp2, x, &group->field, ctx)) goto err;
-			}
-		else
-			{
-			/* field_mul works on standard representation */
-			if (!group->meth->field_mul(group, tmp2, &group->a, x, ctx)) goto err;
-			}
-		
-		if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
-		}
-	
-	/* tmp1 := tmp1 + b */
-	if (group->meth->field_decode)
-		{
-		if (!group->meth->field_decode(group, tmp2, &group->b, ctx)) goto err;
-		if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
-		}
-	else
-		{
-		if (!BN_mod_add_quick(tmp1, tmp1, &group->b, &group->field)) goto err;
-		}
-	
-	if (!BN_mod_sqrt(y, tmp1, &group->field, ctx))
-		{
-		unsigned long err = ERR_peek_error();
-		
-		if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NOT_A_SQUARE)
-			{
-			(void)ERR_get_error();
-			ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT);
-			}
-		else
-			ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_BN_LIB);
-		goto err;
-		}
-
-	if (y_bit != BN_is_odd(y))
-		{
-		if (BN_is_zero(y))
-			{
-			int kron;
-
-			kron = BN_kronecker(x, &group->field, ctx);
-			if (kron == -2) goto err;
-
-			if (kron == 1)
-				ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSION_BIT);
-			else
-				/* BN_mod_sqrt() should have cought this error (not a square) */
-				ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT);
-			goto err;
-			}
-		if (!BN_usub(y, &group->field, y)) goto err;
-		}
-	if (y_bit != BN_is_odd(y))
-		{
-		ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_INTERNAL_ERROR);
-		goto err;
-		}
-
-	if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
-
-	ret = 1;
-
- err:
-	BN_CTX_end(ctx);
-	if (new_ctx != NULL)
-		BN_CTX_free(new_ctx);
-	return ret;
-	}
-
-
-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)
-	{
-	size_t ret;
-	BN_CTX *new_ctx = NULL;
-	int used_ctx = 0;
-	BIGNUM *x, *y;
-	size_t field_len, i, skip;
-
-	if ((form != POINT_CONVERSION_COMPRESSED)
-		&& (form != POINT_CONVERSION_UNCOMPRESSED)
-		&& (form != POINT_CONVERSION_HYBRID))
-		{
-		ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_INVALID_FORM);
-		goto err;
-		}
-
-	if (EC_POINT_is_at_infinity(group, point))
-		{
-		/* encodes to a single 0 octet */
-		if (buf != NULL)
-			{
-			if (len < 1)
-				{
-				ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
-				return 0;
-				}
-			buf[0] = 0;
-			}
-		return 1;
-		}
-
-
-	/* ret := required output buffer length */
-	field_len = BN_num_bytes(&group->field);
-	ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
-
-	/* if 'buf' is NULL, just return required length */
-	if (buf != NULL)
-		{
-		if (len < ret)
-			{
-			ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
-			goto err;
-			}
-
-		if (ctx == NULL)
-			{
-			ctx = new_ctx = BN_CTX_new();
-			if (ctx == NULL)
-				return 0;
-			}
-
-		BN_CTX_start(ctx);
-		used_ctx = 1;
-		x = BN_CTX_get(ctx);
-		y = BN_CTX_get(ctx);
-		if (y == NULL) goto err;
-
-		if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
-
-		if ((form == POINT_CONVERSION_COMPRESSED || form == POINT_CONVERSION_HYBRID) && BN_is_odd(y))
-			buf[0] = form + 1;
-		else
-			buf[0] = form;
-	
-		i = 1;
-		
-		skip = field_len - BN_num_bytes(x);
-		if (skip > field_len)
-			{
-			ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
-			goto err;
-			}
-		while (skip > 0)
-			{
-			buf[i++] = 0;
-			skip--;
-			}
-		skip = BN_bn2bin(x, buf + i);
-		i += skip;
-		if (i != 1 + field_len)
-			{
-			ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
-			goto err;
-			}
-
-		if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID)
-			{
-			skip = field_len - BN_num_bytes(y);
-			if (skip > field_len)
-				{
-				ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
-				goto err;
-				}
-			while (skip > 0)
-				{
-				buf[i++] = 0;
-				skip--;
-				}
-			skip = BN_bn2bin(y, buf + i);
-			i += skip;
-			}
-
-		if (i != ret)
-			{
-			ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
-			goto err;
-			}
-		}
-	
-	if (used_ctx)
-		BN_CTX_end(ctx);
-	if (new_ctx != NULL)
-		BN_CTX_free(new_ctx);
-	return ret;
-
- err:
-	if (used_ctx)
-		BN_CTX_end(ctx);
-	if (new_ctx != NULL)
-		BN_CTX_free(new_ctx);
-	return 0;
-	}
-
-
-int ec_GFp_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
-	const unsigned char *buf, size_t len, BN_CTX *ctx)
-	{
-	point_conversion_form_t form;
-	int y_bit;
-	BN_CTX *new_ctx = NULL;
-	BIGNUM *x, *y;
-	size_t field_len, enc_len;
-	int ret = 0;
-
-	if (len == 0)
-		{
-		ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL);
-		return 0;
-		}
-	form = buf[0];
-	y_bit = form & 1;
-	form = form & ~1;
-	if ((form != 0)	&& (form != POINT_CONVERSION_COMPRESSED)
-		&& (form != POINT_CONVERSION_UNCOMPRESSED)
-		&& (form != POINT_CONVERSION_HYBRID))
-		{
-		ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
-		return 0;
-		}
-	if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit)
-		{
-		ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
-		return 0;
-		}
-
-	if (form == 0)
-		{
-		if (len != 1)
-			{
-			ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
-			return 0;
-			}
-
-		return EC_POINT_set_to_infinity(group, point);
-		}
-	
-	field_len = BN_num_bytes(&group->field);
-	enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
-
-	if (len != enc_len)
-		{
-		ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
-		return 0;
-		}
-
-	if (ctx == NULL)
-		{
-		ctx = new_ctx = BN_CTX_new();
-		if (ctx == NULL)
-			return 0;
-		}
-
-	BN_CTX_start(ctx);
-	x = BN_CTX_get(ctx);
-	y = BN_CTX_get(ctx);
-	if (y == NULL) goto err;
-
-	if (!BN_bin2bn(buf + 1, field_len, x)) goto err;
-	if (BN_ucmp(x, &group->field) >= 0)
-		{
-		ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
-		goto err;
-		}
-
-	if (form == POINT_CONVERSION_COMPRESSED)
-		{
-		if (!EC_POINT_set_compressed_coordinates_GFp(group, point, x, y_bit, ctx)) goto err;
-		}
-	else
-		{
-		if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err;
-		if (BN_ucmp(y, &group->field) >= 0)
-			{
-			ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
-			goto err;
-			}
-		if (form == POINT_CONVERSION_HYBRID)
-			{
-			if (y_bit != BN_is_odd(y))
-				{
-				ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
-				goto err;
-				}
-			}
-
-		if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
-		}
-	
-	if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */
-		{
-		ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE);
-		goto err;
-		}
-
-	ret = 1;
-	
- err:
-	BN_CTX_end(ctx);
-	if (new_ctx != NULL)
-		BN_CTX_free(new_ctx);
-	return ret;
-	}
-
-
 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 *);
@@ -1013,7 +668,7 @@ int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, con
 	
