More method functions for elliptic curves,
authorBodo Möller <bodo@openssl.org>
Thu, 8 Mar 2001 19:14:52 +0000 (19:14 +0000)
committerBodo Möller <bodo@openssl.org>
Thu, 8 Mar 2001 19:14:52 +0000 (19:14 +0000)
and an ectest.c that actually tests something.

CHANGES
config
crypto/ec/ec.h
crypto/ec/ec_err.c
crypto/ec/ec_lcl.h
crypto/ec/ec_lib.c
crypto/ec/ecp_mont.c
crypto/ec/ecp_nist.c
crypto/ec/ecp_recp.c
crypto/ec/ecp_smpl.c
crypto/ec/ectest.c

diff --git a/CHANGES b/CHANGES
index b3a6f2f..1391c8f 100644 (file)
--- a/CHANGES
+++ b/CHANGES
@@ -3,8 +3,8 @@
 
  Changes between 0.9.6 and 0.9.7  [xx XXX 2000]
 
-   *) Replace rdtsc with _emit statements for VC++ version 5.
-      [Jeremy Cooper <jeremy@baymoo.org>]
+  *) Replace rdtsc with _emit statements for VC++ version 5.
+     [Jeremy Cooper <jeremy@baymoo.org>]
 
   *) Hide BN_CTX structure details in bn_lcl.h instead of publishing them
      in <openssl/bn.h>.  Also further increase BN_CTX_NUM to 24.
diff --git a/config b/config
index a641152..2d363d8 100755 (executable)
--- a/config
+++ b/config
@@ -557,7 +557,7 @@ case "$GUESSOS" in
   i386-*) options="$options 386" ;;
 esac
 
-for i in bf cast des dh dsa hmac md2 md5 mdc2 rc2 rc4 rc5 ripemd rsa sha
+for i in bf cast des dh dsa ec hmac md2 md5 mdc2 rc2 rc4 rc5 ripemd rsa sha
 do
   if [ ! -d crypto/$i ]
   then
index 0f0b9e0..16cbf18 100644 (file)
 #ifndef HEADER_EC_H
 #define HEADER_EC_H
 
+#ifdef OPENSSL_NO_EC
+#error Elliptic curves are disabled.
+#endif
+
 #include <openssl/bn.h>
 #include <openssl/symhacks.h>
 
@@ -64,7 +68,6 @@ extern "C" {
 #endif
 
 
-
 typedef enum {
        /* values as defined in X9.62 (ECDSA) and elsewhere */
        POINT_CONVERSION_COMPRESSED = 2,
@@ -81,7 +84,7 @@ typedef struct ec_group_st
         -- field definition
         -- curve coefficients
         -- optional generator with associated information (order, cofactor)
-        -- optional Lim/Lee precomputation table
+        -- optional extra data (Lim/Lee precomputation table)
        */
        EC_GROUP;
 
@@ -103,19 +106,20 @@ EC_GROUP *EC_GROUP_new(const EC_METHOD *);
  * Otherwise we would declare
  *     int EC_GROUP_set_curve(EC_GROUP *, .....);
  */
-int EC_GROUP_set_curve_GFp(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 void EC_GROUP_free(EC_GROUP *);
 void EC_GROUP_clear_free(EC_GROUP *);
 int EC_GROUP_copy(EC_GROUP *, const EC_GROUP*);
+int EC_GROUP_set_curve_GFp(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
+int EC_GROUP_get_curve_GFp(EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
 
 /* EC_GROUP_new_GFp() calls EC_GROUP_new() and EC_GROUP_set_GFp()
  * after choosing an appropriate EC_METHOD */
 EC_GROUP *EC_GROUP_new_curve_GFp(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 
 int EC_GROUP_set_generator(EC_GROUP *, const EC_POINT *generator, const BIGNUM *order, const BIGNUM *cofactor);
-
-/* TODO: 'set' and 'get' functions for EC_GROUPs */
-
+EC_POINT *EC_group_get0_generator(EC_GROUP *);
+int EC_GROUP_get_order(EC_GROUP *, BIGNUM *order, BN_CTX *);
+int EC_GROUP_get_cofactor(EC_GROUP *, BIGNUM *cofactor, BN_CTX *);
 
