text: /*
   * Copyright 2001-2020 The OpenSSL Project Authors. All Rights Reserved.
   * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved
   *
   * Licensed under the Apache License 2.0 (the "License").  You may not use
   * this file except in compliance with the License.  You can obtain a copy
   * in the file LICENSE in the source distribution or at
   * https://www.openssl.org/source/license.html
   */
  
  /*
   * ECDSA low level APIs are deprecated for public use, but still ok for
   * internal use.
   */
  #include "internal/deprecated.h"
  
  #include <string.h>
  #include <openssl/params.h>
  #include <openssl/core_names.h>
  #include <openssl/err.h>
  #include <openssl/opensslv.h>
  #include "crypto/ec.h"
  #include "internal/nelem.h"
  #include "ec_local.h"
  #include "e_os.h" /* strcasecmp */
  
  /* functions for EC_GROUP objects */
  
  EC_GROUP *ec_group_new_ex(OSSL_LIB_CTX *libctx, const char *propq,
                            const EC_METHOD *meth)
  {
      EC_GROUP *ret;
  
      if (meth == NULL) {
          ECerr(0, EC_R_SLOT_FULL);
          return NULL;
      }
      if (meth->group_init == 0) {
          ECerr(0, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
          return NULL;
      }
  
      ret = OPENSSL_zalloc(sizeof(*ret));
      if (ret == NULL) {
          ECerr(0, ERR_R_MALLOC_FAILURE);
          return NULL;
      }
  
      ret->libctx = libctx;
      if (propq != NULL) {
          ret->propq = OPENSSL_strdup(propq);
          if (ret->propq == NULL) {
              ECerr(0, ERR_R_MALLOC_FAILURE);
              goto err;
          }
      }
      ret->meth = meth;
      if ((ret->meth->flags & EC_FLAGS_CUSTOM_CURVE) == 0) {
          ret->order = BN_new();
          if (ret->order == NULL)
              goto err;
          ret->cofactor = BN_new();
          if (ret->cofactor == NULL)
              goto err;
      }
      ret->asn1_flag = OPENSSL_EC_NAMED_CURVE;
      ret->asn1_form = POINT_CONVERSION_UNCOMPRESSED;
      if (!meth->group_init(ret))
          goto err;
      return ret;
  
   err:
      BN_free(ret->order);
      BN_free(ret->cofactor);
      OPENSSL_free(ret->propq);
      OPENSSL_free(ret);
      return NULL;
  }
  
  #ifndef OPENSSL_NO_DEPRECATED_3_0
  # ifndef FIPS_MODULE
  EC_GROUP *EC_GROUP_new(const EC_METHOD *meth)
  {
      return ec_group_new_ex(NULL, NULL, meth);
  }
  # endif
  #endif
  
  void EC_pre_comp_free(EC_GROUP *group)
  {
      switch (group->pre_comp_type) {
      case PCT_none:
          break;
      case PCT_nistz256:
  #ifdef ECP_NISTZ256_ASM
          EC_nistz256_pre_comp_free(group->pre_comp.nistz256);
  #endif
          break;
  #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
      case PCT_nistp224:
          EC_nistp224_pre_comp_free(group->pre_comp.nistp224);
          break;
      case PCT_nistp256:
          EC_nistp256_pre_comp_free(group->pre_comp.nistp256);
          break;
      case PCT_nistp521:
          EC_nistp521_pre_comp_free(group->pre_comp.nistp521);
          break;
  #else
      case PCT_nistp224:
      case PCT_nistp256:
      case PCT_nistp521:
          break;
  #endif
      case PCT_ec:
          EC_ec_pre_comp_free(group->pre_comp.ec);
          break;
      }
      group->pre_comp.ec = NULL;
  }
  
  void EC_GROUP_free(EC_GROUP *group)
  {
      if (!group)
          return;
  
      if (group->meth->group_finish != 0)
          group->meth->group_finish(group);
  
      EC_pre_comp_free(group);
      BN_MONT_CTX_free(group->mont_data);
      EC_POINT_free(group->generator);
      BN_free(group->order);
      BN_free(group->cofactor);
      OPENSSL_free(group->seed);
      OPENSSL_free(group->propq);
      OPENSSL_free(group);
  }
  
  #ifndef OPENSSL_NO_DEPRECATED_3_0
  void EC_GROUP_clear_free(EC_GROUP *group)
  {
      if (!group)
          return;
  
      if (group->meth->group_clear_finish != 0)
          group->meth->group_clear_finish(group);
      else if (group->meth->group_finish != 0)
          group->meth->group_finish(group);
  
      EC_pre_comp_free(group);
      BN_MONT_CTX_free(group->mont_data);
      EC_POINT_clear_free(group->generator);
      BN_clear_free(group->order);
      BN_clear_free(group->cofactor);
      OPENSSL_clear_free(group->seed, group->seed_len);
      OPENSSL_clear_free(group, sizeof(*group));
  }
  #endif
  
  int EC_GROUP_copy(EC_GROUP *dest, const EC_GROUP *src)
  {
      if (dest->meth->group_copy == 0) {
          ECerr(EC_F_EC_GROUP_COPY, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
          return 0;
      }
      if (dest->meth != src->meth) {
          ECerr(EC_F_EC_GROUP_COPY, EC_R_INCOMPATIBLE_OBJECTS);
          return 0;
      }
      if (dest == src)
          return 1;
  
      dest->libctx = src->libctx;
      dest->curve_name = src->curve_name;
  
      /* Copy precomputed */
      dest->pre_comp_type = src->pre_comp_type;
      switch (src->pre_comp_type) {
      case PCT_none:
          dest->pre_comp.ec = NULL;
          break;
      case PCT_nistz256:
  #ifdef ECP_NISTZ256_ASM
          dest->pre_comp.nistz256 = EC_nistz256_pre_comp_dup(src->pre_comp.nistz256);
  #endif
          break;
  #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
      case PCT_nistp224:
          dest->pre_comp.nistp224 = EC_nistp224_pre_comp_dup(src->pre_comp.nistp224);
          break;
      case PCT_nistp256:
          dest->pre_comp.nistp256 = EC_nistp256_pre_comp_dup(src->pre_comp.nistp256);
          break;
      case PCT_nistp521:
          dest->pre_comp.nistp521 = EC_nistp521_pre_comp_dup(src->pre_comp.nistp521);
          break;
  #else
      case PCT_nistp224:
      case PCT_nistp256:
      case PCT_nistp521:
          break;
  #endif
      case PCT_ec:
          dest->pre_comp.ec = EC_ec_pre_comp_dup(src->pre_comp.ec);
          break;
      }
  
      if (src->mont_data != NULL) {
          if (dest->mont_data == NULL) {
              dest->mont_data = BN_MONT_CTX_new();
              if (dest->mont_data == NULL)
                  return 0;
          }
          if (!BN_MONT_CTX_copy(dest->mont_data, src->mont_data))
              return 0;
      } else {
          /* src->generator == NULL */
          BN_MONT_CTX_free(dest->mont_data);
          dest->mont_data = NULL;
      }
  
