C++ EC_POINT_copy函數代碼示例

int ec_group_copy(EC_GROUP *dest, const EC_GROUP *src) {
  if (dest->meth->group_copy == 0) {
    OPENSSL_PUT_ERROR(EC, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
    return 0;
  }
  if (dest->meth != src->meth) {
    OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS);
    return 0;
  }
  if (dest == src) {
    return 1;
  }

  ec_pre_comp_free(dest->pre_comp);
  dest->pre_comp = ec_pre_comp_dup(src->pre_comp);

  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) ||
      !BN_copy(&dest->cofactor, &src->cofactor)) {
    return 0;
  }

  dest->curve_name = src->curve_name;

  return dest->meth->group_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;
	} else
		return t;
}

int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator,
                           const BIGNUM *order, const BIGNUM *cofactor) {
  if (group->curve_name != NID_undef || group->generator != NULL) {
    // |EC_GROUP_set_generator| may only be used with |EC_GROUP|s returned by
    // |EC_GROUP_new_curve_GFp| and may only used once on each group.
    return 0;
  }

  // Require a cofactor of one for custom curves, which implies prime order.
  if (!BN_is_one(cofactor)) {
    OPENSSL_PUT_ERROR(EC, EC_R_INVALID_COFACTOR);
    return 0;
  }

  group->generator = EC_POINT_new(group);
  return group->generator != NULL &&
         EC_POINT_copy(group->generator, generator) &&
         BN_copy(&group->order, order);
}

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;
    }

    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 (order != NULL) {
        if (!BN_copy(group->order, order))
            return 0;
    } else
        BN_zero(group->order);

    if (cofactor != NULL) {
        if (!BN_copy(group->cofactor, cofactor))
            return 0;
    } else
        BN_zero(group->cofactor);

    /*
     * 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;
}

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) {
    OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE);
    return NULL;
  }
  r = EC_POINT_copy(t, a);
  if (!r) {
    EC_POINT_free(t);
    return NULL;
  } else {
    return t;
  }
}

int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator,
                           const BIGNUM *order, const BIGNUM *cofactor) {
  if (group->curve_name != NID_undef) {
    /* |EC_GROUP_set_generator| should only be used with |EC_GROUP|s returned
     * by |EC_GROUP_new_curve_GFp|. */
    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 (order != NULL) {
    if (!BN_copy(&group->order, order)) {
      return 0;
    }
  } else {
    BN_zero(&group->order);
  }

  if (cofactor != NULL) {
    if (!BN_copy(&group->cofactor, cofactor)) {
      return 0;
    }
  } else {
    BN_zero(&group->cofactor);
  }

  return 1;
}

static int eckey_priv_decode(EVP_PKEY *pkey, PKCS8_PRIV_KEY_INFO *p8)
	{
	const unsigned char *p = NULL;
	void *pval;
	int ptype, pklen;
	EC_KEY *eckey = NULL;
	X509_ALGOR *palg;

	if (!PKCS8_pkey_get0(NULL, &p, &pklen, &palg, p8))
		return 0;
	X509_ALGOR_get0(NULL, &ptype, &pval, palg);

	eckey = eckey_type2param(ptype, pval);

	if (!eckey)
		goto ecliberr;

	/* We have parameters now set private key */
	if (!d2i_ECPrivateKey(&eckey, &p, pklen))
		{
		ECerr(EC_F_ECKEY_PRIV_DECODE, EC_R_DECODE_ERROR);
		goto ecerr;
		}

	/* calculate public key (if necessary) */
	if (EC_KEY_get0_public_key(eckey) == NULL)
		{
		const BIGNUM *priv_key;
		const EC_GROUP *group;
		EC_POINT *pub_key;
		/* the public key was not included in the SEC1 private
		 * key => calculate the public key */
		group   = EC_KEY_get0_group(eckey);
		pub_key = EC_POINT_new(group);
		if (pub_key == NULL)
			{
			ECerr(EC_F_ECKEY_PRIV_DECODE, ERR_R_EC_LIB);
			goto ecliberr;
			}
		if (!EC_POINT_copy(pub_key, EC_GROUP_get0_generator(group)))
			{
			EC_POINT_free(pub_key);
			ECerr(EC_F_ECKEY_PRIV_DECODE, ERR_R_EC_LIB);
			goto ecliberr;
			}
		priv_key = EC_KEY_get0_private_key(eckey);
		if (!EC_POINT_mul(group, pub_key, priv_key, NULL, NULL, NULL))
			{
			EC_POINT_free(pub_key);
			ECerr(EC_F_ECKEY_PRIV_DECODE, ERR_R_EC_LIB);
			goto ecliberr;
			}
		if (EC_KEY_set_public_key(eckey, pub_key) == 0)
			{
			EC_POINT_free(pub_key);
			ECerr(EC_F_ECKEY_PRIV_DECODE, ERR_R_EC_LIB);
			goto ecliberr;
			}
		EC_POINT_free(pub_key);
		}