 EC_POINT *EC_POINT_new(const EC_GROUP *);
 void EC_POINT_free(EC_POINT *);
@@ -170,7 +174,10 @@ void ERR_load_EC_strings(void);
 #define EC_F_EC_GFP_SIMPLE_OCT2POINT                    103
 #define EC_F_EC_GFP_SIMPLE_POINT2OCT                    104
 #define EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES_GFP 105
+#define EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES_GFP 128
+#define EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES_GFP 129
 #define EC_F_EC_GROUP_COPY                              106
+#define EC_F_EC_GROUP_GET_CURVE_GFP                     130
 #define EC_F_EC_GROUP_GET_EXTRA_DATA                    107
 #define EC_F_EC_GROUP_NEW                               108
 #define EC_F_EC_GROUP_SET_CURVE_GFP                     109
@@ -196,6 +203,8 @@ void ERR_load_EC_strings(void);
 /* Reason codes. */
 #define EC_R_BUFFER_TOO_SMALL                           100
 #define EC_R_INCOMPATIBLE_OBJECTS                       101
+#define EC_R_INVALID_COMPRESSED_POINT                   110
+#define EC_R_INVALID_COMPRESSION_BIT                    109
 #define EC_R_INVALID_ENCODING                           102
 #define EC_R_INVALID_FIELD                              103
 #define EC_R_INVALID_FORM                               104
index 90b7ddc..4c03f5c 100644 (file)
@@ -72,7 +72,10 @@ static ERR_STRING_DATA EC_str_functs[]=
 {ERR_PACK(0,EC_F_EC_GFP_SIMPLE_OCT2POINT,0),   "ec_GFp_simple_oct2point"},
 {ERR_PACK(0,EC_F_EC_GFP_SIMPLE_POINT2OCT,0),   "ec_GFp_simple_point2oct"},
 {ERR_PACK(0,EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES_GFP,0),    "ec_GFp_simple_point_get_affine_coordinates_GFp"},
+{ERR_PACK(0,EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES_GFP,0),    "ec_GFp_simple_point_set_affine_coordinates_GFp"},
+{ERR_PACK(0,EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES_GFP,0),      "ec_GFp_simple_set_compressed_coordinates_GFp"},
 {ERR_PACK(0,EC_F_EC_GROUP_COPY,0),     "EC_GROUP_copy"},
+{ERR_PACK(0,EC_F_EC_GROUP_GET_CURVE_GFP,0),    "EC_GROUP_get_curve_GFp"},
 {ERR_PACK(0,EC_F_EC_GROUP_GET_EXTRA_DATA,0),   "EC_GROUP_get_extra_data"},
 {ERR_PACK(0,EC_F_EC_GROUP_NEW,0),      "EC_GROUP_new"},
 {ERR_PACK(0,EC_F_EC_GROUP_SET_CURVE_GFP,0),    "EC_GROUP_set_curve_GFp"},
@@ -101,6 +104,8 @@ static ERR_STRING_DATA EC_str_reasons[]=
        {
 {EC_R_BUFFER_TOO_SMALL                   ,"buffer too small"},
 {EC_R_INCOMPATIBLE_OBJECTS               ,"incompatible objects"},
+{EC_R_INVALID_COMPRESSED_POINT           ,"invalid compressed point"},
+{EC_R_INVALID_COMPRESSION_BIT            ,"invalid compression bit"},
 {EC_R_INVALID_ENCODING                   ,"invalid encoding"},
 {EC_R_INVALID_FIELD                      ,"invalid field"},
 {EC_R_INVALID_FORM                       ,"invalid form"},
index 15007d8..ad62beb 100644 (file)
  * so all this may change in future versions. */
 
 struct ec_method_st {
-       /* used by EC_GROUP_new, EC_GROUP_set_curve_GFp, EC_GROUP_free, EC_GROUP_clear_free, EC_GROUP_copy: */
+       /* used by EC_GROUP_new, EC_GROUP_free, EC_GROUP_clear_free, EC_GROUP_copy: */
        int (*group_init)(EC_GROUP *);
-       int (*group_set_curve_GFp)(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
        void (*group_finish)(EC_GROUP *);
        void (*group_clear_finish)(EC_GROUP *);
        int (*group_copy)(EC_GROUP *, const EC_GROUP *);
 
