Add additional parameter to dsa_builtin_paramgen to output the generated
[openssl.git] / crypto / ec / ecp_smpl.c
index e027659..3e56b71 100644 (file)
@@ -1,7 +1,10 @@
-/* TODO */
 /* crypto/ec/ecp_smpl.c */
+/* Includes code written by Lenka Fibikova <fibikova@exp-math.uni-essen.de>
+ * 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
  * 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 "ec_lcl.h"
+#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 =
-               {
-                       0 /* XXX */
-               };
+       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,
+               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,
+               ec_GFp_simple_point_copy,
+               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,
+               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,
+               ec_GFp_simple_dbl,
+               ec_GFp_simple_invert,
+               ec_GFp_simple_is_at_infinity,
+               ec_GFp_simple_is_on_curve,
+               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 */ };
 
        return &ret;
        }
+
+
+/* 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;
+       return 1;
+       }
+
+
+void ec_GFp_simple_group_finish(EC_GROUP *group)
+       {
+       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);
+       }
+
+
+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;
+
+       return 1;
+       }
+
+
+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;
+       BN_CTX *new_ctx = NULL;
+       BIGNUM *tmp_a;
+       
+       /* 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, EC_R_INVALID_FIELD);
+               return 0;
+               }
+
+       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;
+       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; }     
+       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;
+       }
+
+
+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;
+       
+       if (p != NULL)
+               {
+               if (!BN_copy(p, &group->field)) return 0;
+               }
+
+       if (a != NULL || b != NULL)
+               {
+               if (group->meth->field_decode)
+                       {
+                       if (ctx == NULL)
+                               {
+                               ctx = new_ctx = BN_CTX_new();
+                               if (ctx == NULL)
+                                       return 0;
+                               }
+                       if (a != NULL)
+                               {
+                               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;
+                               }
+                       }
+               else
+                       {
+                       if (a != NULL)
+                               {
+                               if (!BN_copy(a, &group->a)) goto err;
+                               }
+                       if (b != NULL)
+                               {
+                               if (!BN_copy(b, &group->b)) goto err;
+                               }
+                       }
+               }
+       
+       ret = 1;
+       
+ err:
+       if (new_ctx)
+               BN_CTX_free(new_ctx);
+       return ret;
+       }
+
+
+int ec_GFp_simple_group_get_degree(const EC_GROUP *group)
+       {
+       return BN_num_bits(&group->field);
+       }
+
+
+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;
+       BN_CTX *new_ctx = NULL;
+
+       if (ctx == NULL)
+               {
+               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->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;
+               }
+       else
+               {
+               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 */
+
+               if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx)) goto err;
+               if (BN_is_zero(a)) goto err;
+               }
+       ret = 1;
+
+err:
+       if (ctx != NULL)
+               BN_CTX_end(ctx);
+       if (new_ctx != NULL)
+               BN_CTX_free(new_ctx);
+       return ret;
+       }
+
+
+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;
+       }
+
+
+int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point)
+       {
+       point->Z_is_one = 0;
+       BN_zero(&point->Z);
+       return 1;
+       }
+
+
+int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group, EC_POINT *point,
+       const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *ctx)
+       {
+       BN_CTX *new_ctx = NULL;
+       int ret = 0;
+       
+       if (ctx == NULL)
+               {
+               ctx = new_ctx = BN_CTX_new();
+               if (ctx == NULL)
+                       return 0;
+               }
+
+       if (x != NULL)
+               {
+               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 (y != NULL)
+               {
+               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 (z != NULL)
+               {
+               int Z_is_one;
+
+               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;
+                               }
+                       else
+                               {
+                               if (!group->meth->field_encode(group, &point->Z, &point->Z, ctx)) goto err;
+                               }
+                       }
+               point->Z_is_one = Z_is_one;
+               }
+
+       if (BN_cmp(&point->X, x) || BN_cmp(&point->Y, y))
+               ret = 2;
+       else
+               ret = 1;
+       
+ err:
+       if (new_ctx != NULL)
+               BN_CTX_free(new_ctx);
+       return ret;
+       }
+
+
+int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group, const EC_POINT *point,
+       BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *ctx)
+       {
+       BN_CTX *new_ctx = NULL;
+       int ret = 0;
+       
+       if (group->meth->field_decode != 0)
+               {
