+/*-
+ * 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;
+}
+