Authenticated encryption

as a symmetric cryptographic primitive

can protect privacy and integrity simultaneously

which plays an important role in information security.Most of the existing authenticated encryption algorithms are designed based on the working mode of block cipher

which needs to call full round of block cipher.Thus the efficiency is quite limited.This paper considers to construct an efficient authenticated encryption algorithm dedicatedly using basic components.We first present a general structure by combining Chinese block cipher standard SM4 and the general Feistel structure.With the mixed integer linear programming (MILP) method

we find several secure structures against the collision attacks with different sate size and efficiency

which can be used as building blocks for MACs and authenticated encryption.Then we design an authenticated encryption using the structure with good state size and efficiency

and give the corresponding security analysis and implemention.Our benchmarks show that it runs about 10 times faster than SM4-GCM.