	EVP_PKEY_assign_EC_KEY(pkey, eckey);
	return 1;

	ecliberr:
	ECerr(EC_F_ECKEY_PRIV_DECODE, ERR_R_EC_LIB);
	ecerr:
	if (eckey)
		EC_KEY_free(eckey);
	return 0;
	}

void *
vg_thread_loop(void *arg)
{
	unsigned char hash_buf[128];
	unsigned char *eckey_buf;
	unsigned char hash1[32];

	int i, c, len, output_interval;
	int hash_len;

	const BN_ULONG rekey_max = 10000000;
	BN_ULONG npoints, rekey_at, nbatch;

	vg_context_t *vcp = (vg_context_t *) arg;
	EC_KEY *pkey = NULL;
	const EC_GROUP *pgroup;
	const EC_POINT *pgen;
	const int ptarraysize = 256;
	EC_POINT *ppnt[ptarraysize];
	EC_POINT *pbatchinc;

	vg_test_func_t test_func = vcp->vc_test;
	vg_exec_context_t ctx;
	vg_exec_context_t *vxcp;

	struct timeval tvstart;


	memset(&ctx, 0, sizeof(ctx));
	vxcp = &ctx;

	vg_exec_context_init(vcp, &ctx);

	pkey = vxcp->vxc_key;
	pgroup = EC_KEY_get0_group(pkey);
	pgen = EC_GROUP_get0_generator(pgroup);

	for (i = 0; i < ptarraysize; i++) {
		ppnt[i] = EC_POINT_new(pgroup);
		if (!ppnt[i]) {
			fprintf(stderr, "ERROR: out of memory?\n");
			exit(1);
		}
	}
	pbatchinc = EC_POINT_new(pgroup);
	if (!pbatchinc) {
		fprintf(stderr, "ERROR: out of memory?\n");
		exit(1);
	}

	BN_set_word(&vxcp->vxc_bntmp, ptarraysize);
	EC_POINT_mul(pgroup, pbatchinc, &vxcp->vxc_bntmp, NULL, NULL,
		     vxcp->vxc_bnctx);
	EC_POINT_make_affine(pgroup, pbatchinc, vxcp->vxc_bnctx);

	npoints = 0;
	rekey_at = 0;
	nbatch = 0;
	vxcp->vxc_key = pkey;
	vxcp->vxc_binres[0] = vcp->vc_addrtype;
	c = 0;
	output_interval = 1000;
	gettimeofday(&tvstart, NULL);

	if (vcp->vc_format == VCF_SCRIPT) {
		hash_buf[ 0] = 0x51;  // OP_1
		hash_buf[ 1] = 0x41;  // pubkey length
		// gap for pubkey
		hash_buf[67] = 0x51;  // OP_1
		hash_buf[68] = 0xae;  // OP_CHECKMULTISIG
		eckey_buf = hash_buf + 2;
		hash_len = 69;

	} else {
		eckey_buf = hash_buf;
		hash_len = 65;
	}

	while (!vcp->vc_halt) {
		if (++npoints >= rekey_at) {
			vg_exec_context_upgrade_lock(vxcp);
			/* Generate a new random private key */
			EC_KEY_generate_key(pkey);
			npoints = 0;

			/* Determine rekey interval */
			EC_GROUP_get_order(pgroup, &vxcp->vxc_bntmp,
					   vxcp->vxc_bnctx);
			BN_sub(&vxcp->vxc_bntmp2,
			       &vxcp->vxc_bntmp,
			       EC_KEY_get0_private_key(pkey));
			rekey_at = BN_get_word(&vxcp->vxc_bntmp2);
			if ((rekey_at == BN_MASK2) || (rekey_at > rekey_max))
				rekey_at = rekey_max;
			assert(rekey_at > 0);

			EC_POINT_copy(ppnt[0], EC_KEY_get0_public_key(pkey));
			vg_exec_context_downgrade_lock(vxcp);

			npoints++;
//.........這裏部分代碼省略.........