      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 */
          EC_POINT_clear_free(dest->generator);
          dest->generator = NULL;
      }
  
      if ((src->meth->flags & EC_FLAGS_CUSTOM_CURVE) == 0) {
          if (!BN_copy(dest->order, src->order))
              return 0;
          if (!BN_copy(dest->cofactor, src->cofactor))
              return 0;
      }
  
      dest->asn1_flag = src->asn1_flag;
      dest->asn1_form = src->asn1_form;
      dest->decoded_from_explicit_params = src->decoded_from_explicit_params;
  
      if (src->seed) {
          OPENSSL_free(dest->seed);
          if ((dest->seed = OPENSSL_malloc(src->seed_len)) == NULL) {
              ECerr(EC_F_EC_GROUP_COPY, ERR_R_MALLOC_FAILURE);
              return 0;
          }
          if (!memcpy(dest->seed, src->seed, src->seed_len))
              return 0;
          dest->seed_len = src->seed_len;
      } else {
          OPENSSL_free(dest->seed);
          dest->seed = NULL;
          dest->seed_len = 0;
      }
  
      return dest->meth->group_copy(dest, src);
  }
  
  EC_GROUP *EC_GROUP_dup(const EC_GROUP *a)
  {
      EC_GROUP *t = NULL;
      int ok = 0;
  
      if (a == NULL)
          return NULL;
  
      if ((t = ec_group_new_ex(a->libctx, a->propq, a->meth)) == NULL)
          return NULL;
      if (!EC_GROUP_copy(t, a))
          goto err;
  
      ok = 1;
  
   err:
      if (!ok) {
          EC_GROUP_free(t);
          return NULL;
      }
          return t;
  }
  
  #ifndef OPENSSL_NO_DEPRECATED_3_0
  const EC_METHOD *EC_GROUP_method_of(const EC_GROUP *group)
  {
      return group->meth;
  }
  
  int EC_METHOD_get_field_type(const EC_METHOD *meth)
  {
      return meth->field_type;
  }
  #endif
  
  static int ec_precompute_mont_data(EC_GROUP *);
  
  /*-
   * Try computing cofactor from the generator order (n) and field cardinality (q).
   * This works for all curves of cryptographic interest.
   *
   * Hasse thm: q + 1 - 2*sqrt(q) <= n*h <= q + 1 + 2*sqrt(q)
   * h_min = (q + 1 - 2*sqrt(q))/n
   * h_max = (q + 1 + 2*sqrt(q))/n
   * h_max - h_min = 4*sqrt(q)/n
   * So if n > 4*sqrt(q) holds, there is only one possible value for h:
   * h = \lfloor (h_min + h_max)/2 \rceil = \lfloor (q + 1)/n \rceil
   *
   * Otherwise, zero cofactor and return success.
   */
  static int ec_guess_cofactor(EC_GROUP *group) {
      int ret = 0;
      BN_CTX *ctx = NULL;
      BIGNUM *q = NULL;
  
      /*-
       * If the cofactor is too large, we cannot guess it.
       * The RHS of below is a strict overestimate of lg(4 * sqrt(q))
       */
      if (BN_num_bits(group->order) <= (BN_num_bits(group->field) + 1) / 2 + 3) {
          /* default to 0 */
          BN_zero(group->cofactor);
          /* return success */
          return 1;
      }
  
      if ((ctx = BN_CTX_new_ex(group->libctx)) == NULL)
          return 0;
  
      BN_CTX_start(ctx);
      if ((q = BN_CTX_get(ctx)) == NULL)
          goto err;
  
      /* set q = 2**m for binary fields; q = p otherwise */
      if (group->meth->field_type == NID_X9_62_characteristic_two_field) {
          BN_zero(q);
          if (!BN_set_bit(q, BN_num_bits(group->field) - 1))
              goto err;
      } else {
          if (!BN_copy(q, group->field))
              goto err;
      }
  
      /* compute h = \lfloor (q + 1)/n \rceil = \lfloor (q + 1 + n/2)/n \rfloor */
      if (!BN_rshift1(group->cofactor, group->order) /* n/2 */
          || !BN_add(group->cofactor, group->cofactor, q) /* q + n/2 */
          /* q + 1 + n/2 */
          || !BN_add(group->cofactor, group->cofactor, BN_value_one())
          /* (q + 1 + n/2)/n */
          || !BN_div(group->cofactor, NULL, group->cofactor, group->order, ctx))
          goto err;
      ret = 1;
   err:
      BN_CTX_end(ctx);
      BN_CTX_free(ctx);
      return ret;
  }
  
  int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator,
                             const BIGNUM *order, const BIGNUM *cofactor)
  {
      if (generator == NULL) {
          ECerr(EC_F_EC_GROUP_SET_GENERATOR, ERR_R_PASSED_NULL_PARAMETER);
          return 0;
      }
  
      /* require group->field >= 1 */
      if (group->field == NULL || BN_is_zero(group->field)
          || BN_is_negative(group->field)) {
          ECerr(EC_F_EC_GROUP_SET_GENERATOR, EC_R_INVALID_FIELD);
          return 0;
      }
  
      /*-
       * - require order >= 1
       * - enforce upper bound due to Hasse thm: order can be no more than one bit
       *   longer than field cardinality
       */
      if (order == NULL || BN_is_zero(order) || BN_is_negative(order)
          || BN_num_bits(order) > BN_num_bits(group->field) + 1) {
          ECerr(EC_F_EC_GROUP_SET_GENERATOR, EC_R_INVALID_GROUP_ORDER);
          return 0;
      }
  
      /*-
       * Unfortunately the cofactor is an optional field in many standards.
       * Internally, the lib uses 0 cofactor as a marker for "unknown cofactor".
       * So accept cofactor == NULL or cofactor >= 0.
       */
      if (cofactor != NULL && BN_is_negative(cofactor)) {
          ECerr(EC_F_EC_GROUP_SET_GENERATOR, EC_R_UNKNOWN_COFACTOR);
          return 0;
      }
  
      if (group->generator == NULL) {
          group->generator = EC_POINT_new(group);
          if (group->generator == NULL)
              return 0;
      }
      if (!EC_POINT_copy(group->generator, generator))
          return 0;
  
      if (!BN_copy(group->order, order))
          return 0;
  
      /* Either take the provided positive cofactor, or try to compute it */
      if (cofactor != NULL && !BN_is_zero(cofactor)) {
          if (!BN_copy(group->cofactor, cofactor))
              return 0;
      } else if (!ec_guess_cofactor(group)) {
          BN_zero(group->cofactor);
          return 0;
      }
  
      /*
       * Some groups have an order with
       * factors of two, which makes the Montgomery setup fail.
       * |group->mont_data| will be NULL in this case.
       */
      if (BN_is_odd(group->order)) {
          return ec_precompute_mont_data(group);
      }
  
      BN_MONT_CTX_free(group->mont_data);
      group->mont_data = NULL;
      return 1;
  }
  
  const EC_POINT *EC_GROUP_get0_generator(const EC_GROUP *group)
  {
      return group->generator;
  }
  