+               if (ctx == NULL)
+                       {
+                       ctx = new_ctx = BN_CTX_new();
+                       if (ctx == NULL)
+                               return 0;
+                       }
+
+               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 (z != NULL)
+                       {
+                       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 (y != NULL)
+                       {
+                       if (!BN_copy(y, &point->Y)) goto err;
+                       }
+               if (z != NULL)
+                       {
+                       if (!BN_copy(z, &point->Z)) goto err;
+                       }
+               }
+       
+       ret = 1;
+
+ err:
+       if (new_ctx != NULL)
+               BN_CTX_free(new_ctx);
+       return ret;
+       }
+
+
+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, ERR_R_PASSED_NULL_PARAMETER);
+               return 0;
+               }
+
+       return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y, BN_value_one(), ctx);
+       }
+
+
+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 *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, EC_R_POINT_AT_INFINITY);
+               return 0;
+               }
+
+       if (ctx == NULL)
+               {
+               ctx = new_ctx = BN_CTX_new();
+               if (ctx == NULL)
+                       return 0;
+               }
+
+       BN_CTX_start(ctx);
+       Z = BN_CTX_get(ctx);
+       Z_1 = BN_CTX_get(ctx);
+       Z_2 = BN_CTX_get(ctx);
+       Z_3 = BN_CTX_get(ctx);
+       if (Z_3 == NULL) goto err;
+
+       /* transform  (X, Y, Z)  into  (x, y) := (X/Z^2, Y/Z^3) */
+       
+       if (group->meth->field_decode)
+               {
+               if (!group->meth->field_decode(group, Z, &point->Z, ctx)) goto err;
+               Z_ = Z;
+               }
+       else
+               {
+               Z_ = &point->Z;
+               }
+       
+       if (BN_is_one(Z_))
+               {
+               if (group->meth->field_decode)
+                       {
+                       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;
+                               }
+                       }
+               else
+                       {
+                       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, ERR_R_BN_LIB);
+                       goto err;
+                       }
+               
+               if (group->meth->field_encode == 0)
+                       {
+                       /* field_sqr works on standard representation */
+                       if (!group->meth->field_sqr(group, Z_2, Z_1, ctx)) goto err;
+                       }
+               else
+                       {
+                       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 (y != NULL)
+                       {
+                       if (group->meth->field_encode == 0)
+                               {
+                               /* field_mul works on standard representation */
+                               if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx)) goto err;
+                               }
+                       else
+                               {
+                               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;
+                       }
+               }
+
+       ret = 1;
+
+ err:
+       BN_CTX_end(ctx);
+       if (new_ctx != NULL)
+               BN_CTX_free(new_ctx);
+       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;
+
+       /* clear error queue*/
+       ERR_clear_error();
+
+       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_last_error();
+               
+               if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NOT_A_SQUARE)
+                       {
+                       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, 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 & ~1U;
+       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 *);
+       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;
+
+       /* Note that in this function we must not read components of 'a' or 'b'
+        * once we have written the corresponding components of 'r'.
+        * ('r' might be one of 'a' or 'b'.)
+        */
+
+       /* 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);
+                       ret = EC_POINT_dbl(group, r, a, ctx);
+                       ctx = NULL;
+                       goto end;
+                       }
+               else
+                       {
+                       /* a is the inverse of b */
+                       BN_zero(&r->Z);
+                       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))
+               {
+               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;
+
+       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;
+
+       /* Note that in this function we must not read components of 'a'
+        * once we have written the corresponding components of 'r'.
+        * ('r' might the same as 'a'.)
+        */
+
+       /* 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_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
+       {
+       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);
+       }
+
+
+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)
+       {
+       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 *rh, *tmp, *Z4, *Z6;
+       int ret = -1;
+
+       if (EC_POINT_is_at_infinity(group, point))
+               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 -1;
+               }
+
+       BN_CTX_start(ctx);
+       rh = 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
+        *      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).
+        * Substituting this and multiplying by  Z^6  transforms the above equation into
+        *      Y^2 = X^3 + a*X*Z^4 + b*Z^6.
+        * To test this, we add up the right-hand side in 'rh'.