-       /* used by EC_GROUP_set_generator: */
+       /* used by EC_GROUP_set_curve_GFp and EC_GROUP_get_curve_GFp: */
+       int (*group_set_curve_GFp)(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
+       int (*group_get_curve_GFp)(EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
+
+       /* used by EC_GROUP_set_generator, EC_group_get0_generator,
+        * EC_GROUP_get_order, EC_GROUP_get_cofactor:
+        */
        int (*group_set_generator)(EC_GROUP *, const EC_POINT *generator,
                const BIGNUM *order, const BIGNUM *cofactor);
-       
-       /* TODO: 'set' and 'get' functions for EC_GROUPs */
-
+       EC_POINT *(*group_get0_generator)(EC_GROUP *);
+       int (*group_get_order)(EC_GROUP *, BIGNUM *order, BN_CTX *);
+       int (*group_get_cofactor)(EC_GROUP *, BIGNUM *cofactor, BN_CTX *);
 
        /* used by EC_POINT_new, EC_POINT_free, EC_POINT_clear_free, EC_POINT_copy: */
        int (*point_init)(EC_POINT *);
@@ -195,13 +200,16 @@ struct ec_point_st {
 
 /* method functions in ecp_smpl.c */
 int ec_GFp_simple_group_init(EC_GROUP *);
-int ec_GFp_simple_group_set_curve_GFp(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 void ec_GFp_simple_group_finish(EC_GROUP *);
 void ec_GFp_simple_group_clear_finish(EC_GROUP *);
 int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *);
+int ec_GFp_simple_group_set_curve_GFp(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
+int ec_GFp_simple_group_get_curve_GFp(EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
 int ec_GFp_simple_group_set_generator(EC_GROUP *, const EC_POINT *generator,
        const BIGNUM *order, const BIGNUM *cofactor);
-/* TODO: 'set' and 'get' functions for EC_GROUPs */
+EC_POINT *ec_GFp_simple_group_get0_generator(EC_GROUP *);
+int ec_GFp_simple_group_get_order(EC_GROUP *, BIGNUM *order, BN_CTX *);
+int ec_GFp_simple_group_get_cofactor(EC_GROUP *, BIGNUM *cofactor, BN_CTX *);
 int ec_GFp_simple_point_init(EC_POINT *);
 void ec_GFp_simple_point_finish(EC_POINT *);
 void ec_GFp_simple_point_clear_finish(EC_POINT *);
index bef6296..6aaacb3 100644 (file)
 #include <string.h>
 
 #include <openssl/err.h>
+#include <openssl/opensslv.h>
 
 #include "ec_lcl.h"
 
+static const char EC_version[] = "EC" OPENSSL_VERSION_PTEXT;
+
 
 /* functions for EC_GROUP objects */
 
@@ -101,17 +104,6 @@ EC_GROUP *EC_GROUP_new(const EC_METHOD *meth)
        }
 
 
-int EC_GROUP_set_curve_GFp(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
-       {
-       if (group->meth->group_set_curve_GFp == 0)
-               {
-               ECerr(EC_F_EC_GROUP_SET_CURVE_GFP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
-               return 0;
-               }
-       return group->meth->group_set_curve_GFp(group, p, a, b, ctx);
-       }
-
-
 void EC_GROUP_free(EC_GROUP *group)
        {
        if (group->meth->group_finish != 0)
@@ -171,6 +163,28 @@ int EC_GROUP_copy(EC_GROUP *dest, const EC_GROUP *src)
        }
 
 
+int EC_GROUP_set_curve_GFp(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
+       {
+       if (group->meth->group_set_curve_GFp == 0)
+               {
+               ECerr(EC_F_EC_GROUP_SET_CURVE_GFP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
+               return 0;
+               }
+       return group->meth->group_set_curve_GFp(group, p, a, b, ctx);
+       }
+
+
+int EC_GROUP_get_curve_GFp(EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
+       {
+       if (group->meth->group_get_curve_GFp == 0)
+               {
+               ECerr(EC_F_EC_GROUP_GET_CURVE_GFP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
+               return 0;
+               }
+       return group->meth->group_get_curve_GFp(group, p, a, b, ctx);
+       }
+
+
 int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator, const BIGNUM *order, const BIGNUM *cofactor)
        {
        if (group->meth->group_set_generator == 0)
@@ -182,9 +196,6 @@ int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator, const BIG
        }
 