//.........這裏部分代碼省略.........

	if (!BN_hex2bn(&x, "D")) ABORT;
	if (!EC_POINT_set_compressed_coordinates_GFp(group, Q, x, 1, ctx)) ABORT;
	if (!EC_POINT_is_on_curve(group, Q, ctx))
		{
		if (!EC_POINT_get_affine_coordinates_GFp(group, Q, x, y, ctx)) ABORT;
		fprintf(stderr, "Point is not on curve: x = 0x");
		BN_print_fp(stderr, x);
		fprintf(stderr, ", y = 0x");
		BN_print_fp(stderr, y);
		fprintf(stderr, "\n");
		ABORT;
		}

	fprintf(stdout, "A cyclic subgroup:\n");
	k = 100;
	do
		{
		if (k-- == 0) ABORT;

		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 */
		{
			EC_POINT *points[3];
		
			points[0] = R;
			points[1] = Q;
			points[2] = P;
			if (!EC_POINTs_make_affine(group, 2, points, 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]);

void
vg_output_match_console(vg_context_t *vcp, EC_KEY *pkey, const char *pattern)
{
	unsigned char key_buf[512], *pend;
	char addr_buf[64], addr2_buf[64];
	char privkey_buf[VG_PROTKEY_MAX_B58];
	const char *keytype = "Privkey";
	int len;
	int isscript = (vcp->vc_format == VCF_SCRIPT);

	EC_POINT *ppnt;
	int free_ppnt = 0;
	if (vcp->vc_pubkey_base) {
		ppnt = EC_POINT_new(EC_KEY_get0_group(pkey));
		EC_POINT_copy(ppnt, EC_KEY_get0_public_key(pkey));
		EC_POINT_add(EC_KEY_get0_group(pkey),
			     ppnt,
			     ppnt,
			     vcp->vc_pubkey_base,
			     NULL);
		free_ppnt = 1;
		keytype = "PrivkeyPart";
	} else {
		ppnt = (EC_POINT *) EC_KEY_get0_public_key(pkey);
	}

	assert(EC_KEY_check_key(pkey));
	vg_encode_address(ppnt,
			  EC_KEY_get0_group(pkey),
			  vcp->vc_pubkeytype, addr_buf);
	if (isscript)
		vg_encode_script_address(ppnt,
					 EC_KEY_get0_group(pkey),
					 vcp->vc_addrtype, addr2_buf);

	if (vcp->vc_key_protect_pass) {
		len = vg_protect_encode_privkey(privkey_buf,
						pkey, vcp->vc_privtype,
						VG_PROTKEY_DEFAULT,
						vcp->vc_key_protect_pass);
		if (len) {
			keytype = "Protkey";
		} else {
			fprintf(stderr,
				"ERROR: could not password-protect key\n");
			vcp->vc_key_protect_pass = NULL;
		}
	}
	if (!vcp->vc_key_protect_pass) {
		vg_encode_privkey(pkey, vcp->vc_privtype, privkey_buf);
	}

	if (!vcp->vc_result_file || (vcp->vc_verbose > 0)) {
		printf("\r%79s\r\nPattern: %s\n", "", pattern);
	}

	if (vcp->vc_verbose > 0) {
		if (vcp->vc_verbose > 1) {
			pend = key_buf;
			len = i2o_ECPublicKey(pkey, &pend);
			printf("Pubkey (hex): ");
			dumphex(key_buf, len);
			printf("Privkey (hex): ");
			dumpbn(EC_KEY_get0_private_key(pkey));
			pend = key_buf;
			len = i2d_ECPrivateKey(pkey, &pend);
			printf("Privkey (ASN1): ");
			dumphex(key_buf, len);
		}

	}

	if (!vcp->vc_result_file || (vcp->vc_verbose > 0)) {
		if (isscript)
			printf("P2SHAddress: %s\n", addr2_buf);
		printf("Address: %s\n"
		       "%s: %s\n",
		       addr_buf, keytype, privkey_buf);
	}

	if (vcp->vc_result_file) {
		FILE *fp = fopen(vcp->vc_result_file, "a");
		if (!fp) {
			fprintf(stderr,
				"ERROR: could not open result file: %s\n",
				strerror(errno));
		} else {
			fprintf(fp,
				"Pattern: %s\n"
				, pattern);
			if (isscript)
				fprintf(fp, "P2SHAddress: %s\n", addr2_buf);
			fprintf(fp,
				"Address: %s\n"
				"%s: %s\n",
				addr_buf, keytype, privkey_buf);
			fclose(fp);
		}
	}
	if (free_ppnt)
//.........這裏部分代碼省略.........

