1 files changed, 167 insertions, 168 deletions

diff --git a/src/lib/libcrypto/ec/ecp_smpl.c b/src/lib/libcrypto/ec/ecp_smpl.c
index e9a51fb87a..4d26f8bdf6 100644
--- a/src/lib/libcrypto/ec/ecp_smpl.c
+++ b/src/lib/libcrypto/ec/ecp_smpl.c
@@ -1,8 +1,10 @@
 /* crypto/ec/ecp_smpl.c */
 /* Includes code written by Lenka Fibikova <fibikova@exp-math.uni-essen.de>
- * for the OpenSSL project. */
+ * for the OpenSSL project. 
+ * Includes code written by Bodo Moeller for the OpenSSL project.
+*/
 /* ====================================================================
- * Copyright (c) 1998-2001 The OpenSSL Project.  All rights reserved.
+ * Copyright (c) 1998-2002 The OpenSSL Project.  All rights reserved.
  *
  * Redistribution and use in source and binary forms, with or without
  * modification, are permitted provided that the following conditions
@@ -54,25 +56,29 @@
  * Hudson (tjh@cryptsoft.com).
  *
  */
+/* ====================================================================
+ * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
+ * Portions of this software developed by SUN MICROSYSTEMS, INC.,
+ * and contributed to the OpenSSL project.
+ */
 
 #include <openssl/err.h>
+#include <openssl/symhacks.h>
 
 #include "ec_lcl.h"
 
-
 const EC_METHOD *EC_GFp_simple_method(void)
         {
         static const EC_METHOD ret = {
+                NID_X9_62_prime_field,
                 ec_GFp_simple_group_init,
                 ec_GFp_simple_group_finish,
                 ec_GFp_simple_group_clear_finish,
                 ec_GFp_simple_group_copy,
-                ec_GFp_simple_group_set_curve_GFp,
-                ec_GFp_simple_group_get_curve_GFp,
-                ec_GFp_simple_group_set_generator,
-                ec_GFp_simple_group_get0_generator,
-                ec_GFp_simple_group_get_order,
-                ec_GFp_simple_group_get_cofactor,
+                ec_GFp_simple_group_set_curve,
+                ec_GFp_simple_group_get_curve,
+                ec_GFp_simple_group_get_degree,
+                ec_GFp_simple_group_check_discriminant,
                 ec_GFp_simple_point_init,
                 ec_GFp_simple_point_finish,
                 ec_GFp_simple_point_clear_finish,
@@ -80,9 +86,9 @@ const EC_METHOD *EC_GFp_simple_method(void)
                 ec_GFp_simple_point_set_to_infinity,
                 ec_GFp_simple_set_Jprojective_coordinates_GFp,
                 ec_GFp_simple_get_Jprojective_coordinates_GFp,
-                ec_GFp_simple_point_set_affine_coordinates_GFp,
-                ec_GFp_simple_point_get_affine_coordinates_GFp,
-                ec_GFp_simple_set_compressed_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,
                 ec_GFp_simple_add,
@@ -93,8 +99,12 @@ const EC_METHOD *EC_GFp_simple_method(void)
                 ec_GFp_simple_cmp,
                 ec_GFp_simple_make_affine,
                 ec_GFp_simple_points_make_affine,
+                0 /* mul */,
+                0 /* precompute_mult */,
+                0 /* have_precompute_mult */,   
                 ec_GFp_simple_field_mul,
                 ec_GFp_simple_field_sqr,
+                0 /* field_div */,
                 0 /* field_encode */,
                 0 /* field_decode */,
                 0 /* field_set_to_one */ };
@@ -103,15 +113,26 @@ const EC_METHOD *EC_GFp_simple_method(void)
         }
 
 
+/* Most method functions in this file are designed to work with
+ * non-trivial representations of field elements if necessary
+ * (see ecp_mont.c): while standard modular addition and subtraction
+ * are used, the field_mul and field_sqr methods will be used for
+ * multiplication, and field_encode and field_decode (if defined)
+ * will be used for converting between representations.
+
+ * Functions ec_GFp_simple_points_make_affine() and
+ * ec_GFp_simple_point_get_affine_coordinates() specifically assume
+ * that if a non-trivial representation is used, it is a Montgomery
+ * representation (i.e. 'encoding' means multiplying by some factor R).
+ */
+
+
 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;
         }
 