 
-/* TODO: 'set' and 'get' functions for EC_GROUPs */
-
-
 /* this has 'package' visibility */
 int EC_GROUP_set_extra_data(EC_GROUP *group, void *extra_data, void *(*extra_data_dup_func)(void *),
        void (*extra_data_free_func)(void *), void (*extra_data_clear_free_func)(void *))
index 5db65ae..873d142 100644 (file)
@@ -60,12 +60,15 @@ const EC_METHOD *EC_GFp_mont_method(void)
        {
        static const EC_METHOD ret = {
                ec_GFp_mont_group_init,
-               ec_GFp_mont_group_set_curve_GFp,
                ec_GFp_mont_group_finish,
                ec_GFp_mont_group_clear_finish,
                ec_GFp_mont_group_copy,
+               ec_GFp_mont_group_set_curve_GFp,
+               ec_GFp_simple_group_get_curve_GFp,
                ec_GFp_simple_group_set_generator,
-               /* TODO: 'set' and 'get' functions for EC_GROUPs */
+               ec_GFp_simple_group_get0_generator,
+               ec_GFp_simple_group_get_order,
+               ec_GFp_simple_group_get_cofactor,
                ec_GFp_simple_point_init,
                ec_GFp_simple_point_finish,
                ec_GFp_simple_point_clear_finish,
index 089e2c6..acf2164 100644 (file)
@@ -60,12 +60,15 @@ const EC_METHOD *EC_GFp_nist_method(void)
        {
        static const EC_METHOD ret = {
                ec_GFp_nist_group_init,
-               ec_GFp_nist_group_set_curve_GFp,
                ec_GFp_nist_group_finish,
                ec_GFp_nist_group_clear_finish,
                ec_GFp_nist_group_copy,
+               ec_GFp_nist_group_set_curve_GFp,
+               ec_GFp_simple_group_get_curve_GFp,
                ec_GFp_simple_group_set_generator,
-               /* TODO: 'set' and 'get' functions for EC_GROUPs */
+               ec_GFp_simple_group_get0_generator,
+               ec_GFp_simple_group_get_order,
+               ec_GFp_simple_group_get_cofactor,
                ec_GFp_simple_point_init,
                ec_GFp_simple_point_finish,
                ec_GFp_simple_point_clear_finish,
index 8afdca1..2419a30 100644 (file)
@@ -60,12 +60,15 @@ const EC_METHOD *EC_GFp_recp_method(void)
        {
        static const EC_METHOD ret = {
                ec_GFp_recp_group_init,
-               ec_GFp_recp_group_set_curve_GFp,
                ec_GFp_recp_group_finish,
                ec_GFp_recp_group_clear_finish,
                ec_GFp_recp_group_copy,
+               ec_GFp_recp_group_set_curve_GFp,
+               ec_GFp_simple_group_get_curve_GFp,
                ec_GFp_simple_group_set_generator,
-               /* TODO: 'set' and 'get' functions for EC_GROUPs */
+               ec_GFp_simple_group_get0_generator,
+               ec_GFp_simple_group_get_order,
+               ec_GFp_simple_group_get_cofactor,
                ec_GFp_simple_point_init,
                ec_GFp_simple_point_finish,
                ec_GFp_simple_point_clear_finish,
index d6c3f63..a857560 100644 (file)
@@ -64,12 +64,15 @@ const EC_METHOD *EC_GFp_simple_method(void)
        {
        static const EC_METHOD ret = {
                ec_GFp_simple_group_init,
-               ec_GFp_simple_group_set_curve_GFp,
                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,
-               /* TODO: 'set' and 'get' functions for EC_GROUPs */
+               ec_GFp_simple_group_get0_generator,
+               ec_GFp_simple_group_get_order,
+               ec_GFp_simple_group_get_cofactor,
                ec_GFp_simple_point_init,
                ec_GFp_simple_point_finish,
                ec_GFp_simple_point_clear_finish,
@@ -111,6 +114,67 @@ 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);
+       if (group->generator != NULL)
+               EC_POINT_free(group->generator);
+       BN_free(&group->order);
+       BN_free(&group->cofactor);
+       }
+
+
+void ec_GFp_simple_group_clear_finish(EC_GROUP *group)
+       {
+       BN_clear_free(&group->field);
+       BN_clear_free(&group->a);
+       BN_clear_free(&group->b);
+       if (group->generator != NULL)
+               {
+               EC_POINT_clear_free(group->generator);
+               group->generator = NULL;
+               }
+       BN_clear_free(&group->order);
+       BN_clear_free(&group->cofactor);
+       }
+
+
+int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
+       {
+       if (!BN_copy(&dest->field, &src->field)) return 0;
+       if (!BN_copy(&dest->a, &src->a)) return 0;
+       if (!BN_copy(&dest->b, &src->b)) return 0;
+
+       dest->a_is_minus3 = src->a_is_minus3;
+
+       if (src->generator != NULL)
+               {
+               if (dest->generator == NULL)
+                       {
+                       dest->generator = EC_POINT_new(dest);
+                       if (dest->generator == NULL) return 0;
+                       }
+               if (!EC_POINT_copy(dest->generator, src->generator)) return 0;
+               }
+       else
+               {
+               /* src->generator == NULL */
+               if (dest->generator != NULL)
+                       {
+                       EC_POINT_clear_free(dest->generator);
+                       dest->generator = NULL;
+                       }
+               }
+
+       if (!BN_copy(&dest->order, &src->order)) return 0;
+       if (!BN_copy(&dest->cofactor, &src->cofactor)) return 0;
+
+       return 1;
+       }
+
+
 int ec_GFp_simple_group_set_curve_GFp(EC_GROUP *group,
        const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
        {
@@ -166,67 +230,58 @@ int ec_GFp_simple_group_set_curve_GFp(EC_GROUP *group,
        }
 