  BN_MONT_CTX *EC_GROUP_get_mont_data(const EC_GROUP *group)
  {
      return group->mont_data;
  }
  
  int EC_GROUP_get_order(const EC_GROUP *group, BIGNUM *order, BN_CTX *ctx)
  {
      if (group->order == NULL)
          return 0;
      if (!BN_copy(order, group->order))
          return 0;
  
      return !BN_is_zero(order);
  }
  
  const BIGNUM *EC_GROUP_get0_order(const EC_GROUP *group)
  {
      return group->order;
  }
  
  int EC_GROUP_order_bits(const EC_GROUP *group)
  {
      return group->meth->group_order_bits(group);
  }
  
  int EC_GROUP_get_cofactor(const EC_GROUP *group, BIGNUM *cofactor,
                            BN_CTX *ctx)
  {
  
      if (group->cofactor == NULL)
          return 0;
      if (!BN_copy(cofactor, group->cofactor))
          return 0;
  
      return !BN_is_zero(group->cofactor);
  }
  
  const BIGNUM *EC_GROUP_get0_cofactor(const EC_GROUP *group)
  {
      return group->cofactor;
  }
  
  void EC_GROUP_set_curve_name(EC_GROUP *group, int nid)
  {
      group->curve_name = nid;
  }
  
  int EC_GROUP_get_curve_name(const EC_GROUP *group)
  {
      return group->curve_name;
  }
  
  const BIGNUM *EC_GROUP_get0_field(const EC_GROUP *group)
  {
      return group->field;
  }
  
  int EC_GROUP_get_field_type(const EC_GROUP *group)
  {
      return group->meth->field_type;
  }
  
  void EC_GROUP_set_asn1_flag(EC_GROUP *group, int flag)
  {
      group->asn1_flag = flag;
  }
  
  int EC_GROUP_get_asn1_flag(const EC_GROUP *group)
  {
      return group->asn1_flag;
  }
  
  void EC_GROUP_set_point_conversion_form(EC_GROUP *group,
                                          point_conversion_form_t form)
  {
      group->asn1_form = form;
  }
  
  point_conversion_form_t EC_GROUP_get_point_conversion_form(const EC_GROUP
                                                             *group)
  {
      return group->asn1_form;
  }
  
  size_t EC_GROUP_set_seed(EC_GROUP *group, const unsigned char *p, size_t len)
  {
      OPENSSL_free(group->seed);
      group->seed = NULL;
      group->seed_len = 0;
  
      if (!len || !p)
          return 1;
  
      if ((group->seed = OPENSSL_malloc(len)) == NULL) {
          ECerr(EC_F_EC_GROUP_SET_SEED, ERR_R_MALLOC_FAILURE);
          return 0;
      }
      memcpy(group->seed, p, len);
      group->seed_len = len;
  
      return len;
  }
  
  unsigned char *EC_GROUP_get0_seed(const EC_GROUP *group)
  {
      return group->seed;
  }
  
  size_t EC_GROUP_get_seed_len(const EC_GROUP *group)
  {
      return group->seed_len;
  }
  
  int EC_GROUP_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a,
                         const BIGNUM *b, BN_CTX *ctx)
  {
      if (group->meth->group_set_curve == 0) {
          ECerr(EC_F_EC_GROUP_SET_CURVE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
          return 0;
      }
      return group->meth->group_set_curve(group, p, a, b, ctx);
  }
  
  int EC_GROUP_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b,
                         BN_CTX *ctx)
  {
      if (group->meth->group_get_curve == NULL) {
          ECerr(EC_F_EC_GROUP_GET_CURVE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
          return 0;
      }
      return group->meth->group_get_curve(group, p, a, b, ctx);
  }
  
  #ifndef OPENSSL_NO_DEPRECATED_3_0
  int EC_GROUP_set_curve_GFp(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a,
                             const BIGNUM *b, BN_CTX *ctx)
  {
      return EC_GROUP_set_curve(group, p, a, b, ctx);
  }
  
  int EC_GROUP_get_curve_GFp(const EC_GROUP *group, BIGNUM *p, BIGNUM *a,
                             BIGNUM *b, BN_CTX *ctx)
  {
      return EC_GROUP_get_curve(group, p, a, b, ctx);
  }
  
  # ifndef OPENSSL_NO_EC2M
  int EC_GROUP_set_curve_GF2m(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a,
                              const BIGNUM *b, BN_CTX *ctx)
  {
      return EC_GROUP_set_curve(group, p, a, b, ctx);
  }
  
  int EC_GROUP_get_curve_GF2m(const EC_GROUP *group, BIGNUM *p, BIGNUM *a,
                              BIGNUM *b, BN_CTX *ctx)
  {
      return EC_GROUP_get_curve(group, p, a, b, ctx);
  }
  # endif
  #endif
  
  int EC_GROUP_get_degree(const EC_GROUP *group)
  {
      if (group->meth->group_get_degree == 0) {
          ECerr(EC_F_EC_GROUP_GET_DEGREE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
          return 0;
      }
      return group->meth->group_get_degree(group);
  }
  
  int EC_GROUP_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
  {
      if (group->meth->group_check_discriminant == 0) {
          ECerr(EC_F_EC_GROUP_CHECK_DISCRIMINANT,
                ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
          return 0;
      }
      return group->meth->group_check_discriminant(group, ctx);
  }
  
  int EC_GROUP_cmp(const EC_GROUP *a, const EC_GROUP *b, BN_CTX *ctx)
  {
      int r = 0;
      BIGNUM *a1, *a2, *a3, *b1, *b2, *b3;
  #ifndef FIPS_MODULE
      BN_CTX *ctx_new = NULL;
  #endif
  
      /* compare the field types */
      if (EC_GROUP_get_field_type(a) != EC_GROUP_get_field_type(b))
          return 1;
      /* compare the curve name (if present in both) */
      if (EC_GROUP_get_curve_name(a) && EC_GROUP_get_curve_name(b) &&
          EC_GROUP_get_curve_name(a) != EC_GROUP_get_curve_name(b))
          return 1;
      if (a->meth->flags & EC_FLAGS_CUSTOM_CURVE)
          return 0;
  
  #ifndef FIPS_MODULE
      if (ctx == NULL)
          ctx_new = ctx = BN_CTX_new();
  #endif
      if (ctx == NULL)
          return -1;
  
      BN_CTX_start(ctx);
      a1 = BN_CTX_get(ctx);
      a2 = BN_CTX_get(ctx);
      a3 = BN_CTX_get(ctx);
      b1 = BN_CTX_get(ctx);
      b2 = BN_CTX_get(ctx);
      b3 = BN_CTX_get(ctx);
      if (b3 == NULL) {
          BN_CTX_end(ctx);
  #ifndef FIPS_MODULE
          BN_CTX_free(ctx_new);
  #endif
          return -1;
      }
  
      /*
       * XXX This approach assumes that the external representation of curves
       * over the same field type is the same.
       */
      if (!a->meth->group_get_curve(a, a1, a2, a3, ctx) ||
          !b->meth->group_get_curve(b, b1, b2, b3, ctx))
          r = 1;
  
      /* return 1 if the curve parameters are different */
      if (r || BN_cmp(a1, b1) != 0 || BN_cmp(a2, b2) != 0 || BN_cmp(a3, b3) != 0)
          r = 1;
  
