text: /* crypto/ec/ecp_oct.c */
  /*
   * Includes code written by Lenka Fibikova <fibikova@exp-math.uni-essen.de>
   * for the OpenSSL project. Includes code written by Bodo Moeller for the
   * OpenSSL project.
   */
  /* ====================================================================
   * Copyright (c) 1998-2002 The OpenSSL Project.  All rights reserved.
   *
   * Redistribution and use in source and binary forms, with or without
   * modification, are permitted provided that the following conditions
   * are met:
   *
   * 1. Redistributions of source code must retain the above copyright
   *    notice, this list of conditions and the following disclaimer.
   *
   * 2. Redistributions in binary form must reproduce the above copyright
   *    notice, this list of conditions and the following disclaimer in
   *    the documentation and/or other materials provided with the
   *    distribution.
   *
   * 3. All advertising materials mentioning features or use of this
   *    software must display the following acknowledgment:
   *    "This product includes software developed by the OpenSSL Project
   *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
   *
   * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
   *    endorse or promote products derived from this software without
   *    prior written permission. For written permission, please contact
   *    openssl-core@openssl.org.
   *
   * 5. Products derived from this software may not be called "OpenSSL"
   *    nor may "OpenSSL" appear in their names without prior written
   *    permission of the OpenSSL Project.
   *
   * 6. Redistributions of any form whatsoever must retain the following
   *    acknowledgment:
   *    "This product includes software developed by the OpenSSL Project
   *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
   *
   * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
   * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
   * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
   * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
   * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
   * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
   * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
   * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
   * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
   * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
   * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
   * OF THE POSSIBILITY OF SUCH DAMAGE.
   * ====================================================================
   *
   * This product includes cryptographic software written by Eric Young
   * (eay@cryptsoft.com).  This product includes software written by Tim
   * Hudson (tjh@cryptsoft.com).
   *
   */
  /* ====================================================================
   * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
   * Portions of this software developed by SUN MICROSYSTEMS, INC.,
   * and contributed to the OpenSSL project.
   */
  
  #include <openssl/err.h>
  #include <openssl/symhacks.h>
  
  #include "ec_lcl.h"
  
  int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *group,
                                               EC_POINT *point,
                                               const BIGNUM *x_, int y_bit,
                                               BN_CTX *ctx)
  {
      BN_CTX *new_ctx = NULL;
      BIGNUM *tmp1, *tmp2, *x, *y;
      int ret = 0;
  
      /* clear error queue */
      ERR_clear_error();
  
      if (ctx == NULL) {
          ctx = new_ctx = BN_CTX_new();
          if (ctx == NULL)
              return 0;
      }
  
      y_bit = (y_bit != 0);
  
      BN_CTX_start(ctx);
      tmp1 = BN_CTX_get(ctx);
      tmp2 = BN_CTX_get(ctx);
      x = BN_CTX_get(ctx);
      y = BN_CTX_get(ctx);
      if (y == NULL)
          goto err;
  
      /*-
       * Recover y.  We have a Weierstrass equation
       *     y^2 = x^3 + a*x + b,
       * so  y  is one of the square roots of  x^3 + a*x + b.
       */
  
      /* tmp1 := x^3 */
      if (!BN_nnmod(x, x_, &group->field, ctx))
          goto err;
      if (group->meth->field_decode == 0) {
          /* field_{sqr,mul} work on standard representation */
          if (!group->meth->field_sqr(group, tmp2, x_, ctx))
              goto err;
          if (!group->meth->field_mul(group, tmp1, tmp2, x_, ctx))
              goto err;
      } else {
          if (!BN_mod_sqr(tmp2, x_, &group->field, ctx))
              goto err;
          if (!BN_mod_mul(tmp1, tmp2, x_, &group->field, ctx))
              goto err;
      }
  