@@ -121,10 +142,6 @@ 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);
         }
 
 
@@ -133,13 +150,6 @@ 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);
         }
 
 
@@ -151,33 +161,11 @@ int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
 
         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_curve_GFp(EC_GROUP *group,
+int ec_GFp_simple_group_set_curve(EC_GROUP *group,
         const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
         {
         int ret = 0;
@@ -187,7 +175,7 @@ int ec_GFp_simple_group_set_curve_GFp(EC_GROUP *group,
         /* p must be a prime > 3 */
         if (BN_num_bits(p) <= 2 || !BN_is_odd(p))
                 {
-                ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE_GFP, EC_R_INVALID_FIELD);
+                ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE, EC_R_INVALID_FIELD);
                 return 0;
                 }
 
@@ -204,7 +192,7 @@ int ec_GFp_simple_group_set_curve_GFp(EC_GROUP *group,
 
         /* group->field */
         if (!BN_copy(&group->field, p)) goto err;
-        group->field.neg = 0;
+        BN_set_negative(&group->field, 0);
 
         /* group->a */
         if (!BN_nnmod(tmp_a, a, p, ctx)) goto err;
@@ -232,7 +220,7 @@ int ec_GFp_simple_group_set_curve_GFp(EC_GROUP *group,
         }
 
 
-int ec_GFp_simple_group_get_curve_GFp(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
+int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
         {
         int ret = 0;
         BN_CTX *new_ctx = NULL;
@@ -283,58 +271,76 @@ int ec_GFp_simple_group_get_curve_GFp(const EC_GROUP *group, BIGNUM *p, BIGNUM *
         }
 
 
+int ec_GFp_simple_group_get_degree(const EC_GROUP *group)
+        {
+        return BN_num_bits(&group->field);
+        }
+
 
-int ec_GFp_simple_group_set_generator(EC_GROUP *group, const EC_POINT *generator,
-        const BIGNUM *order, const BIGNUM *cofactor)
+int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
         {
-        if (generator == NULL)
+        int ret = 0;
+        BIGNUM *a,*b,*order,*tmp_1,*tmp_2;
+        const BIGNUM *p = &group->field;
+        BN_CTX *new_ctx = NULL;
+
+        if (ctx == NULL)
                 {
-                ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_GENERATOR, ERR_R_PASSED_NULL_PARAMETER);
-                return 0   ;
+                ctx = new_ctx = BN_CTX_new();
+                if (ctx == NULL)
+                        {
+                        ECerr(EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE);
+                        goto err;
+                        }
                 }
+        BN_CTX_start(ctx);
+        a = BN_CTX_get(ctx);
+        b = BN_CTX_get(ctx);
+        tmp_1 = BN_CTX_get(ctx);
+        tmp_2 = BN_CTX_get(ctx);
+        order = BN_CTX_get(ctx);
+        if (order == NULL) goto err;
 
-        if (group->generator == NULL)
+        if (group->meth->field_decode)
                 {
-                group->generator = EC_POINT_new(group);
-                if (group->generator == NULL) return 0;
+                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 (!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;
-        }
-
-
-EC_POINT *ec_GFp_simple_group_get0_generator(const EC_GROUP *group)
-        {
-        return group->generator;
-        }
-
-
-int ec_GFp_simple_group_get_order(const EC_GROUP *group, BIGNUM *order, BN_CTX *ctx)
-        {
-        if (!BN_copy(order, &group->order))
-                return 0;
-
-        return !BN_is_zero(&group->order);
-        }
+                {
+                if (!BN_copy(a, &group->a)) goto err;
+                if (!BN_copy(b, &group->b)) goto err;
+                }
+        
+        /* 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 */
+        if (BN_is_zero(a))
+                {
+                if (BN_is_zero(b)) goto err;
+                }
+        else if (!BN_is_zero(b))
+                {
+                if (!BN_mod_sqr(tmp_1, a, p, ctx)) goto err;
+                if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx)) goto err;
+                if (!BN_lshift(tmp_1, tmp_2, 2)) goto err;
+                /* tmp_1 = 4*a^3 */
 