 	field_mul = group->meth->field_mul;
 	field_sqr = group->meth->field_sqr;
-	p = &group->field;
+	p = group->field;
 
 	if (ctx == NULL)
 		{
@@ -1040,38 +695,38 @@ int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, con
 	/* n1, n2 */
 	if (b->Z_is_one)
 		{
-		if (!BN_copy(n1, &a->X)) goto end;
-		if (!BN_copy(n2, &a->Y)) goto end;
+		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;
+		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;
+		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;
+		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;
+		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;
+		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 */
 		}
 
@@ -1094,7 +749,7 @@ int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, con
 		else
 			{
 			/* a is the inverse of b */
-			BN_zero(&r->Z);
+			BN_zero(r->Z);
 			r->Z_is_one = 0;
 			ret = 1;
 			goto end;
@@ -1110,17 +765,17 @@ int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, con
 	/* Z_r */
 	if (a->Z_is_one && b->Z_is_one)
 		{
-		if (!BN_copy(&r->Z, n5)) goto end;
+		if (!BN_copy(r->Z, n5)) goto end;
 		}
 	else
 		{
 		if (a->Z_is_one)
-			{ if (!BN_copy(n0, &b->Z)) goto end; }
+			{ if (!BN_copy(n0, b->Z)) goto end; }
 		else if (b->Z_is_one)
-			{ if (!BN_copy(n0, &a->Z)) goto end; }
+			{ 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;
+			{ 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 */
@@ -1129,11 +784,11 @@ int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, con
 	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;
+	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_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 */
 