 
-void ec_GFp_simple_group_finish(EC_GROUP *group)
-       {
-       BN_free(&group->field);
-       BN_free(&group->a);
-       BN_free(&group->b);
-       if (group->generator != NULL)
-               EC_POINT_free(group->generator);
-       BN_free(&group->order);
-       BN_free(&group->cofactor);
-       }
-
-
-void ec_GFp_simple_group_clear_finish(EC_GROUP *group)
+int ec_GFp_simple_group_get_curve_GFp(EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
        {
-       BN_clear_free(&group->field);
-       BN_clear_free(&group->a);
-       BN_clear_free(&group->b);
-       if (group->generator != NULL)
+       int ret = 0;
+       BN_CTX *new_ctx = NULL;
+       
+       if (p != NULL)
                {
-               EC_POINT_clear_free(group->generator);
-               group->generator = NULL;
+               if (!BN_copy(p, &group->field)) return 0;
                }
-       BN_clear_free(&group->order);
-       BN_clear_free(&group->cofactor);
-       }
 
-
-int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
-       {
-       if (!BN_copy(&dest->field, &src->field)) return 0;
-       if (!BN_copy(&dest->a, &src->a)) return 0;
-       if (!BN_copy(&dest->b, &src->b)) return 0;
-
-       dest->a_is_minus3 = src->a_is_minus3;
-
-       if (src->generator != NULL)
+       if (a != NULL || b != NULL)
                {
-               if (dest->generator == NULL)
+               if (group->meth->field_decode)
                        {
-                       dest->generator = EC_POINT_new(dest);
-                       if (dest->generator == NULL) return 0;
+                       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;
+                               }
                        }
-               if (!EC_POINT_copy(dest->generator, src->generator)) return 0;
-               }
-       else
-               {
-               /* src->generator == NULL */
-               if (dest->generator != NULL)
+               else
                        {
-                       EC_POINT_clear_free(dest->generator);
-                       dest->generator = NULL;
+                       if (a != NULL)
+                               {
+                               if (!BN_copy(a, &group->a)) goto err;
+                               }
+                       if (b != NULL)
+                               {
+                               if (!BN_copy(b, &group->b)) goto err;
+                               }
                        }
                }
-
-       if (!BN_copy(&dest->order, &src->order)) return 0;
-       if (!BN_copy(&dest->cofactor, &src->cofactor)) return 0;
-
-       return 1;
+       
+       ret = 1;
+       
+ err:
+       if (new_ctx)
+               BN_CTX_free(new_ctx);
+       return ret;
        }
 