      /* XXX EC_POINT_cmp() assumes that the methods are equal */
      /* return 1 if the generators are different */
      if (r || EC_POINT_cmp(a, EC_GROUP_get0_generator(a),
                            EC_GROUP_get0_generator(b), ctx) != 0)
          r = 1;
  
      if (!r) {
          const BIGNUM *ao, *bo, *ac, *bc;
          /* compare the orders */
          ao = EC_GROUP_get0_order(a);
          bo = EC_GROUP_get0_order(b);
          if (ao == NULL || bo == NULL) {
              /* return an error if either order is NULL */
              r = -1;
              goto end;
          }
          if (BN_cmp(ao, bo) != 0) {
              /* return 1 if orders are different */
              r = 1;
              goto end;
          }
          /*
           * It gets here if the curve parameters and generator matched.
           * Now check the optional cofactors (if both are present).
           */
          ac = EC_GROUP_get0_cofactor(a);
          bc = EC_GROUP_get0_cofactor(b);
          /* Returns 1 (mismatch) if both cofactors are specified and different */
          if (!BN_is_zero(ac) && !BN_is_zero(bc) && BN_cmp(ac, bc) != 0)
              r = 1;
          /* Returns 0 if the parameters matched */
      }
  end:
      BN_CTX_end(ctx);
  #ifndef FIPS_MODULE
      BN_CTX_free(ctx_new);
  #endif
      return r;
  }
  
  /* functions for EC_POINT objects */
  
  EC_POINT *EC_POINT_new(const EC_GROUP *group)
  {
      EC_POINT *ret;
  
      if (group == NULL) {
          ECerr(EC_F_EC_POINT_NEW, ERR_R_PASSED_NULL_PARAMETER);
          return NULL;
      }
      if (group->meth->point_init == NULL) {
          ECerr(EC_F_EC_POINT_NEW, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
          return NULL;
      }
  
      ret = OPENSSL_zalloc(sizeof(*ret));
      if (ret == NULL) {
          ECerr(EC_F_EC_POINT_NEW, ERR_R_MALLOC_FAILURE);
          return NULL;
      }
  
      ret->meth = group->meth;
      ret->curve_name = group->curve_name;
  
      if (!ret->meth->point_init(ret)) {
          OPENSSL_free(ret);
          return NULL;
      }
  
      return ret;
  }
  
  void EC_POINT_free(EC_POINT *point)
  {
      if (point == NULL)
          return;
  
      if (point->meth->point_finish != 0)
          point->meth->point_finish(point);
      OPENSSL_free(point);
  }
  
  void EC_POINT_clear_free(EC_POINT *point)
  {
      if (point == NULL)
          return;
  
      if (point->meth->point_clear_finish != 0)
          point->meth->point_clear_finish(point);
      else if (point->meth->point_finish != 0)
          point->meth->point_finish(point);
      OPENSSL_clear_free(point, sizeof(*point));
  }
  
  int EC_POINT_copy(EC_POINT *dest, const EC_POINT *src)
  {
      if (dest->meth->point_copy == 0) {
          ECerr(EC_F_EC_POINT_COPY, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
          return 0;
      }
      if (dest->meth != src->meth
              || (dest->curve_name != src->curve_name
                   && dest->curve_name != 0
                   && src->curve_name != 0)) {
          ECerr(EC_F_EC_POINT_COPY, EC_R_INCOMPATIBLE_OBJECTS);
          return 0;
      }
      if (dest == src)
          return 1;
      return dest->meth->point_copy(dest, src);
  }
  
  EC_POINT *EC_POINT_dup(const EC_POINT *a, const EC_GROUP *group)
  {
      EC_POINT *t;
      int r;
  
      if (a == NULL)
          return NULL;
  
      t = EC_POINT_new(group);
      if (t == NULL)
          return NULL;
      r = EC_POINT_copy(t, a);
      if (!r) {
          EC_POINT_free(t);
          return NULL;
      }
      return t;
  }
  
  #ifndef OPENSSL_NO_DEPRECATED_3_0
  const EC_METHOD *EC_POINT_method_of(const EC_POINT *point)
  {
      return point->meth;
  }
  #endif
  
  int EC_POINT_set_to_infinity(const EC_GROUP *group, EC_POINT *point)
  {
      if (group->meth->point_set_to_infinity == 0) {
          ECerr(EC_F_EC_POINT_SET_TO_INFINITY,
                ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
          return 0;
      }
      if (group->meth != point->meth) {
          ECerr(EC_F_EC_POINT_SET_TO_INFINITY, EC_R_INCOMPATIBLE_OBJECTS);
          return 0;
      }
      return group->meth->point_set_to_infinity(group, point);
  }
  
  #ifndef OPENSSL_NO_DEPRECATED_3_0
  int EC_POINT_set_Jprojective_coordinates_GFp(const EC_GROUP *group,
                                               EC_POINT *point, const BIGNUM *x,
                                               const BIGNUM *y, const BIGNUM *z,
                                               BN_CTX *ctx)
  {
      if (group->meth->field_type != NID_X9_62_prime_field) {
          ECerr(EC_F_EC_POINT_SET_JPROJECTIVE_COORDINATES_GFP,
                ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
          return 0;
      }
      if (!ec_point_is_compat(point, group)) {
          ECerr(EC_F_EC_POINT_SET_JPROJECTIVE_COORDINATES_GFP,
                EC_R_INCOMPATIBLE_OBJECTS);
          return 0;
      }
      return ec_GFp_simple_set_Jprojective_coordinates_GFp(group, point, x, y, z, ctx);
  }
  
  int EC_POINT_get_Jprojective_coordinates_GFp(const EC_GROUP *group,
                                               const EC_POINT *point, BIGNUM *x,
                                               BIGNUM *y, BIGNUM *z,
                                               BN_CTX *ctx)
  {
      if (group->meth->field_type != NID_X9_62_prime_field) {
          ECerr(EC_F_EC_POINT_GET_JPROJECTIVE_COORDINATES_GFP,
                ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
          return 0;
      }
      if (!ec_point_is_compat(point, group)) {
          ECerr(EC_F_EC_POINT_GET_JPROJECTIVE_COORDINATES_GFP,
                EC_R_INCOMPATIBLE_OBJECTS);
          return 0;
      }
      return ec_GFp_simple_get_Jprojective_coordinates_GFp(group, point, x, y, z, ctx);
  }
  #endif
  
  int EC_POINT_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point,
                                      const BIGNUM *x, const BIGNUM *y,
                                      BN_CTX *ctx)
  {
      if (group->meth->point_set_affine_coordinates == NULL) {
          ECerr(EC_F_EC_POINT_SET_AFFINE_COORDINATES,
                ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
          return 0;
      }
      if (!ec_point_is_compat(point, group)) {
          ECerr(EC_F_EC_POINT_SET_AFFINE_COORDINATES, EC_R_INCOMPATIBLE_OBJECTS);
          return 0;
      }
      if (!group->meth->point_set_affine_coordinates(group, point, x, y, ctx))
          return 0;
  
      if (EC_POINT_is_on_curve(group, point, ctx) <= 0) {
          ECerr(EC_F_EC_POINT_SET_AFFINE_COORDINATES, EC_R_POINT_IS_NOT_ON_CURVE);
          return 0;
      }
      return 1;
  }
  
  #ifndef OPENSSL_NO_DEPRECATED_3_0
  int EC_POINT_set_affine_coordinates_GFp(const EC_GROUP *group,
                                          EC_POINT *point, const BIGNUM *x,
                                          const BIGNUM *y, BN_CTX *ctx)
  {
      return EC_POINT_set_affine_coordinates(group, point, x, y, ctx);
  }
  