@@ -1145,7 +800,7 @@ int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, con
 	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;
+	if (!BN_rshift1(r->Y, n0)) goto end;
 	/* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */
 
 	ret = 1;
@@ -1170,14 +825,14 @@ int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_
 	
 	if (EC_POINT_is_at_infinity(group, a))
 		{
-		BN_zero(&r->Z);
+		BN_zero(r->Z);
 		r->Z_is_one = 0;
 		return 1;
 		}
 
 	field_mul = group->meth->field_mul;
 	field_sqr = group->meth->field_sqr;
-	p = &group->field;
+	p = group->field;
 
 	if (ctx == NULL)
 		{
@@ -1201,17 +856,17 @@ int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_
 	/* n1 */
 	if (a->Z_is_one)
 		{
-		if (!field_sqr(group, n0, &a->X, ctx)) goto err;
+		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;
+		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_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;
@@ -1220,12 +875,12 @@ int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_
 		}
 	else
 		{
-		if (!field_sqr(group, n0, &a->X, ctx)) goto err;
+		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, 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 (!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 */
 		}
@@ -1233,26 +888,26 @@ int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_
 	/* Z_r */
 	if (a->Z_is_one)
 		{
-		if (!BN_copy(n0, &a->Y)) goto err;
+		if (!BN_copy(n0, a->Y)) goto err;
 		}
 	else
 		{
-		if (!field_mul(group, n0, &a->Y, &a->Z, ctx)) goto err;
+		if (!field_mul(group, n0, a->Y, a->Z, ctx)) goto err;
 		}
-	if (!BN_mod_lshift1_quick(&r->Z, n0, p)) 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 (!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;
+	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 */
@@ -1261,9 +916,9 @@ int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_
 	/* n3 = 8 * Y_a^4 */
 	
 	/* Y_r */
-	if (!BN_mod_sub_quick(n0, n2, &r->X, p)) goto err;
+	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;
+	if (!BN_mod_sub_quick(r->Y, n0, n3, p)) goto err;
 	/* Y_r = n1 * (n2 - X_r) - n3 */
 
 	ret = 1;
@@ -1278,17 +933,17 @@ int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_
 
 int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
 	{
-	if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y))
+	if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(point->Y))
 		/* point is its own inverse */
 		return 1;
 	
-	return BN_usub(&point->Y, &group->field, &point->Y);
+	return BN_usub(point->Y, group->field, point->Y);
 	}
 
 
 int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
 	{
-	return BN_is_zero(&point->Z);
+	return BN_is_zero(point->Z);
 	}
 
 
@@ -1298,7 +953,7 @@ int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_C
 	int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
 	const BIGNUM *p;
 	BN_CTX *new_ctx = NULL;
-	BIGNUM *rh, *tmp1, *tmp2, *Z4, *Z6;
+	BIGNUM *rh, *tmp, *Z4, *Z6;
 	int ret = -1;
 
 	if (EC_POINT_is_at_infinity(group, point))
@@ -1306,7 +961,7 @@ int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_C
 	
 	field_mul = group->meth->field_mul;
 	field_sqr = group->meth->field_sqr;
-	p = &group->field;
+	p = group->field;
 
 	if (ctx == NULL)
 		{
@@ -1317,13 +972,13 @@ int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_C
 
 	BN_CTX_start(ctx);
 	rh = BN_CTX_get(ctx);
-	tmp1 = BN_CTX_get(ctx);
-	tmp2 = BN_CTX_get(ctx);
+	tmp = BN_CTX_get(ctx);
 	Z4 = BN_CTX_get(ctx);
 	Z6 = BN_CTX_get(ctx);
 	if (Z6 == NULL) goto err;
 
-	/* We have a curve defined by a Weierstrass equation
+	/*-
+	 * We have a curve defined by a Weierstrass equation
 	 *      y^2 = x^3 + a*x + b.
 	 * The point to consider is given in Jacobian projective coordinates
 	 * where  (X, Y, Z)  represents  (x, y) = (X/Z^2, Y/Z^3).
@@ -1332,59 +987,49 @@ int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_C
 	 * To test this, we add up the right-hand side in 'rh'.
 	 */
 