EC_KEY *EC_KEY_copy(EC_KEY *dest, const EC_KEY *src)
	{
	EC_EXTRA_DATA *d;

	if (dest == NULL || src == NULL)
		{
		ECerr(EC_F_EC_KEY_COPY, ERR_R_PASSED_NULL_PARAMETER);
		return NULL;
		}
	/* copy the parameters */
	if (src->group)
		{
		const EC_METHOD *meth = EC_GROUP_method_of(src->group);
		/* clear the old group */
		if (dest->group)
			EC_GROUP_free(dest->group);
		dest->group = EC_GROUP_new(meth);
		if (dest->group == NULL)
			return NULL;
		if (!EC_GROUP_copy(dest->group, src->group))
			return NULL;
		}
	/*  copy the public key */
	if (src->pub_key && src->group)
		{
		if (dest->pub_key)
			EC_POINT_free(dest->pub_key);
		dest->pub_key = EC_POINT_new(src->group);
		if (dest->pub_key == NULL)
			return NULL;
		if (!EC_POINT_copy(dest->pub_key, src->pub_key))
			return NULL;
		}
	/* copy the private key */
	if (src->priv_key)
		{
		if (dest->priv_key == NULL)
			{
			dest->priv_key = BN_new();
			if (dest->priv_key == NULL)
				return NULL;
			}
		if (!BN_copy(dest->priv_key, src->priv_key))
			return NULL;
		}
	/* copy method/extra data */
	EC_EX_DATA_free_all_data(&dest->method_data);

	for (d = src->method_data; d != NULL; d = d->next)
		{
		void *t = d->dup_func(d->data);
		
		if (t == NULL)
			return 0;
		if (!EC_EX_DATA_set_data(&dest->method_data, t, d->dup_func, d->free_func, d->clear_free_func))
			return 0;
		}

	/* copy the rest */
	dest->enc_flag  = src->enc_flag;
	dest->conv_form = src->conv_form;
	dest->version   = src->version;

	return dest;
	}

//.........這裏部分代碼省略.........
      plen = param->value.sequence->length;

      if (!(eckey = d2i_ECParameters(NULL, &cp, plen)))
      {
        EVPerr(EVP_F_EVP_PKCS82PKEY,
          EVP_R_DECODE_ERROR);
        goto ecerr;
      }
    }
    else
    {
      EC_GROUP *group;
      cp = p = param->value.object->data;
      plen = param->value.object->length;

      /* type == V_ASN1_OBJECT => the parameters are given
       * by an asn1 OID
       */
      if ((eckey = EC_KEY_new()) == NULL)
      {
        EVPerr(EVP_F_EVP_PKCS82PKEY,
          ERR_R_MALLOC_FAILURE);
        goto ecerr;
      }
      group = EC_GROUP_new_by_curve_name(OBJ_obj2nid(a->parameter->value.object));
      if (group == NULL)
        goto ecerr;
      EC_GROUP_set_asn1_flag(group, OPENSSL_EC_NAMED_CURVE);
      if (EC_KEY_set_group(eckey, group) == 0)
        goto ecerr;
      EC_GROUP_free(group);
    }

    /* We have parameters now set private key */
    if (!d2i_ECPrivateKey(&eckey, &p_tmp, pkeylen))
    {
      EVPerr(EVP_F_EVP_PKCS82PKEY, EVP_R_DECODE_ERROR);
      goto ecerr;
    }

    /* calculate public key (if necessary) */
    if (EC_KEY_get0_public_key(eckey) == NULL)
    {
      const BIGNUM *priv_key;
      const EC_GROUP *group;
      EC_POINT *pub_key;
      /* the public key was not included in the SEC1 private
       * key => calculate the public key */
      group   = EC_KEY_get0_group(eckey);
      pub_key = EC_POINT_new(group);
      if (pub_key == NULL)
      {
        EVPerr(EVP_F_EVP_PKCS82PKEY, ERR_R_EC_LIB);
        goto ecerr;
      }
      if (!EC_POINT_copy(pub_key, EC_GROUP_get0_generator(group)))
      {
        EC_POINT_free(pub_key);
        EVPerr(EVP_F_EVP_PKCS82PKEY, ERR_R_EC_LIB);
        goto ecerr;
      }
      priv_key = EC_KEY_get0_private_key(eckey);
      if (!EC_POINT_mul(group, pub_key, priv_key, NULL, NULL, ctx))
      {
        EC_POINT_free(pub_key);
        EVPerr(EVP_F_EVP_PKCS82PKEY, ERR_R_EC_LIB);
        goto ecerr;
      }
      if (EC_KEY_set_public_key(eckey, pub_key) == 0)
      {
        EC_POINT_free(pub_key);
        EVPerr(EVP_F_EVP_PKCS82PKEY, ERR_R_EC_LIB);
        goto ecerr;
      }
      EC_POINT_free(pub_key);
    }