  # ifndef OPENSSL_NO_EC2M
  int EC_POINT_set_affine_coordinates_GF2m(const EC_GROUP *group,
                                           EC_POINT *point, const BIGNUM *x,
                                           const BIGNUM *y, BN_CTX *ctx)
  {
      return EC_POINT_set_affine_coordinates(group, point, x, y, ctx);
  }
  # endif
  #endif
  
  int EC_POINT_get_affine_coordinates(const EC_GROUP *group,
                                      const EC_POINT *point, BIGNUM *x, BIGNUM *y,
                                      BN_CTX *ctx)
  {
      if (group->meth->point_get_affine_coordinates == NULL) {
          ECerr(EC_F_EC_POINT_GET_AFFINE_COORDINATES,
                ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
          return 0;
      }
      if (!ec_point_is_compat(point, group)) {
          ECerr(EC_F_EC_POINT_GET_AFFINE_COORDINATES, EC_R_INCOMPATIBLE_OBJECTS);
          return 0;
      }
      if (EC_POINT_is_at_infinity(group, point)) {
          ECerr(EC_F_EC_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY);
          return 0;
      }
      return group->meth->point_get_affine_coordinates(group, point, x, y, ctx);
  }
  
  #ifndef OPENSSL_NO_DEPRECATED_3_0
  int EC_POINT_get_affine_coordinates_GFp(const EC_GROUP *group,
                                          const EC_POINT *point, BIGNUM *x,
                                          BIGNUM *y, BN_CTX *ctx)
  {
      return EC_POINT_get_affine_coordinates(group, point, x, y, ctx);
  }
  
  # ifndef OPENSSL_NO_EC2M
  int EC_POINT_get_affine_coordinates_GF2m(const EC_GROUP *group,
                                           const EC_POINT *point, BIGNUM *x,
                                           BIGNUM *y, BN_CTX *ctx)
  {
      return EC_POINT_get_affine_coordinates(group, point, x, y, ctx);
  }
  # endif
  #endif
  
  int EC_POINT_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
                   const EC_POINT *b, BN_CTX *ctx)
  {
      if (group->meth->add == 0) {
          ECerr(EC_F_EC_POINT_ADD, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
          return 0;
      }
      if (!ec_point_is_compat(r, group) || !ec_point_is_compat(a, group)
          || !ec_point_is_compat(b, group)) {
          ECerr(EC_F_EC_POINT_ADD, EC_R_INCOMPATIBLE_OBJECTS);
          return 0;
      }
      return group->meth->add(group, r, a, b, ctx);
  }
  
  int EC_POINT_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
                   BN_CTX *ctx)
  {
      if (group->meth->dbl == 0) {
          ECerr(EC_F_EC_POINT_DBL, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
          return 0;
      }
      if (!ec_point_is_compat(r, group) || !ec_point_is_compat(a, group)) {
          ECerr(EC_F_EC_POINT_DBL, EC_R_INCOMPATIBLE_OBJECTS);
          return 0;
      }
      return group->meth->dbl(group, r, a, ctx);
  }
  
  int EC_POINT_invert(const EC_GROUP *group, EC_POINT *a, BN_CTX *ctx)
  {
      if (group->meth->invert == 0) {
          ECerr(EC_F_EC_POINT_INVERT, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
          return 0;
      }
      if (!ec_point_is_compat(a, group)) {
          ECerr(EC_F_EC_POINT_INVERT, EC_R_INCOMPATIBLE_OBJECTS);
          return 0;
      }
      return group->meth->invert(group, a, ctx);
  }
  
  int EC_POINT_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
  {
      if (group->meth->is_at_infinity == 0) {
          ECerr(EC_F_EC_POINT_IS_AT_INFINITY,
                ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
          return 0;
      }
      if (!ec_point_is_compat(point, group)) {
          ECerr(EC_F_EC_POINT_IS_AT_INFINITY, EC_R_INCOMPATIBLE_OBJECTS);
          return 0;
      }
      return group->meth->is_at_infinity(group, point);
  }
  
  /*
   * Check whether an EC_POINT is on the curve or not. Note that the return
   * value for this function should NOT be treated as a boolean. Return values:
   *  1: The point is on the curve
   *  0: The point is not on the curve
   * -1: An error occurred
   */
  int EC_POINT_is_on_curve(const EC_GROUP *group, const EC_POINT *point,
                           BN_CTX *ctx)
  {
      if (group->meth->is_on_curve == 0) {
          ECerr(EC_F_EC_POINT_IS_ON_CURVE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
          return 0;
      }
      if (!ec_point_is_compat(point, group)) {
          ECerr(EC_F_EC_POINT_IS_ON_CURVE, EC_R_INCOMPATIBLE_OBJECTS);
          return 0;
      }
      return group->meth->is_on_curve(group, point, ctx);
  }
  
  int EC_POINT_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b,
                   BN_CTX *ctx)
  {
      if (group->meth->point_cmp == 0) {
          ECerr(EC_F_EC_POINT_CMP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
          return -1;
      }
      if (!ec_point_is_compat(a, group) || !ec_point_is_compat(b, group)) {
          ECerr(EC_F_EC_POINT_CMP, EC_R_INCOMPATIBLE_OBJECTS);
          return -1;
      }
      return group->meth->point_cmp(group, a, b, ctx);
  }
  
  #ifndef OPENSSL_NO_DEPRECATED_3_0
  int EC_POINT_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
  {
      if (group->meth->make_affine == 0) {
          ECerr(EC_F_EC_POINT_MAKE_AFFINE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
          return 0;
      }
      if (!ec_point_is_compat(point, group)) {
          ECerr(EC_F_EC_POINT_MAKE_AFFINE, EC_R_INCOMPATIBLE_OBJECTS);
          return 0;
      }
      return group->meth->make_affine(group, point, ctx);
  }
  
  int EC_POINTs_make_affine(const EC_GROUP *group, size_t num,
                            EC_POINT *points[], BN_CTX *ctx)
  {
      size_t i;
  
      if (group->meth->points_make_affine == 0) {
          ECerr(EC_F_EC_POINTS_MAKE_AFFINE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
          return 0;
      }
      for (i = 0; i < num; i++) {
          if (!ec_point_is_compat(points[i], group)) {
              ECerr(EC_F_EC_POINTS_MAKE_AFFINE, EC_R_INCOMPATIBLE_OBJECTS);
              return 0;
          }
      }
      return group->meth->points_make_affine(group, num, points, ctx);
  }
  #endif
  
  /*
   * Functions for point multiplication. If group->meth->mul is 0, we use the
   * wNAF-based implementations in ec_mult.c; otherwise we dispatch through
   * methods.
   */
  
  #ifndef OPENSSL_NO_DEPRECATED_3_0
  int EC_POINTs_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
                    size_t num, const EC_POINT *points[],
                    const BIGNUM *scalars[], BN_CTX *ctx)
  {
      int ret = 0;
      size_t i = 0;
  #ifndef FIPS_MODULE
      BN_CTX *new_ctx = NULL;
  #endif
  
      if (!ec_point_is_compat(r, group)) {
          ECerr(EC_F_EC_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
          return 0;
      }
  
      if (scalar == NULL && num == 0)
          return EC_POINT_set_to_infinity(group, r);
  
      for (i = 0; i < num; i++) {
          if (!ec_point_is_compat(points[i], group)) {
              ECerr(EC_F_EC_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
              return 0;
          }
      }
  