-	/* rh := X^3 */
-	if (!field_sqr(group, rh, &point->X, ctx)) goto err;
-	if (!field_mul(group, rh, rh, &point->X, ctx)) goto err;
+	/* rh := X^2 */
+	if (!field_sqr(group, rh, point->X, ctx)) goto err;
 
 	if (!point->Z_is_one)
 		{
-		if (!field_sqr(group, tmp1, &point->Z, ctx)) goto err;
-		if (!field_sqr(group, Z4, tmp1, ctx)) goto err;
-		if (!field_mul(group, Z6, Z4, tmp1, ctx)) goto err;
+		if (!field_sqr(group, tmp, point->Z, ctx)) goto err;
+		if (!field_sqr(group, Z4, tmp, ctx)) goto err;
+		if (!field_mul(group, Z6, Z4, tmp, ctx)) goto err;
 
-		/* rh := rh + a*X*Z^4 */
-		if (!field_mul(group, tmp1, &point->X, Z4, ctx)) goto err;
+		/* rh := (rh + a*Z^4)*X */
 		if (group->a_is_minus3)
 			{
-			if (!BN_mod_lshift1_quick(tmp2, tmp1, p)) goto err;
-			if (!BN_mod_add_quick(tmp2, tmp2, tmp1, p)) goto err;
-			if (!BN_mod_sub_quick(rh, rh, tmp2, p)) goto err;
+			if (!BN_mod_lshift1_quick(tmp, Z4, p)) goto err;
+			if (!BN_mod_add_quick(tmp, tmp, Z4, p)) goto err;
+			if (!BN_mod_sub_quick(rh, rh, tmp, p)) goto err;
+			if (!field_mul(group, rh, rh, point->X, ctx)) goto err;
 			}
 		else
 			{
-			if (!field_mul(group, tmp2, tmp1, &group->a, ctx)) goto err;
-			if (!BN_mod_add_quick(rh, rh, tmp2, p)) goto err;
+			if (!field_mul(group, tmp, Z4, group->a, ctx)) goto err;
+			if (!BN_mod_add_quick(rh, rh, tmp, p)) goto err;
+			if (!field_mul(group, rh, rh, point->X, ctx)) goto err;
 			}
 
 		/* rh := rh + b*Z^6 */
-		if (!field_mul(group, tmp1, &group->b, Z6, ctx)) goto err;
-		if (!BN_mod_add_quick(rh, rh, tmp1, p)) goto err;
+		if (!field_mul(group, tmp, group->b, Z6, ctx)) goto err;
+		if (!BN_mod_add_quick(rh, rh, tmp, p)) goto err;
 		}
 	else
 		{
 		/* point->Z_is_one */
 
-		/* rh := rh + a*X */
-		if (group->a_is_minus3)
-			{
-			if (!BN_mod_lshift1_quick(tmp2, &point->X, p)) goto err;
-			if (!BN_mod_add_quick(tmp2, tmp2, &point->X, p)) goto err;
-			if (!BN_mod_sub_quick(rh, rh, tmp2, p)) goto err;
-			}
-		else
-			{
-			if (!field_mul(group, tmp2, &point->X, &group->a, ctx)) goto err;
-			if (!BN_mod_add_quick(rh, rh, tmp2, p)) goto err;
-			}
-
+		/* rh := (rh + a)*X */
+		if (!BN_mod_add_quick(rh, rh, group->a, p)) goto err;
+		if (!field_mul(group, rh, rh, point->X, ctx)) goto err;
 		/* rh := rh + b */
-		if (!BN_mod_add_quick(rh, rh, &group->b, p)) goto err;
+		if (!BN_mod_add_quick(rh, rh, group->b, p)) goto err;
 		}
 
 	/* 'lh' := Y^2 */
-	if (!field_sqr(group, tmp1, &point->Y, ctx)) goto err;
+	if (!field_sqr(group, tmp, point->Y, ctx)) goto err;
 
-	ret = (0 == BN_cmp(tmp1, rh));
+	ret = (0 == BN_ucmp(tmp, rh));
 
  err:
 	BN_CTX_end(ctx);
@@ -1413,10 +1058,13 @@ int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *
 		{
 		return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
 		}
+
+	if (EC_POINT_is_at_infinity(group, b))
+		return 1;
 	
 	if (a->Z_is_one && b->Z_is_one)
 		{
-		return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1;
+		return ((BN_cmp(a->X, b->X) == 0) && BN_cmp(a->Y, b->Y) == 0) ? 0 : 1;
 		}
 
 	field_mul = group->meth->field_mul;
@@ -1436,7 +1084,8 @@ int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *
 	Zb23 = BN_CTX_get(ctx);
 	if (Zb23 == NULL) goto end;
 