+        */
+
+       /* rh := X^2 */
+       if (!field_sqr(group, rh, &point->X, ctx)) goto err;
+
+       if (!point->Z_is_one)
+               {
+               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*Z^4)*X */
+               if (group->a_is_minus3)
+                       {
+                       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, 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, 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 (!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, tmp, &point->Y, ctx)) goto err;
+
+       ret = (0 == BN_ucmp(tmp, rh));
+
+ err:
+       BN_CTX_end(ctx);
+       if (new_ctx != NULL)
+               BN_CTX_free(new_ctx);
+       return ret;
+       }
+
+
+int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
+       {
+       /* return values:
+        *  -1   error
+        *   0   equal (in affine coordinates)
+        *   1   not equal
+        */
+
+       int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
+       int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
+       BN_CTX *new_ctx = NULL;
+       BIGNUM *tmp1, *tmp2, *Za23, *Zb23;
+       const BIGNUM *tmp1_, *tmp2_;
+       int ret = -1;
+       
+       if (EC_POINT_is_at_infinity(group, a))
+               {
+               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;
+               }
+
+       field_mul = group->meth->field_mul;
+       field_sqr = group->meth->field_sqr;
+
+       if (ctx == NULL)
+               {
+               ctx = new_ctx = BN_CTX_new();
+               if (ctx == NULL)
+                       return -1;
+               }
+
+       BN_CTX_start(ctx);
+       tmp1 = BN_CTX_get(ctx);
+       tmp2 = BN_CTX_get(ctx);
+       Za23 = BN_CTX_get(ctx);
+       Zb23 = BN_CTX_get(ctx);
+       if (Zb23 == NULL) goto end;
+
+       /* 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).
+        */
+
+       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;
+               tmp1_ = tmp1;
+               }
+       else
+               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;
+               tmp2_ = tmp2;
+               }
+       else
+               tmp2_ = &b->X;
+       
+       /* compare  X_a*Z_b^2  with  X_b*Z_a^2 */
+       if (BN_cmp(tmp1_, tmp2_) != 0)
+               {
+               ret = 1; /* points differ */
+               goto end;
+               }
+
+
+       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;
+               /* tmp1_ = tmp1 */
+               }
+       else
+               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;
+               /* tmp2_ = tmp2 */
+               }
+       else
+               tmp2_ = &b->Y;
+
+       /* compare  Y_a*Z_b^3  with  Y_b*Z_a^3 */
+       if (BN_cmp(tmp1_, tmp2_) != 0)
+               {
+               ret = 1; /* points differ */
+               goto end;
+               }
+
+       /* points are equal */
+       ret = 0;
+
+ end:
+       BN_CTX_end(ctx);
+       if (new_ctx != NULL)
+               BN_CTX_free(new_ctx);
+       return ret;
+       }
+
+int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
+       {
+       BN_CTX *new_ctx = NULL;
+       BIGNUM *x, *y;
+       int ret = 0;
+
+       if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
+               return 1;
+
+       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 (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
+       if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
+       if (!point->Z_is_one)
+               {
+               ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR);
+               goto err;
+               }
+       
+       ret = 1;
+
+ err:
+       BN_CTX_end(ctx);
+       if (new_ctx != NULL)
+               BN_CTX_free(new_ctx);
+       return ret;
+       }
+
+
+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;
+       size_t i;
+       int ret = 0;
+
+       if (num == 0)
+               return 1;
+
+       if (ctx == NULL)
+               {
+               ctx = new_ctx = BN_CTX_new();
+               if (ctx == NULL)
+                       return 0;
+               }
+
+       BN_CTX_start(ctx);
+       tmp0 = BN_CTX_get(ctx);
+       tmp1 = BN_CTX_get(ctx);
+       if (tmp0  == NULL || tmp1 == 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.
+        */
+
+       pow2 = 1;
+       while (num > pow2)
+               pow2 <<= 1;
+       /* Now pow2 is the smallest power of 2 satifsying pow2 >= num.
+        * We need twice that. */
+       pow2 <<= 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--)
+               {
+               heap[i] = BN_new();
+               if (heap[i] == NULL) goto err;
+               
+               if (heap[2*i] != NULL)
+                       {
+                       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;
+                                       }
+                               }
+                       }
+               }
+
+       /* invert heap[1] */
+       if (!BN_is_zero(heap[1]))
+               {
+               if (!BN_mod_inverse(heap[1], heap[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)
+                * 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;
+               }
+
+       /* set other heap[i]'s to their inverses */
+       for (i = 2; i < pow2/2 + num; i += 2)
+               {
+               /* i is even */
+               if ((heap[i + 1] != NULL) && !BN_is_zero(heap[i + 1]))
+                       {
+                       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;
+                       }
+               }
+
+       /* we have replaced all non-zero Z's by their inverses, now fix up all the points */
+       for (i = 0; i < num; i++)
+               {
+               EC_POINT *p = points[i];
+               
+               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_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;
+                               }
+                       else
+                               {
+                               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)
+               {
+               /* heap[pow2/2] .. heap[pow2-1] have not been allocated locally! */
+               for (i = pow2/2 - 1; i > 0; i--)
+                       {
+                       if (heap[i] != NULL)
+                               BN_clear_free(heap[i]);
+                       }
+               OPENSSL_free(heap);
+               }
+       return ret;
+       }
+
+
+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);
+       }