  #ifndef FIPS_MODULE
      if (ctx == NULL)
          ctx = new_ctx = BN_CTX_secure_new();
  #endif
      if (ctx == NULL) {
          ECerr(EC_F_EC_POINTS_MUL, ERR_R_INTERNAL_ERROR);
          return 0;
      }
  
      if (group->meth->mul != NULL)
          ret = group->meth->mul(group, r, scalar, num, points, scalars, ctx);
      else
          /* use default */
          ret = ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx);
  
  #ifndef FIPS_MODULE
      BN_CTX_free(new_ctx);
  #endif
      return ret;
  }
  #endif
  
  int EC_POINT_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar,
                   const EC_POINT *point, const BIGNUM *p_scalar, BN_CTX *ctx)
  {
      int ret = 0;
      size_t num;
  #ifndef FIPS_MODULE
      BN_CTX *new_ctx = NULL;
  #endif
  
      if (!ec_point_is_compat(r, group)
          || (point != NULL && !ec_point_is_compat(point, group))) {
          ECerr(EC_F_EC_POINT_MUL, EC_R_INCOMPATIBLE_OBJECTS);
          return 0;
      }
  
      if (g_scalar == NULL && p_scalar == NULL)
          return EC_POINT_set_to_infinity(group, r);
  
  #ifndef FIPS_MODULE
      if (ctx == NULL)
          ctx = new_ctx = BN_CTX_secure_new();
  #endif
      if (ctx == NULL) {
          ECerr(EC_F_EC_POINT_MUL, ERR_R_INTERNAL_ERROR);
          return 0;
      }
  
      num = (point != NULL && p_scalar != NULL) ? 1 : 0;
      if (group->meth->mul != NULL)
          ret = group->meth->mul(group, r, g_scalar, num, &point, &p_scalar, ctx);
      else
          /* use default */
          ret = ec_wNAF_mul(group, r, g_scalar, num, &point, &p_scalar, ctx);
  
  #ifndef FIPS_MODULE
      BN_CTX_free(new_ctx);
  #endif
      return ret;
  }
  
  #ifndef OPENSSL_NO_DEPRECATED_3_0
  int EC_GROUP_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
  {
      if (group->meth->mul == 0)
          /* use default */
          return ec_wNAF_precompute_mult(group, ctx);
  
      if (group->meth->precompute_mult != 0)
          return group->meth->precompute_mult(group, ctx);
      else
          return 1;               /* nothing to do, so report success */
  }
  
  int EC_GROUP_have_precompute_mult(const EC_GROUP *group)
  {
      if (group->meth->mul == 0)
          /* use default */
          return ec_wNAF_have_precompute_mult(group);
  
      if (group->meth->have_precompute_mult != 0)
          return group->meth->have_precompute_mult(group);
      else
          return 0;               /* cannot tell whether precomputation has
                                   * been performed */
  }
  #endif
  
  /*
   * ec_precompute_mont_data sets |group->mont_data| from |group->order| and
   * returns one on success. On error it returns zero.
   */
  static int ec_precompute_mont_data(EC_GROUP *group)
  {
      BN_CTX *ctx = BN_CTX_new_ex(group->libctx);
      int ret = 0;
  
      BN_MONT_CTX_free(group->mont_data);
      group->mont_data = NULL;
  
      if (ctx == NULL)
          goto err;
  
      group->mont_data = BN_MONT_CTX_new();
      if (group->mont_data == NULL)
          goto err;
  
      if (!BN_MONT_CTX_set(group->mont_data, group->order, ctx)) {
          BN_MONT_CTX_free(group->mont_data);
          group->mont_data = NULL;
          goto err;
      }
  
      ret = 1;
  
   err:
  
      BN_CTX_free(ctx);
      return ret;
  }
  
  #ifndef FIPS_MODULE
  int EC_KEY_set_ex_data(EC_KEY *key, int idx, void *arg)
  {
      return CRYPTO_set_ex_data(&key->ex_data, idx, arg);
  }
  
  void *EC_KEY_get_ex_data(const EC_KEY *key, int idx)
  {
      return CRYPTO_get_ex_data(&key->ex_data, idx);
  }
  #endif
  
  int ec_group_simple_order_bits(const EC_GROUP *group)
  {
      if (group->order == NULL)
          return 0;
      return BN_num_bits(group->order);
  }
  
  static int ec_field_inverse_mod_ord(const EC_GROUP *group, BIGNUM *r,
                                      const BIGNUM *x, BN_CTX *ctx)
  {
      BIGNUM *e = NULL;
      int ret = 0;
  #ifndef FIPS_MODULE
      BN_CTX *new_ctx = NULL;
  #endif
  
      if (group->mont_data == NULL)
          return 0;
  
  #ifndef FIPS_MODULE
      if (ctx == NULL)
          ctx = new_ctx = BN_CTX_secure_new();
  #endif
      if (ctx == NULL)
          return 0;
  
      BN_CTX_start(ctx);
      if ((e = BN_CTX_get(ctx)) == NULL)
          goto err;
  
      /*-
       * We want inverse in constant time, therefore we utilize the fact
       * order must be prime and use Fermats Little Theorem instead.
       */
      if (!BN_set_word(e, 2))
          goto err;
      if (!BN_sub(e, group->order, e))
          goto err;
      /*-
       * Exponent e is public.
       * No need for scatter-gather or BN_FLG_CONSTTIME.
       */
      if (!BN_mod_exp_mont(r, x, e, group->order, ctx, group->mont_data))
          goto err;
  
      ret = 1;
  
   err:
      BN_CTX_end(ctx);
  #ifndef FIPS_MODULE
      BN_CTX_free(new_ctx);
  #endif
      return ret;
  }
  
  /*-
   * Default behavior, if group->meth->field_inverse_mod_ord is NULL:
   * - When group->order is even, this function returns an error.
   * - When group->order is otherwise composite, the correctness
   *   of the output is not guaranteed.
   * - When x is outside the range [1, group->order), the correctness
   *   of the output is not guaranteed.
   * - Otherwise, this function returns the multiplicative inverse in the
   *   range [1, group->order).
   *
   * EC_METHODs must implement their own field_inverse_mod_ord for
   * other functionality.
   */
  int ec_group_do_inverse_ord(const EC_GROUP *group, BIGNUM *res,
                              const BIGNUM *x, BN_CTX *ctx)
  {
      if (group->meth->field_inverse_mod_ord != NULL)
          return group->meth->field_inverse_mod_ord(group, res, x, ctx);
      else
          return ec_field_inverse_mod_ord(group, res, x, ctx);
  }
  
  /*-
   * Coordinate blinding for EC_POINT.
   *
   * The underlying EC_METHOD can optionally implement this function:
   * underlying implementations should return 0 on errors, or 1 on
   * success.
   *
   * This wrapper returns 1 in case the underlying EC_METHOD does not
   * support coordinate blinding.
   */
  int ec_point_blind_coordinates(const EC_GROUP *group, EC_POINT *p, BN_CTX *ctx)
  {
      if (group->meth->blind_coordinates == NULL)
          return 1; /* ignore if not implemented */
  
      return group->meth->blind_coordinates(group, p, ctx);
  }
  
  int EC_GROUP_get_basis_type(const EC_GROUP *group)
  {
      int i;
  
      if (EC_GROUP_get_field_type(group) != NID_X9_62_characteristic_two_field)
          /* everything else is currently not supported */
          return 0;
  