-	/* We have to decide whether
+	/*-
+	 * We have to decide whether
 	 *     (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3),
 	 * or equivalently, whether
 	 *     (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3).
@@ -1444,20 +1093,20 @@ int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *
 
 	if (!b->Z_is_one)
 		{
-		if (!field_sqr(group, Zb23, &b->Z, ctx)) goto end;
-		if (!field_mul(group, tmp1, &a->X, Zb23, ctx)) goto end;
+		if (!field_sqr(group, Zb23, b->Z, ctx)) goto end;
+		if (!field_mul(group, tmp1, a->X, Zb23, ctx)) goto end;
 		tmp1_ = tmp1;
 		}
 	else
-		tmp1_ = &a->X;
+		tmp1_ = a->X;
 	if (!a->Z_is_one)
 		{
-		if (!field_sqr(group, Za23, &a->Z, ctx)) goto end;
-		if (!field_mul(group, tmp2, &b->X, Za23, ctx)) goto end;
+		if (!field_sqr(group, Za23, a->Z, ctx)) goto end;
+		if (!field_mul(group, tmp2, b->X, Za23, ctx)) goto end;
 		tmp2_ = tmp2;
 		}
 	else
-		tmp2_ = &b->X;
+		tmp2_ = b->X;
 	
 	/* compare  X_a*Z_b^2  with  X_b*Z_a^2 */
 	if (BN_cmp(tmp1_, tmp2_) != 0)
@@ -1469,20 +1118,20 @@ int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *
 
 	if (!b->Z_is_one)
 		{
-		if (!field_mul(group, Zb23, Zb23, &b->Z, ctx)) goto end;
-		if (!field_mul(group, tmp1, &a->Y, Zb23, ctx)) goto end;
+		if (!field_mul(group, Zb23, Zb23, b->Z, ctx)) goto end;
+		if (!field_mul(group, tmp1, a->Y, Zb23, ctx)) goto end;
 		/* tmp1_ = tmp1 */
 		}
 	else
-		tmp1_ = &a->Y;
+		tmp1_ = a->Y;
 	if (!a->Z_is_one)
 		{
-		if (!field_mul(group, Za23, Za23, &a->Z, ctx)) goto end;
-		if (!field_mul(group, tmp2, &b->Y, Za23, ctx)) goto end;
+		if (!field_mul(group, Za23, Za23, a->Z, ctx)) goto end;
+		if (!field_mul(group, tmp2, b->Y, Za23, ctx)) goto end;
 		/* tmp2_ = tmp2 */
 		}
 	else
-		tmp2_ = &b->Y;
+		tmp2_ = b->Y;
 
 	/* compare  Y_a*Z_b^3  with  Y_b*Z_a^3 */
 	if (BN_cmp(tmp1_, tmp2_) != 0)
@@ -1544,9 +1193,8 @@ int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ct
 int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx)
 	{
 	BN_CTX *new_ctx = NULL;
-	BIGNUM *tmp0, *tmp1;
-	size_t pow2 = 0;
-	BIGNUM **heap = NULL;
+	BIGNUM *tmp, *tmp_Z;
+	BIGNUM **prod_Z = NULL;
 	size_t i;
 	int ret = 0;
 
@@ -1561,151 +1209,130 @@ int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT
 		}
 
 	BN_CTX_start(ctx);
-	tmp0 = BN_CTX_get(ctx);
-	tmp1 = BN_CTX_get(ctx);
-	if (tmp0  == NULL || tmp1 == NULL) goto err;
+	tmp = BN_CTX_get(ctx);
+	tmp_Z = BN_CTX_get(ctx);
+	if (tmp == NULL || tmp_Z == NULL) goto err;
 
-	/* Before converting the individual points, compute inverses of all Z values.
-	 * Modular inversion is rather slow, but luckily we can do with a single
-	 * explicit inversion, plus about 3 multiplications per input value.
-	 */
+	prod_Z = OPENSSL_malloc(num * sizeof prod_Z[0]);
+	if (prod_Z == NULL) goto err;
+	for (i = 0; i < num; i++)
+		{
+		prod_Z[i] = BN_new();
+		if (prod_Z[i] == NULL) goto err;
+		}
 