+                if (!BN_mod_sqr(tmp_2, b, p, ctx)) goto err;
+                if (!BN_mul_word(tmp_2, 27)) goto err;
+                /* tmp_2 = 27*b^2 */
 
-int ec_GFp_simple_group_get_cofactor(const EC_GROUP *group, BIGNUM *cofactor, BN_CTX *ctx)
-        {
-        if (!BN_copy(cofactor, &group->cofactor))
-                return 0;
+                if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx)) goto err;
+                if (BN_is_zero(a)) goto err;
+                }
+        ret = 1;
 
-        return !BN_is_zero(&group->cofactor);
+err:
+        if (ctx != NULL)
+                BN_CTX_end(ctx);
+        if (new_ctx != NULL)
+                BN_CTX_free(new_ctx);
+        return ret;
         }
 
 
@@ -380,7 +386,8 @@ 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;
-        return (BN_zero(&point->Z));
+        BN_zero(&point->Z);
+        return 1;
         }
 
 
@@ -497,13 +504,13 @@ int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group, const E
         }
 
 
-int ec_GFp_simple_point_set_affine_coordinates_GFp(const EC_GROUP *group, EC_POINT *point,
+int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point,
         const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx)
         {
         if (x == NULL || y == NULL)
                 {
                 /* unlike for projective coordinates, we do not tolerate this */
-                ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES_GFP, ERR_R_PASSED_NULL_PARAMETER);
+                ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER);
                 return 0;
                 }
 
@@ -511,17 +518,17 @@ int ec_GFp_simple_point_set_affine_coordinates_GFp(const EC_GROUP *group, EC_POI
         }
 
 
-int ec_GFp_simple_point_get_affine_coordinates_GFp(const EC_GROUP *group, const EC_POINT *point,
+int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point,
         BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
         {
         BN_CTX *new_ctx = NULL;
-        BIGNUM *X, *Y, *Z, *Z_1, *Z_2, *Z_3;
-        const BIGNUM *X_, *Y_, *Z_;
+        BIGNUM *Z, *Z_1, *Z_2, *Z_3;
+        const BIGNUM *Z_;
         int ret = 0;
 
         if (EC_POINT_is_at_infinity(group, point))
                 {
-                ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES_GFP, EC_R_POINT_AT_INFINITY);
+                ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY);
                 return 0;
                 }
 
@@ -533,8 +540,6 @@ int ec_GFp_simple_point_get_affine_coordinates_GFp(const EC_GROUP *group, const
                 }
 
         BN_CTX_start(ctx);
-        X = BN_CTX_get(ctx);
-        Y = BN_CTX_get(ctx);
         Z = BN_CTX_get(ctx);
         Z_1 = BN_CTX_get(ctx);
         Z_2 = BN_CTX_get(ctx);
@@ -545,34 +550,44 @@ int ec_GFp_simple_point_get_affine_coordinates_GFp(const EC_GROUP *group, const
         
         if (group->meth->field_decode)
                 {
-                if (!group->meth->field_decode(group, X, &point->X, ctx)) goto err;
-                if (!group->meth->field_decode(group, Y, &point->Y, ctx)) goto err;
                 if (!group->meth->field_decode(group, Z, &point->Z, ctx)) goto err;
-                X_ = X; Y_ = Y; Z_ = Z;
+                Z_ = Z;
                 }
         else
                 {
-                X_ = &point->X;
-                Y_ = &point->Y;
                 Z_ = &point->Z;
                 }
         
         if (BN_is_one(Z_))
                 {
-                if (x != NULL)
+                if (group->meth->field_decode)
                         {
-                        if (!BN_copy(x, X_)) goto err;
+                        if (x != NULL)
+                                {
+                                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 (y != NULL)
+                else
                         {
-                        if (!BN_copy(y, Y_)) goto err;
+                        if (x != NULL)
+                                {
+                                if (!BN_copy(x, &point->X)) goto err;
+                                }
+                        if (y != NULL)
+                                {
+                                if (!BN_copy(y, &point->Y)) goto err;
+                                }
                         }
                 }
         else
                 {
                 if (!BN_mod_inverse(Z_1, Z_, &group->field, ctx))
                         {
-                        ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES_GFP, ERR_R_BN_LIB);
+                        ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_BN_LIB);
                         goto err;
                         }
                 