    EVP_PKEY_assign_EC_KEY(pkey, eckey);
    if (ctx)
      BN_CTX_free(ctx);
    break;
ecerr:
    if (ctx)
      BN_CTX_free(ctx);
    if (eckey)
      EC_KEY_free(eckey);
    if (pkey)
      EVP_PKEY_free(pkey);
    return NULL;
#endif
    default:
    EVPerr(EVP_F_EVP_PKCS82PKEY, EVP_R_UNSUPPORTED_PRIVATE_KEY_ALGORITHM);
    if (!a->algorithm) BUF_strlcpy (obj_tmp, "NULL", sizeof obj_tmp);
    else i2t_ASN1_OBJECT(obj_tmp, 80, a->algorithm);
    ERR_add_error_data(2, "TYPE=", obj_tmp);
    EVP_PKEY_free (pkey);
    return NULL;
  }
  return pkey;
}

int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
                      const EC_POINT *b, BN_CTX *ctx) {
  int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *,
                   BN_CTX *);
  int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
  const BIGNUM *p;
  BN_CTX *new_ctx = NULL;
  BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6;
  int ret = 0;

  if (a == b) {
    return EC_POINT_dbl(group, r, a, ctx);
  }
  if (EC_POINT_is_at_infinity(group, a)) {
    return EC_POINT_copy(r, b);
  }
  if (EC_POINT_is_at_infinity(group, b)) {
    return EC_POINT_copy(r, a);
  }

  field_mul = group->meth->field_mul;
  field_sqr = group->meth->field_sqr;
  p = &group->field;

  if (ctx == NULL) {
    ctx = new_ctx = BN_CTX_new();
    if (ctx == NULL) {
      return 0;
    }
  }

  BN_CTX_start(ctx);
  n0 = BN_CTX_get(ctx);
  n1 = BN_CTX_get(ctx);
  n2 = BN_CTX_get(ctx);
  n3 = BN_CTX_get(ctx);
  n4 = BN_CTX_get(ctx);
  n5 = BN_CTX_get(ctx);
  n6 = BN_CTX_get(ctx);
  if (n6 == NULL) {
    goto end;
  }

  // Note that in this function we must not read components of 'a' or 'b'
  // once we have written the corresponding components of 'r'.
  // ('r' might be one of 'a' or 'b'.)

  // n1, n2
  int b_Z_is_one = BN_cmp(&b->Z, &group->one) == 0;

  if (b_Z_is_one) {
    if (!BN_copy(n1, &a->X) || !BN_copy(n2, &a->Y)) {
      goto end;
    }
    // n1 = X_a
    // n2 = Y_a
  } else {
    if (!field_sqr(group, n0, &b->Z, ctx) ||
        !field_mul(group, n1, &a->X, n0, ctx)) {
      goto end;
    }
    // n1 = X_a * Z_b^2

    if (!field_mul(group, n0, n0, &b->Z, ctx) ||
        !field_mul(group, n2, &a->Y, n0, ctx)) {
      goto end;
    }
    // n2 = Y_a * Z_b^3
  }

  // n3, n4
  int a_Z_is_one = BN_cmp(&a->Z, &group->one) == 0;
  if (a_Z_is_one) {
    if (!BN_copy(n3, &b->X) || !BN_copy(n4, &b->Y)) {
      goto end;
    }
    // n3 = X_b
    // n4 = Y_b
  } else {
    if (!field_sqr(group, n0, &a->Z, ctx) ||
        !field_mul(group, n3, &b->X, n0, ctx)) {
      goto end;
    }
    // n3 = X_b * Z_a^2

    if (!field_mul(group, n0, n0, &a->Z, ctx) ||
        !field_mul(group, n4, &b->Y, n0, ctx)) {
      goto end;
    }
    // n4 = Y_b * Z_a^3
  }

  // n5, n6
  if (!bn_mod_sub_consttime(n5, n1, n3, p, ctx) ||
      !bn_mod_sub_consttime(n6, n2, n4, p, ctx)) {
    goto end;
  }
  // n5 = n1 - n3
  // n6 = n2 - n4

//.........這裏部分代碼省略.........

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;

    /* 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->curve_name = src->curve_name;
    dest->asn1_flag = src->asn1_flag;
    dest->asn1_form = src->asn1_form;

    if (src->seed) {
        OPENSSL_free(dest->seed);
        dest->seed = OPENSSL_malloc(src->seed_len);
        if (dest->seed == NULL)
            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);
}

int
MKEM_export_public_key_pt(const MKEM *kp, EC_POINT *p0, EC_POINT *p1)
{
  return (EC_POINT_copy(p0, kp->p0) && EC_POINT_copy(p1, kp->p1)) ? 0 : -1;
}