-	pow2 = 1;
-	while (num > pow2)
-		pow2 <<= 1;
-	/* Now pow2 is the smallest power of 2 satifsying pow2 >= num.
-	 * We need twice that. */
-	pow2 <<= 1;
+	/* Set each prod_Z[i] to the product of points[0]->Z .. points[i]->Z,
+	 * skipping any zero-valued inputs (pretend that they're 1). */
 
-	heap = OPENSSL_malloc(pow2 * sizeof heap[0]);
-	if (heap == NULL) goto err;
-	
-	/* The array is used as a binary tree, exactly as in heapsort:
-	 *
-	 *                               heap[1]
-	 *                 heap[2]                     heap[3]
-	 *          heap[4]       heap[5]       heap[6]       heap[7]
-	 *   heap[8]heap[9] heap[10]heap[11] heap[12]heap[13] heap[14] heap[15]
-	 *
-	 * We put the Z's in the last line;
-	 * then we set each other node to the product of its two child-nodes (where
-	 * empty or 0 entries are treated as ones);
-	 * then we invert heap[1];
-	 * then we invert each other node by replacing it by the product of its
-	 * parent (after inversion) and its sibling (before inversion).
-	 */
-	heap[0] = NULL;
-	for (i = pow2/2 - 1; i > 0; i--)
-		heap[i] = NULL;
-	for (i = 0; i < num; i++)
-		heap[pow2/2 + i] = &points[i]->Z;
-	for (i = pow2/2 + num; i < pow2; i++)
-		heap[i] = NULL;
-	
-	/* set each node to the product of its children */
-	for (i = pow2/2 - 1; i > 0; i--)
+	if (!BN_is_zero(points[0]->Z))
 		{
-		heap[i] = BN_new();
-		if (heap[i] == NULL) goto err;
-		
-		if (heap[2*i] != NULL)
+		if (!BN_copy(prod_Z[0], points[0]->Z)) goto err;
+		}
+	else
+		{
+		if (group->meth->field_set_to_one != 0)
 			{
-			if ((heap[2*i + 1] == NULL) || BN_is_zero(heap[2*i + 1]))
-				{
-				if (!BN_copy(heap[i], heap[2*i])) goto err;
-				}
-			else
-				{
-				if (BN_is_zero(heap[2*i]))
-					{
-					if (!BN_copy(heap[i], heap[2*i + 1])) goto err;
-					}
-				else
-					{
-					if (!group->meth->field_mul(group, heap[i],
-						heap[2*i], heap[2*i + 1], ctx)) goto err;
-					}
-				}
+			if (!group->meth->field_set_to_one(group, prod_Z[0], ctx)) goto err;
+			}
+		else
+			{
+			if (!BN_one(prod_Z[0])) goto err;
 			}
 		}
 
-	/* invert heap[1] */
-	if (!BN_is_zero(heap[1]))
+	for (i = 1; i < num; i++)
 		{
-		if (!BN_mod_inverse(heap[1], heap[1], &group->field, ctx))
+		if (!BN_is_zero(points[i]->Z))
 			{
-			ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB);
-			goto err;
+			if (!group->meth->field_mul(group, prod_Z[i], prod_Z[i - 1], points[i]->Z, ctx)) goto err;
+			}
+		else
+			{
+			if (!BN_copy(prod_Z[i], prod_Z[i - 1])) goto err;
 			}
 		}
+
+	/* Now use a single explicit inversion to replace every
+	 * non-zero points[i]->Z by its inverse. */
+
+	if (!BN_mod_inverse(tmp, prod_Z[num - 1], group->field, ctx))
+		{
+		ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB);
+		goto err;
+		}
 	if (group->meth->field_encode != 0)
 		{
-		/* in the Montgomery case, we just turned  R*H  (representing H)
+		/* In the Montgomery case, we just turned  R*H  (representing H)
 		 * into  1/(R*H),  but we need  R*(1/H)  (representing 1/H);
-		 * i.e. we have need to multiply by the Montgomery factor twice */
-		if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) goto err;
-		if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) goto err;
+		 * i.e. we need to multiply by the Montgomery factor twice. */
+		if (!group->meth->field_encode(group, tmp, tmp, ctx)) goto err;
+		if (!group->meth->field_encode(group, tmp, tmp, ctx)) goto err;
 		}
 