@@ -588,15 +603,8 @@ int ec_GFp_simple_point_get_affine_coordinates_GFp(const EC_GROUP *group, const
         
                 if (x != NULL)
                         {
-                        if (group->meth->field_encode == 0)
-                                {
-                                /* field_mul works on standard representation */
-                                if (!group->meth->field_mul(group, x, X_, Z_2, ctx)) goto err;
-                                }
-                        else
-                                {
-                                if (!BN_mod_mul(x, X_, Z_2, &group->field, ctx)) goto err;
-                                }
+                        /* 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 (y != NULL)
@@ -605,14 +613,14 @@ int ec_GFp_simple_point_get_affine_coordinates_GFp(const EC_GROUP *group, const
                                 {
                                 /* field_mul works on standard representation */
                                 if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx)) goto err;
-                                if (!group->meth->field_mul(group, y, Y_, Z_3, ctx)) goto err;
-                                
                                 }
                         else
                                 {
                                 if (!BN_mod_mul(Z_3, Z_2, Z_1, &group->field, ctx)) goto err;
-                                if (!BN_mod_mul(y, Y_, Z_3, &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;
                         }
                 }
 
@@ -626,13 +634,16 @@ int ec_GFp_simple_point_get_affine_coordinates_GFp(const EC_GROUP *group, const
         }
 
 
-int ec_GFp_simple_set_compressed_coordinates_GFp(const EC_GROUP *group, EC_POINT *point,
+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;
 
+        /* clear error queue*/
+        ERR_clear_error();
+
         if (ctx == NULL)
                 {
                 ctx = new_ctx = BN_CTX_new();
@@ -704,19 +715,17 @@ int ec_GFp_simple_set_compressed_coordinates_GFp(const EC_GROUP *group, EC_POINT
         
         if (!BN_mod_sqrt(y, tmp1, &group->field, ctx))
                 {
-                unsigned long err = ERR_peek_error();
+                unsigned long err = ERR_peek_last_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_GFP, EC_R_INVALID_COMPRESSED_POINT);
+                        ERR_clear_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_GFP, ERR_R_BN_LIB);
+                        ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_BN_LIB);
                 goto err;
                 }
-        /* If tmp1 is not a square (i.e. there is no point on the curve with
-         * our x), then y now is a nonsense value too */
 
         if (y_bit != BN_is_odd(y))
                 {
@@ -728,16 +737,17 @@ int ec_GFp_simple_set_compressed_coordinates_GFp(const EC_GROUP *group, EC_POINT
                         if (kron == -2) goto err;
 
                         if (kron == 1)
-                                ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES_GFP, EC_R_INVALID_COMPRESSION_BIT);
+                                ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSION_BIT);
                         else
-                                ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES_GFP, EC_R_INVALID_COMPRESSED_POINT);
+                                /* 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_GFP, ERR_R_INTERNAL_ERROR);
+                ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_INTERNAL_ERROR);
                 goto err;
                 }
 
@@ -1088,7 +1098,7 @@ int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, con
                 else
                         {
                         /* a is the inverse of b */
-                        if (!BN_zero(&r->Z)) goto end;
+                        BN_zero(&r->Z);
                         r->Z_is_one = 0;
                         ret = 1;
                         goto end;
@@ -1164,7 +1174,7 @@ 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))
                 {
-                if (!BN_zero(&r->Z)) return 0;
+                BN_zero(&r->Z);
                 r->Z_is_one = 0;
                 return 1;
                 }
@@ -1292,7 +1302,7 @@ 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))
@@ -1311,8 +1321,7 @@ 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;
@@ -1326,59 +1335,49 @@ 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 */
+        /* rh := X^2 */
         if (!field_sqr(group, rh, &point->X, ctx)) goto err;
-        if (!field_mul(group, rh, 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;
                 }
 
         /* '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);