      /* Find the last non-zero element of group->poly[] */
      for (i = 0;
           i < (int)OSSL_NELEM(group->poly) && group->poly[i] != 0;
           i++)
          continue;
  
      if (i == 4)
          return NID_X9_62_ppBasis;
      else if (i == 2)
          return NID_X9_62_tpBasis;
      else
          /* everything else is currently not supported */
          return 0;
  }
  
  #ifndef OPENSSL_NO_EC2M
  int EC_GROUP_get_trinomial_basis(const EC_GROUP *group, unsigned int *k)
  {
      if (group == NULL)
          return 0;
  
      if (EC_GROUP_get_field_type(group) != NID_X9_62_characteristic_two_field
          || !((group->poly[0] != 0) && (group->poly[1] != 0)
               && (group->poly[2] == 0))) {
          ECerr(EC_F_EC_GROUP_GET_TRINOMIAL_BASIS,
                ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
          return 0;
      }
  
      if (k)
          *k = group->poly[1];
  
      return 1;
  }
  
  int EC_GROUP_get_pentanomial_basis(const EC_GROUP *group, unsigned int *k1,
                                     unsigned int *k2, unsigned int *k3)
  {
      if (group == NULL)
          return 0;
  
      if (EC_GROUP_get_field_type(group) != NID_X9_62_characteristic_two_field
          || !((group->poly[0] != 0) && (group->poly[1] != 0)
               && (group->poly[2] != 0) && (group->poly[3] != 0)
               && (group->poly[4] == 0))) {
          ECerr(EC_F_EC_GROUP_GET_PENTANOMIAL_BASIS,
                ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
          return 0;
      }
  
      if (k1)
          *k1 = group->poly[3];
      if (k2)
          *k2 = group->poly[2];
      if (k3)
          *k3 = group->poly[1];
  
      return 1;
  }
  #endif
  
  /*
   * Check if the explicit parameters group matches any built-in curves.
   *
   * We create a copy of the group just built, so that we can remove optional
   * fields for the lookup: we do this to avoid the possibility that one of
   * the optional parameters is used to force the library into using a less
   * performant and less secure EC_METHOD instead of the specialized one.
   * In any case, `seed` is not really used in any computation, while a
   * cofactor different from the one in the built-in table is just
   * mathematically wrong anyway and should not be used.
   */
  static EC_GROUP *ec_group_explicit_to_named(const EC_GROUP *group,
                                              OSSL_LIB_CTX *libctx,
                                              const char *propq,
                                              BN_CTX *ctx)
  {
      EC_GROUP *ret_group = NULL, *dup = NULL;
      int curve_name_nid;
  
      const EC_POINT *point = EC_GROUP_get0_generator(group);
      const BIGNUM *order = EC_GROUP_get0_order(group);
      int no_seed = (EC_GROUP_get0_seed(group) == NULL);
  
      if ((dup = EC_GROUP_dup(group)) == NULL
              || EC_GROUP_set_seed(dup, NULL, 0) != 1
              || !EC_GROUP_set_generator(dup, point, order, NULL))
          goto err;
      if ((curve_name_nid = ec_curve_nid_from_params(dup, ctx)) != NID_undef) {
          /*
           * The input explicit parameters successfully matched one of the
           * built-in curves: often for built-in curves we have specialized
           * methods with better performance and hardening.
           *
           * In this case we replace the `EC_GROUP` created through explicit
           * parameters with one created from a named group.
           */
  
  #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
          /*
           * NID_wap_wsg_idm_ecid_wtls12 and NID_secp224r1 are both aliases for
           * the same curve, we prefer the SECP nid when matching explicit
           * parameters as that is associated with a specialized EC_METHOD.
           */
          if (curve_name_nid == NID_wap_wsg_idm_ecid_wtls12)
              curve_name_nid = NID_secp224r1;
  #endif /* !def(OPENSSL_NO_EC_NISTP_64_GCC_128) */
  
          ret_group = EC_GROUP_new_by_curve_name_ex(libctx, propq, curve_name_nid);
          if (ret_group == NULL)
              goto err;
  
          /*
           * Set the flag so that EC_GROUPs created from explicit parameters are
           * serialized using explicit parameters by default.
           */
          EC_GROUP_set_asn1_flag(ret_group, OPENSSL_EC_EXPLICIT_CURVE);
  
          /*
           * If the input params do not contain the optional seed field we make
           * sure it is not added to the returned group.
           *
           * The seed field is not really used inside libcrypto anyway, and
           * adding it to parsed explicit parameter keys would alter their DER
           * encoding output (because of the extra field) which could impact
           * applications fingerprinting keys by their DER encoding.
           */
          if (no_seed) {
              if (EC_GROUP_set_seed(ret_group, NULL, 0) != 1)
                  goto err;
          }
      } else {
          ret_group = (EC_GROUP *)group;
      }
      EC_GROUP_free(dup);
      return ret_group;
  err:
      EC_GROUP_free(dup);
      EC_GROUP_free(ret_group);
      return NULL;
  }
  
  static int ec_encoding_param2id(const OSSL_PARAM *p, int *id)
  {
      const char *name = NULL;
      int status = 0;
  
      switch (p->data_type) {
      case OSSL_PARAM_UTF8_STRING:
          /* The OSSL_PARAM functions have no support for this */
          name = p->data;
          status = (name != NULL);
          break;
      case OSSL_PARAM_UTF8_PTR:
          status = OSSL_PARAM_get_utf8_ptr(p, &name);
          break;
      }
      if (status) {
          int i = ec_encoding_name2id(name);
  
          if (i >= 0) {
              *id = i;
              return 1;
          }
      }
      return 0;
  }
  
  static EC_GROUP *group_new_from_name(const OSSL_PARAM *p,
                                       OSSL_LIB_CTX *libctx, const char *propq)
  {
      int ok = 0, nid;
      const char *curve_name = NULL;
  
      switch (p->data_type) {
      case OSSL_PARAM_UTF8_STRING:
          /* The OSSL_PARAM functions have no support for this */
          curve_name = p->data;
          ok = (curve_name != NULL);
          break;
      case OSSL_PARAM_UTF8_PTR:
          ok = OSSL_PARAM_get_utf8_ptr(p, &curve_name);
          break;
      }
  
      if (ok) {
          nid = ec_curve_name2nid(curve_name);
          if (nid == NID_undef) {
              ECerr(0, EC_R_INVALID_CURVE);
              return NULL;
          } else {
              return EC_GROUP_new_by_curve_name_ex(libctx, propq, nid);
          }
      }
      return NULL;
  }
  
