Recently, research on database encryption for data protection and query result authentication methods has been performed more actively in the database outsourcing environment. Existing database encryption schemes are vulnerable to order matching and counting attack of intruders who have background knowledge of the original database domain. Existing query result integrity auditing methods suffer from the transmission overhead of verification object. To resolve these problems, we propose a group-order preserving encryption index and a query result authentication method based on the encryption index. Our group-order preserving encryption index groups the original data for data encryption and support query processing without data decryption. We generate group ids by using the Hilbert-curve so that we can protect the group information while processing a query. Finally, our periodic function based data grouping and query result authentication scheme can reduce the data size of the query result verification. Through performance evaluation, we show that our method achieves better performance than an existing bucket-based verification scheme, it is 1.6 times faster in terms of query processing time and produces verification data that is 20 times smaller.