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As a linear structure, cryptosystems based on lattice has the incomparable advantage of lower energy consumption, so in the future they will also have a wide range of use for intelligent terminal. Compared with traditional public key cryptosystem: RSA, ECC, the based lattice cryptosystems can be proved secure, it have shown the important role in post-quantum cryptography era. The core of the algorithm's problems are base reduction, for 20 years, being inspired LLL lattice reduction algorithm, there are some stronger, and faster algorithm, no matter in accurate, or approximate, they has an important role to cryptanalysis and cryptosystem's design. This article attempts to give a survey of state-of-the-art lattice reduction algorithm.