  EC_GROUP *EC_GROUP_new_from_params(const OSSL_PARAM params[],
                                     OSSL_LIB_CTX *libctx, const char *propq)
  {
      const OSSL_PARAM *ptmp, *pa, *pb;
      int ok = 0;
      EC_GROUP *group = NULL, *named_group = NULL;
      BIGNUM *p = NULL, *a = NULL, *b = NULL, *order = NULL, *cofactor = NULL;
      EC_POINT *point = NULL;
      int field_bits = 0;
      int is_prime_field = 1;
      BN_CTX *bnctx = NULL;
      const unsigned char *buf = NULL;
      int encoding_flag = -1;
  
      ptmp = OSSL_PARAM_locate_const(params, OSSL_PKEY_PARAM_EC_ENCODING);
      if (ptmp != NULL && !ec_encoding_param2id(ptmp, &encoding_flag)) {
          ECerr(0, EC_R_INVALID_ENCODING);
          return 0;
      }
  
      ptmp = OSSL_PARAM_locate_const(params, OSSL_PKEY_PARAM_GROUP_NAME);
      if (ptmp != NULL) {
          group = group_new_from_name(ptmp, libctx, propq);
          if (group != NULL)
              EC_GROUP_set_asn1_flag(group, encoding_flag);
          return group;
      }
      bnctx = BN_CTX_new_ex(libctx);
      if (bnctx == NULL) {
          ECerr(0, ERR_R_MALLOC_FAILURE);
          return 0;
      }
      BN_CTX_start(bnctx);
  
      p = BN_CTX_get(bnctx);
      a = BN_CTX_get(bnctx);
      b = BN_CTX_get(bnctx);
      order = BN_CTX_get(bnctx);
      if (order == NULL) {
          ECerr(0, ERR_R_MALLOC_FAILURE);
          goto err;
      }
  
      ptmp = OSSL_PARAM_locate_const(params, OSSL_PKEY_PARAM_EC_FIELD_TYPE);
      if (ptmp == NULL || ptmp->data_type != OSSL_PARAM_UTF8_STRING) {
          ECerr(0, EC_R_INVALID_FIELD);
          goto err;
      }
      if (strcasecmp(ptmp->data, SN_X9_62_prime_field) == 0) {
          is_prime_field = 1;
      } else if (strcasecmp(ptmp->data, SN_X9_62_characteristic_two_field) == 0) {
          is_prime_field = 0;
      } else {
          /* Invalid field */
          ECerr(0, EC_R_UNSUPPORTED_FIELD);
          goto err;
      }
  
      pa = OSSL_PARAM_locate_const(params, OSSL_PKEY_PARAM_EC_A);
      if (!OSSL_PARAM_get_BN(pa, &a)) {
          ECerr(0, EC_R_INVALID_A);
          goto err;
      }
      pb = OSSL_PARAM_locate_const(params, OSSL_PKEY_PARAM_EC_B);
      if (!OSSL_PARAM_get_BN(pb, &b)) {
          ECerr(0, EC_R_INVALID_B);
          goto err;
      }
  
      /* extract the prime number or irreducible polynomial */
      ptmp = OSSL_PARAM_locate_const(params, OSSL_PKEY_PARAM_EC_P);
      if (!OSSL_PARAM_get_BN(ptmp, &p)) {
          ECerr(0, EC_R_INVALID_P);
          goto err;
      }
  
      if (is_prime_field) {
          if (BN_is_negative(p) || BN_is_zero(p)) {
              ECerr(0, EC_R_INVALID_P);
              goto err;
          }
          field_bits = BN_num_bits(p);
          if (field_bits > OPENSSL_ECC_MAX_FIELD_BITS) {
              ECerr(0, EC_R_FIELD_TOO_LARGE);
              goto err;
          }
  
          /* create the EC_GROUP structure */
          group = EC_GROUP_new_curve_GFp(p, a, b, bnctx);
      } else {
  #ifdef OPENSSL_NO_EC2M
          ECerr(0, EC_R_GF2M_NOT_SUPPORTED);
          goto err;
  #else
          /* create the EC_GROUP structure */
          group = EC_GROUP_new_curve_GF2m(p, a, b, NULL);
          if (group != NULL) {
              field_bits = EC_GROUP_get_degree(group);
              if (field_bits > OPENSSL_ECC_MAX_FIELD_BITS) {
                  ECerr(0, EC_R_FIELD_TOO_LARGE);
                  goto err;
              }
          }
  #endif /* OPENSSL_NO_EC2M */
      }
  
      if (group == NULL) {
          ECerr(0, ERR_R_EC_LIB);
          goto err;
      }
  
      /* Optional seed */
      ptmp = OSSL_PARAM_locate_const(params, OSSL_PKEY_PARAM_EC_SEED);
      if (ptmp != NULL) {
          if (ptmp->data_type != OSSL_PARAM_OCTET_STRING) {
              ECerr(0, EC_R_INVALID_SEED);
              goto err;
          }
          if (!EC_GROUP_set_seed(group, ptmp->data, ptmp->data_size))
              goto err;
      }
  
      /* generator base point */
      ptmp = OSSL_PARAM_locate_const(params, OSSL_PKEY_PARAM_EC_GENERATOR);
      if (ptmp == NULL
          || ptmp->data_type != OSSL_PARAM_OCTET_STRING) {
          ECerr(0, EC_R_INVALID_GENERATOR);
          goto err;
      }
      buf = (const unsigned char *)(ptmp->data);
      if ((point = EC_POINT_new(group)) == NULL)
          goto err;
      EC_GROUP_set_point_conversion_form(group,
                                         (point_conversion_form_t)buf[0] & ~0x01);
      if (!EC_POINT_oct2point(group, point, buf, ptmp->data_size, bnctx)) {
          ECerr(0, EC_R_INVALID_GENERATOR);
          goto err;
      }
  
      /* order */
      ptmp = OSSL_PARAM_locate_const(params, OSSL_PKEY_PARAM_EC_ORDER);
      if (!OSSL_PARAM_get_BN(ptmp, &order)
          || (BN_is_negative(order) || BN_is_zero(order))
          || (BN_num_bits(order) > (int)field_bits + 1)) { /* Hasse bound */
          ECerr(0, EC_R_INVALID_GROUP_ORDER);
          goto err;
      }
  
      /* Optional cofactor */
      ptmp = OSSL_PARAM_locate_const(params, OSSL_PKEY_PARAM_EC_COFACTOR);
      if (ptmp != NULL) {
          cofactor = BN_CTX_get(bnctx);
          if (cofactor == NULL || !OSSL_PARAM_get_BN(ptmp, &cofactor)) {
              ECerr(0, EC_R_INVALID_COFACTOR);
              goto err;
          }
      }
  
      /* set the generator, order and cofactor (if present) */
      if (!EC_GROUP_set_generator(group, point, order, cofactor)) {
          ECerr(0, EC_R_INVALID_GENERATOR);
          goto err;
      }
  
      named_group = ec_group_explicit_to_named(group, libctx, propq, bnctx);
      if (named_group == NULL) {
          ECerr(0, EC_R_INVALID_NAMED_GROUP_CONVERSION);
          goto err;
      }
      if (named_group == group) {
          /*
           * If we did not find a named group then the encoding should be explicit
           * if it was specified
           */
          if (encoding_flag == OPENSSL_EC_NAMED_CURVE) {
              ECerr(0, EC_R_INVALID_ENCODING);
              goto err;
          }
          EC_GROUP_set_asn1_flag(group, OPENSSL_EC_EXPLICIT_CURVE);
      } else {
          EC_GROUP_free(group);
          group = named_group;
      }
      ok = 1;
   err:
      if (!ok) {
          EC_GROUP_free(group);
          group = NULL;
      }
      EC_POINT_free(point);
      BN_CTX_end(bnctx);
      BN_CTX_free(bnctx);
  
      return group;
  }
  