      /* tmp1 := tmp1 + a*x */
      if (group->a_is_minus3) {
          if (!BN_mod_lshift1_quick(tmp2, x, &group->field))
              goto err;
          if (!BN_mod_add_quick(tmp2, tmp2, x, &group->field))
              goto err;
          if (!BN_mod_sub_quick(tmp1, tmp1, tmp2, &group->field))
              goto err;
      } else {
          if (group->meth->field_decode) {
              if (!group->meth->field_decode(group, tmp2, &group->a, ctx))
                  goto err;
              if (!BN_mod_mul(tmp2, tmp2, x, &group->field, ctx))
                  goto err;
          } else {
              /* field_mul works on standard representation */
              if (!group->meth->field_mul(group, tmp2, &group->a, x, ctx))
                  goto err;
          }
  
          if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field))
              goto err;
      }
  
      /* tmp1 := tmp1 + b */
      if (group->meth->field_decode) {
          if (!group->meth->field_decode(group, tmp2, &group->b, ctx))
              goto err;
          if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field))
              goto err;
      } else {
          if (!BN_mod_add_quick(tmp1, tmp1, &group->b, &group->field))
              goto err;
      }
  
      if (!BN_mod_sqrt(y, tmp1, &group->field, ctx)) {
          unsigned long err = ERR_peek_last_error();
  
          if (ERR_GET_LIB(err) == ERR_LIB_BN
              && ERR_GET_REASON(err) == BN_R_NOT_A_SQUARE) {
              ERR_clear_error();
              ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES,
                    EC_R_INVALID_COMPRESSED_POINT);
          } else
              ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES,
                    ERR_R_BN_LIB);
          goto err;
      }
  
      if (y_bit != BN_is_odd(y)) {
          if (BN_is_zero(y)) {
              int kron;
  
              kron = BN_kronecker(x, &group->field, ctx);
              if (kron == -2)
                  goto err;
  
              if (kron == 1)
                  ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES,
                        EC_R_INVALID_COMPRESSION_BIT);
              else
                  /*
                   * BN_mod_sqrt() should have cought this error (not a square)
                   */
                  ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES,
                        EC_R_INVALID_COMPRESSED_POINT);
              goto err;
          }
          if (!BN_usub(y, &group->field, y))
              goto err;
      }
      if (y_bit != BN_is_odd(y)) {
          ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES,
                ERR_R_INTERNAL_ERROR);
          goto err;
      }
  
      if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx))
          goto err;
  
      ret = 1;
  
   err:
      BN_CTX_end(ctx);
      if (new_ctx != NULL)
          BN_CTX_free(new_ctx);
      return ret;
  }
  
  size_t ec_GFp_simple_point2oct(const EC_GROUP *group, const EC_POINT *point,
                                 point_conversion_form_t form,
                                 unsigned char *buf, size_t len, BN_CTX *ctx)
  {
      size_t ret;
      BN_CTX *new_ctx = NULL;
      int used_ctx = 0;
      BIGNUM *x, *y;
      size_t field_len, i, skip;
  
      if ((form != POINT_CONVERSION_COMPRESSED)
          && (form != POINT_CONVERSION_UNCOMPRESSED)
          && (form != POINT_CONVERSION_HYBRID)) {
          ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_INVALID_FORM);
          goto err;
      }
  
      if (EC_POINT_is_at_infinity(group, point)) {
          /* encodes to a single 0 octet */
          if (buf != NULL) {
              if (len < 1) {
                  ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
                  return 0;
              }
              buf[0] = 0;
          }
          return 1;
      }
  
      /* ret := required output buffer length */
      field_len = BN_num_bytes(&group->field);
      ret =
          (form ==
           POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2 * field_len;
  
      /* if 'buf' is NULL, just return required length */
      if (buf != NULL) {
          if (len < ret) {
              ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
              goto err;
          }
  
          if (ctx == NULL) {
              ctx = new_ctx = BN_CTX_new();
              if (ctx == NULL)
                  return 0;
          }
  