 
+
 int ec_GFp_simple_group_set_generator(EC_GROUP *group, const EC_POINT *generator,
        const BIGNUM *order, const BIGNUM *cofactor)
        {
@@ -257,7 +312,28 @@ int ec_GFp_simple_group_set_generator(EC_GROUP *group, const EC_POINT *generator
        }
 
 
-/* TODO: 'set' and 'get' functions for EC_GROUPs */
+EC_POINT *ec_GFp_simple_group_get0_generator(EC_GROUP *group)
+       {
+       return group->generator;
+       }
+
+
+int ec_GFp_simple_group_get_order(EC_GROUP *group, BIGNUM *order, BN_CTX *ctx)
+       {
+       if (!BN_copy(order, &group->order))
+               return 0;
+
+       return !BN_is_zero(&group->order);
+       }
+
+
+int ec_GFp_simple_group_get_cofactor(EC_GROUP *group, BIGNUM *cofactor, BN_CTX *ctx)
+       {
+       if (!BN_copy(cofactor, &group->cofactor))
+               return 0;
+
+       return !BN_is_zero(&group->cofactor);
+       }
 
 
 int ec_GFp_simple_point_init(EC_POINT *point)
@@ -307,26 +383,65 @@ int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point)
 
 
 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);
-/* TODO */
+       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;
 
-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);
-/* TODO */
+               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 (!group->meth->field_encode(group, &point->Z, &point->Z, ctx)) goto err;
+                       }
+               point->Z_is_one = Z_is_one;
+               }
+       
+       ret = 1;
+       
+ err:
+       if (new_ctx != NULL)
+               BN_CTX_free(new_ctx);
+       return ret;
+       }
 
 
-int ec_GFp_simple_point_set_affine_coordinates_GFp(const EC_GROUP *group, EC_POINT *point,
-       const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx)
+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 (!BN_copy(&point->X, x)) goto err;
-       if (!BN_copy(&point->Y, y)) goto err;
-       if (!BN_one(&point->Z)) goto err;
-
-       if (group->meth->field_encode)
+       
+       if (group->meth->field_decode != 0)
                {
                if (ctx == NULL)
                        {
@@ -334,14 +449,38 @@ int ec_GFp_simple_point_set_affine_coordinates_GFp(const EC_GROUP *group, EC_POI
                        if (ctx == NULL)
                                return 0;
                        }
-               
-               if (!group->meth->field_encode(group, &point->X, &point->X, ctx)) goto err;
-               if (!group->meth->field_encode(group, &point->Y, &point->Y, ctx)) goto err;
-               if (!group->meth->field_encode(group, &point->Z, &point->Z, ctx)) goto err;
-               }
 
-       point->Z_is_one = 1;
+               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);
@@ -349,6 +488,20 @@ int ec_GFp_simple_point_set_affine_coordinates_GFp(const EC_GROUP *group, EC_POI
        }
 
 
+int ec_GFp_simple_point_set_affine_coordinates_GFp(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);
+               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_GFp(const EC_GROUP *group, const EC_POINT *point,
        BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
        {
@@ -438,8 +591,93 @@ 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,
-       const BIGNUM *x, int y_bit, BN_CTX *);
-/* TODO */
+       const BIGNUM *x, int y_bit, BN_CTX *ctx)
+       {
+       BN_CTX *new_ctx = NULL;
+       BIGNUM *tmp1, *tmp2, *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);
+       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_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 (!BN_mod_mul(tmp2, &group->a, x, &group->field, ctx)) goto err;
+               if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
+               }
+       
+       /* tmp1 := tmp1 + b */
+       if (!BN_mod_add_quick(tmp1, tmp1, &group->b, &group->field)) goto err;
+       
+       if (!BN_mod_sqrt(y, tmp1, &group->field, ctx))
+               {
+               ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES_GFP, 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))
+               {
+               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_GFP, EC_R_INVALID_COMPRESSION_BIT);
+                       else
+                               ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES_GFP, 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);
+               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,
@@ -638,7 +876,11 @@ int ec_GFp_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
                goto err;
                }
 