-	/* set other heap[i]'s to their inverses */
-	for (i = 2; i < pow2/2 + num; i += 2)
+	for (i = num - 1; i > 0; --i)
 		{
-		/* i is even */
-		if ((heap[i + 1] != NULL) && !BN_is_zero(heap[i + 1]))
+		/* Loop invariant: tmp is the product of the inverses of
+		 * points[0]->Z .. points[i]->Z (zero-valued inputs skipped). */
+		if (!BN_is_zero(points[i]->Z))
 			{
-			if (!group->meth->field_mul(group, tmp0, heap[i/2], heap[i + 1], ctx)) goto err;
-			if (!group->meth->field_mul(group, tmp1, heap[i/2], heap[i], ctx)) goto err;
-			if (!BN_copy(heap[i], tmp0)) goto err;
-			if (!BN_copy(heap[i + 1], tmp1)) goto err;
-			}
-		else
-			{
-			if (!BN_copy(heap[i], heap[i/2])) goto err;
+			/* Set tmp_Z to the inverse of points[i]->Z (as product
+			 * of Z inverses 0 .. i, Z values 0 .. i - 1). */
+			if (!group->meth->field_mul(group, tmp_Z, prod_Z[i - 1], tmp, ctx)) goto err;
+			/* Update tmp to satisfy the loop invariant for i - 1. */
+			if (!group->meth->field_mul(group, tmp, tmp, points[i]->Z, ctx)) goto err;
+			/* Replace points[i]->Z by its inverse. */
+			if (!BN_copy(points[i]->Z, tmp_Z)) goto err;
 			}
 		}
 
-	/* we have replaced all non-zero Z's by their inverses, now fix up all the points */
+	if (!BN_is_zero(points[0]->Z))
+		{
+		/* Replace points[0]->Z by its inverse. */
+		if (!BN_copy(points[0]->Z, tmp)) goto err;
+		}
+
+	/* Finally, fix up the X and Y coordinates for all points. */
+
 	for (i = 0; i < num; i++)
 		{
 		EC_POINT *p = points[i];
-		
-		if (!BN_is_zero(&p->Z))
+
+		if (!BN_is_zero(p->Z))
 			{
 			/* turn  (X, Y, 1/Z)  into  (X/Z^2, Y/Z^3, 1) */
 
-			if (!group->meth->field_sqr(group, tmp1, &p->Z, ctx)) goto err;
-			if (!group->meth->field_mul(group, &p->X, &p->X, tmp1, ctx)) goto err;
+			if (!group->meth->field_sqr(group, tmp, p->Z, ctx)) goto err;
+			if (!group->meth->field_mul(group, p->X, p->X, tmp, ctx)) goto err;
+
+			if (!group->meth->field_mul(group, tmp, tmp, p->Z, ctx)) goto err;
+			if (!group->meth->field_mul(group, p->Y, p->Y, tmp, ctx)) goto err;
 
-			if (!group->meth->field_mul(group, tmp1, tmp1, &p->Z, ctx)) goto err;
-			if (!group->meth->field_mul(group, &p->Y, &p->Y, tmp1, ctx)) goto err;
-		
 			if (group->meth->field_set_to_one != 0)
 				{
-				if (!group->meth->field_set_to_one(group, &p->Z, ctx)) goto err;
+				if (!group->meth->field_set_to_one(group, p->Z, ctx)) goto err;
 				}
 			else
 				{
-				if (!BN_one(&p->Z)) goto err;
+				if (!BN_one(p->Z)) goto err;
 				}
 			p->Z_is_one = 1;
 			}
 		}
 
 	ret = 1;
-		
+
  err:
 	BN_CTX_end(ctx);
 	if (new_ctx != NULL)
 		BN_CTX_free(new_ctx);
-	if (heap != NULL)
+	if (prod_Z != NULL)
 		{
-		/* heap[pow2/2] .. heap[pow2-1] have not been allocated locally! */
-		for (i = pow2/2 - 1; i > 0; i--)
+		for (i = 0; i < num; i++)
 			{
-			if (heap[i] != NULL)
-				BN_clear_free(heap[i]);
+			if (prod_Z[i] == NULL) break;
+			BN_clear_free(prod_Z[i]);
 			}
-		OPENSSL_free(heap);
+		OPENSSL_free(prod_Z);
 		}
 	return ret;
 	}
@@ -1713,11 +1340,11 @@ int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT
 
 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);
+	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);
+	return BN_mod_sqr(r, a, group->field, ctx);
 	}