          BN_CTX_start(ctx);
          used_ctx = 1;
          x = BN_CTX_get(ctx);
          y = BN_CTX_get(ctx);
          if (y == NULL)
              goto err;
  
          if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx))
              goto err;
  
          if ((form == POINT_CONVERSION_COMPRESSED
               || form == POINT_CONVERSION_HYBRID) && BN_is_odd(y))
              buf[0] = form + 1;
          else
              buf[0] = form;
  
          i = 1;
  
          skip = field_len - BN_num_bytes(x);
          if (skip > field_len) {
              ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
              goto err;
          }
          while (skip > 0) {
              buf[i++] = 0;
              skip--;
          }
          skip = BN_bn2bin(x, buf + i);
          i += skip;
          if (i != 1 + field_len) {
              ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
              goto err;
          }
  
          if (form == POINT_CONVERSION_UNCOMPRESSED
              || form == POINT_CONVERSION_HYBRID) {
              skip = field_len - BN_num_bytes(y);
              if (skip > field_len) {
                  ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
                  goto err;
              }
              while (skip > 0) {
                  buf[i++] = 0;
                  skip--;
              }
              skip = BN_bn2bin(y, buf + i);
              i += skip;
          }
  
          if (i != ret) {
              ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
              goto err;
          }
      }
  
      if (used_ctx)
          BN_CTX_end(ctx);
      if (new_ctx != NULL)
          BN_CTX_free(new_ctx);
      return ret;
  
   err:
      if (used_ctx)
          BN_CTX_end(ctx);
      if (new_ctx != NULL)
          BN_CTX_free(new_ctx);
      return 0;
  }
  
  int ec_GFp_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
                              const unsigned char *buf, size_t len, BN_CTX *ctx)
  {
      point_conversion_form_t form;
      int y_bit;
      BN_CTX *new_ctx = NULL;
      BIGNUM *x, *y;
      size_t field_len, enc_len;
      int ret = 0;
  
      if (len == 0) {
          ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL);
          return 0;
      }
      form = buf[0];
      y_bit = form & 1;
      form = form & ~1U;
      if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED)
          && (form != POINT_CONVERSION_UNCOMPRESSED)
          && (form != POINT_CONVERSION_HYBRID)) {
          ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
          return 0;
      }
      if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit) {
          ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
          return 0;
      }
  
      if (form == 0) {
          if (len != 1) {
              ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
              return 0;
          }
  
          return EC_POINT_set_to_infinity(group, point);
      }
  
      field_len = BN_num_bytes(&group->field);
      enc_len =
          (form ==
           POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2 * field_len;
  
      if (len != enc_len) {
          ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
          return 0;
      }
  
      if (ctx == NULL) {
          ctx = new_ctx = BN_CTX_new();
          if (ctx == NULL)
              return 0;
      }
  
      BN_CTX_start(ctx);
      x = BN_CTX_get(ctx);
      y = BN_CTX_get(ctx);
      if (y == NULL)
          goto err;
  
      if (!BN_bin2bn(buf + 1, field_len, x))
          goto err;
      if (BN_ucmp(x, &group->field) >= 0) {
          ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
          goto err;
      }
  
      if (form == POINT_CONVERSION_COMPRESSED) {
          if (!EC_POINT_set_compressed_coordinates_GFp
              (group, point, x, y_bit, ctx))
              goto err;
      } else {
          if (!BN_bin2bn(buf + 1 + field_len, field_len, y))
              goto err;
          if (BN_ucmp(y, &group->field) >= 0) {
              ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
              goto err;
          }
          if (form == POINT_CONVERSION_HYBRID) {
              if (y_bit != BN_is_odd(y)) {
                  ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
                  goto err;
              }
          }
  
          if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx))
              goto err;
      }
  
      /* test required by X9.62 */
      if (EC_POINT_is_on_curve(group, point, ctx) <= 0) {
          ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE);
          goto err;
      }
  
      ret = 1;
  
   err:
      BN_CTX_end(ctx);
      if (new_ctx != NULL)
          BN_CTX_free(new_ctx);
      return ret;
  }
  