-       if (form != POINT_CONVERSION_COMPRESSED)
+       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)
@@ -654,65 +896,10 @@ int ec_GFp_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
                                goto err;
                                }
                        }
-               }
 
-       if (form == POINT_CONVERSION_COMPRESSED)
-               {
-               /* 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.
-                */
-
-               BIGNUM *tmp1, *tmp2;
-               
-               tmp1 = BN_CTX_get(ctx);
-               tmp2 = BN_CTX_get(ctx);
-               if (tmp2 == NULL) goto err;
-               
-               /* tmp1 := x^3 */
-               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 (!BN_mod_mul(tmp2, &group->a, x, &group->field, ctx)) goto err;
-                       if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
-                       }
-               
-               /* tmp1 := tmp1 + b */
-               if (!BN_mod_add_quick(tmp1, tmp1, &group->b, &group->field)) goto err;
-
-               if (!BN_mod_sqrt(y, tmp1, &group->field, ctx))
-                       {
-                       ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, ERR_R_BN_LIB);
-                       goto err;
-                       }
-
-               if (y_bit != BN_is_odd(y))
-                       {
-                       if (BN_is_zero(y))
-                               {
-                               ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
-                               goto err;
-                               }
-                       if (!BN_usub(y, &group->field, y)) goto err;
-                       }
-               if (y_bit != BN_is_odd(y))
-                       {
-                       ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, ERR_R_INTERNAL_ERROR);
-                       goto err;
-                       }
+               if (!EC_POINT_set_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 (!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);
@@ -1010,8 +1197,14 @@ 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);
-/* TODO */
+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)
@@ -1072,7 +1265,7 @@ int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_C
 
                /* rh := rh + a*X*Z^4 */
                if (!field_mul(group, tmp1, &point->X, Z4, ctx)) goto err;
-               if (&group->a_is_minus3)
+               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;
@@ -1093,7 +1286,7 @@ int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_C
                /* point->Z_is_one */
 
                /* rh := rh + a*X */
-               if (&group->a_is_minus3)
+               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;
@@ -1122,8 +1315,107 @@ int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_C
        }
 
 
-int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
-/* TODO */
+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 (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;
+               }
+       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;
+               }
+       /* tmp1_ and tmp2_ are still ok */
+
+       /* 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)
index f557480..5425dce 100644 (file)
@@ -1,4 +1,3 @@
-/* TODO */
 /* crypto/ec/ectest.c */
 /* ====================================================================
  * Copyright (c) 1998-2001 The OpenSSL Project.  All rights reserved.
 #include <stdio.h>
 #include <stdlib.h>
 
+
+#ifdef OPENSSL_NO_EC
+int main(int argc, char * argv[]) { puts("Elliptic curves are disabled."); return 0; }
+#else
+
+
 #include <openssl/ec.h>
 #include <openssl/err.h>
 
-
 #define ABORT do { \
-       fprintf(stderr, "%s:%d: Error\n", __FILE__, __LINE__); \
+       fprintf(stderr, "%s:%d: ABORT\n", __FILE__, __LINE__); \
        ERR_print_errors_fp(stderr); \
        exit(1); \
 } while (0)
 
 int main(int argc, char *argv[])
        {       
+       BN_CTX *ctx = NULL;
+       BIGNUM *p, *a, *b;
        EC_GROUP *group;
-
+       EC_POINT *P, *Q, *R;
+       BIGNUM *x, *y, *z;
+       unsigned char buf[100];
+       size_t i, len;
+       
+       CRYPTO_mem_ctrl(CRYPTO_MEM_CHECK_ON);
        ERR_load_crypto_strings();
 
