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@@ -294,6 +294,67 @@ int EC_METHOD_get_field_type(const EC_METHOD *meth)
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return meth->field_type;
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}
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+/*-
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+ * Try computing cofactor from the generator order (n) and field cardinality (q).
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+ * This works for all curves of cryptographic interest.
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+ *
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+ * Hasse thm: q + 1 - 2*sqrt(q) <= n*h <= q + 1 + 2*sqrt(q)
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+ * h_min = (q + 1 - 2*sqrt(q))/n
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+ * h_max = (q + 1 + 2*sqrt(q))/n
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+ * h_max - h_min = 4*sqrt(q)/n
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+ * So if n > 4*sqrt(q) holds, there is only one possible value for h:
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+ * h = \lfloor (h_min + h_max)/2 \rceil = \lfloor (q + 1)/n \rceil
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+ *
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+ * Otherwise, zero cofactor and return success.
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+ */
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+static int ec_guess_cofactor(EC_GROUP *group) {
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+ int ret = 0;
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+ BN_CTX *ctx = NULL;
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+ BIGNUM *q = NULL;
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+
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+ /*-
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+ * If the cofactor is too large, we cannot guess it.
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+ * The RHS of below is a strict overestimate of lg(4 * sqrt(q))
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+ */
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+ if (BN_num_bits(&group->order) <= (BN_num_bits(&group->field) + 1) / 2 + 3) {
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+ /* default to 0 */
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+ BN_zero(&group->cofactor);
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+ /* return success */
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+ return 1;
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+ }
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+
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+ if ((ctx = BN_CTX_new()) == NULL)
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+ return 0;
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+
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+ BN_CTX_start(ctx);
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+ if ((q = BN_CTX_get(ctx)) == NULL)
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+ goto err;
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+
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+ /* set q = 2**m for binary fields; q = p otherwise */
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+ if (group->meth->field_type == NID_X9_62_characteristic_two_field) {
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+ BN_zero(q);
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+ if (!BN_set_bit(q, BN_num_bits(&group->field) - 1))
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+ goto err;
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+ } else {
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+ if (!BN_copy(q, &group->field))
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+ goto err;
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+ }
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+
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+ /* compute h = \lfloor (q + 1)/n \rceil = \lfloor (q + 1 + n/2)/n \rfloor */
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+ if (!BN_rshift1(&group->cofactor, &group->order) /* n/2 */
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+ || !BN_add(&group->cofactor, &group->cofactor, q) /* q + n/2 */
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+ /* q + 1 + n/2 */
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+ || !BN_add(&group->cofactor, &group->cofactor, BN_value_one())
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+ /* (q + 1 + n/2)/n */
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+ || !BN_div(&group->cofactor, NULL, &group->cofactor, &group->order, ctx))
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+ goto err;
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+ ret = 1;
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+ err:
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+ BN_CTX_end(ctx);
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+ BN_CTX_free(ctx);
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+ return ret;
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+}
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+
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int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator,
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const BIGNUM *order, const BIGNUM *cofactor)
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{
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@@ -302,6 +363,33 @@ int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator,
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return 0;
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}
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+ /* require group->field >= 1 */
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+ if (BN_is_zero(&group->field) || BN_is_negative(&group->field)) {
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+ ECerr(EC_F_EC_GROUP_SET_GENERATOR, EC_R_INVALID_FIELD);
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+ return 0;
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+ }
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+
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+ /*-
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+ * - require order >= 1
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+ * - enforce upper bound due to Hasse thm: order can be no more than one bit
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+ * longer than field cardinality
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+ */
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+ if (order == NULL || BN_is_zero(order) || BN_is_negative(order)
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+ || BN_num_bits(order) > BN_num_bits(&group->field) + 1) {
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+ ECerr(EC_F_EC_GROUP_SET_GENERATOR, EC_R_INVALID_GROUP_ORDER);
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+ return 0;
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+ }
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+
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+ /*-
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+ * Unfortunately the cofactor is an optional field in many standards.
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+ * Internally, the lib uses 0 cofactor as a marker for "unknown cofactor".
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+ * So accept cofactor == NULL or cofactor >= 0.
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+ */
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+ if (cofactor != NULL && BN_is_negative(cofactor)) {
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+ ECerr(EC_F_EC_GROUP_SET_GENERATOR, EC_R_UNKNOWN_COFACTOR);
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+ return 0;
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+ }
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+
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if (group->generator == NULL) {
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group->generator = EC_POINT_new(group);
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if (group->generator == NULL)
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@@ -310,17 +398,17 @@ int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator,
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if (!EC_POINT_copy(group->generator, generator))
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return 0;
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- if (order != NULL) {
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- if (!BN_copy(&group->order, order))
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- return 0;
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- } else
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- BN_zero(&group->order);
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+ if (!BN_copy(&group->order, order))
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+ return 0;
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- if (cofactor != NULL) {
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+ /* Either take the provided positive cofactor, or try to compute it */
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+ if (cofactor != NULL && !BN_is_zero(cofactor)) {
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if (!BN_copy(&group->cofactor, cofactor))
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return 0;
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- } else
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+ } else if (!ec_guess_cofactor(group)) {
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BN_zero(&group->cofactor);
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+ return 0;
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+ }
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/*-
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* Access to the `mont_data` field of an EC_GROUP struct should always be
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@@ -1169,3 +1257,60 @@ int ec_precompute_mont_data(EC_GROUP *group)
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BN_CTX_free(ctx);
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return ret;
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}
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+
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+/*
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+ * This is just a wrapper around the public functions
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+ * - EC_GROUP_get_curve_GF2m
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+ * - EC_GROUP_get_curve_GFp
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+ *
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+ * It is meant to facilitate backporting of code from newer branches, where
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+ * the public API includes a "field agnostic" version of it.
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+ */
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+int ec_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a,
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+ BIGNUM *b, BN_CTX *ctx)
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+{
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+ int field_nid;
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+
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+ field_nid = EC_METHOD_get_field_type(EC_GROUP_method_of(group));
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+
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+#ifndef OPENSSL_NO_EC2M
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+ if (field_nid == NID_X9_62_characteristic_two_field) {
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+ return EC_GROUP_get_curve_GF2m(group, p, a, b, ctx);
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+ } else
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+#endif /* !def(OPENSSL_NO_EC2M) */
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+ if (field_nid == NID_X9_62_prime_field) {
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+ return EC_GROUP_get_curve_GFp(group, p, a, b, ctx);
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+ } else {
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+ /* this should never happen */
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+ return 0;
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+ }
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+}
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+
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+/*
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+ * This is just a wrapper around the public functions
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+ * - EC_POINT_get_affine_coordinates_GF2m
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+ * - EC_POINT_get_affine_coordinates_GFp
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+ *
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+ * It is meant to facilitate backporting of code from newer branches, where
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+ * the public API includes a "field agnostic" version of it.
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+ */
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+int ec_point_get_affine_coordinates(const EC_GROUP *group,
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+ const EC_POINT *point, BIGNUM *x,
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+ BIGNUM *y, BN_CTX *ctx)
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+{
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+ int field_nid;
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+
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+ field_nid = EC_METHOD_get_field_type(EC_GROUP_method_of(group));
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+
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+#ifndef OPENSSL_NO_EC2M
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+ if (field_nid == NID_X9_62_characteristic_two_field) {
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+ return EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx);
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+ } else
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+#endif /* !def(OPENSSL_NO_EC2M) */
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+ if (field_nid == NID_X9_62_prime_field) {
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+ return EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx);
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+ } else {
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+ /* this should never happen */
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+ return 0;
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+ }
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+}
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