-#if 0
-       group = EC_GROUP_new(NULL);
+#if 0 /* optional */
+       ctx = BN_CTX_new();
+       if (!ctx) ABORT;
+#endif
+
+       p = BN_new();
+       a = BN_new();
+       b = BN_new();
+       if (!p || !a || !b) ABORT;
+
+       if (!BN_hex2bn(&p, "D")) ABORT;
+       if (!BN_hex2bn(&a, "7")) ABORT;
+       if (!BN_hex2bn(&b, "C")) ABORT;
+       
+       group = EC_GROUP_new_curve_GFp(p, a, b, NULL);
        if (!group) ABORT;
+
+       fprintf(stdout, "Curve defined by Weierstrass equation\n     y^2 = x^3 + a*x + b  (mod 0x");
+       BN_print_fp(stdout, p);
+       fprintf(stdout, ")\n     a = 0x");
+       BN_print_fp(stdout, a);
+       fprintf(stdout, "\n     b = 0x");
+       BN_print_fp(stdout, b);
+       fprintf(stdout, "\n");
+
+       P = EC_POINT_new(group);
+       Q = EC_POINT_new(group);
+       R = EC_POINT_new(group);
+       if (!P || !Q || !R) ABORT;
+       
+       if (!EC_POINT_set_to_infinity(group, P)) ABORT;
+       if (!EC_POINT_is_at_infinity(group, P)) ABORT;
+
+       buf[0] = 0;
+       if (!EC_POINT_oct2point(group, Q, buf, 1, ctx)) ABORT;
+
+       if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
+       if (!EC_POINT_is_at_infinity(group, P)) ABORT;
+
+       x = BN_new();
+       y = BN_new();
+       z = BN_new();
+       if (!x || !y || !z) ABORT;
+
+       if (!BN_hex2bn(&x, "C")) ABORT;
+       if (!EC_POINT_set_compressed_coordinates_GFp(group, Q, x, 1, ctx)) ABORT;
+       if (!EC_POINT_is_on_curve(group, Q, ctx))
+               {
+               fprintf(stderr, "Point is not on curve, x = 0x");
+               BN_print_fp(stderr, x);
+               fprintf(stderr, "\n");
+               ABORT;
+               }
+
+       fprintf(stdout, "A cyclic subgroup:\n");
+       do
+               {
+               if (EC_POINT_is_at_infinity(group, P))
+                       fprintf(stdout, "     point at infinity\n");
+               else
+                       {
+                       if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
+
+                       fprintf(stdout, "     x = 0x");
+                       BN_print_fp(stdout, x);
+                       fprintf(stdout, ", y = 0x");
+                       BN_print_fp(stdout, y);
+                       fprintf(stdout, "\n");
+                       }
+               
+               if (!EC_POINT_copy(R, P)) ABORT;
+               if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
+
+#if 0 /* optional */
+               if (!EC_POINT_make_affine(group, P, ctx)) ABORT;
 #endif
+               }
+       while (!EC_POINT_is_at_infinity(group, P));
+
+       if (!EC_POINT_add(group, P, Q, R, ctx)) ABORT;
+       if (!EC_POINT_is_at_infinity(group, P)) ABORT;
 
+       len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf, sizeof buf, ctx);
+       if (len == 0) ABORT;
+       if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
+       if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
+       fprintf(stdout, "Generator as octect string, compressed form:\n     ");
+       for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
+       
+       len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, sizeof buf, ctx);
+       if (len == 0) ABORT;
+       if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
+       if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
+       fprintf(stdout, "\nGenerator as octect string, uncompressed form:\n     ");
+       for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
+       
+       len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf, ctx);
+       if (len == 0) ABORT;
+       if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
+       if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
+       fprintf(stdout, "\nGenerator as octect string, hybrid form:\n     ");
+       for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
+       
+       if (!EC_POINT_get_Jprojective_coordinates_GFp(group, R, x, y, z, ctx)) ABORT;
+       fprintf(stdout, "\nA representation of the inverse of that generator in\nJacobian projective coordinates:\n     X = 0x");
+       BN_print_fp(stdout, x);
+       fprintf(stdout, ", Y = 0x");
+       BN_print_fp(stdout, y);
+       fprintf(stdout, ", Z = 0x");
+       BN_print_fp(stdout, z);
+       fprintf(stdout, "\n");
+
+       if (!EC_POINT_invert(group, P, ctx)) ABORT;
+       if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
+
+       /* ... */
+
+       if (ctx)
+               BN_CTX_free(ctx);
+       BN_free(p); BN_free(a); BN_free(b);
+       EC_GROUP_free(group);
+       EC_POINT_free(P);
+       EC_POINT_free(Q);
+       EC_POINT_free(R);
+       BN_free(x); BN_free(y); BN_free(z);
+
+       ERR_free_strings();
+       ERR_remove_state(0);
+       CRYPTO_mem_leaks_fp(stderr);
+       
        return 0;
        }
+#endif