Abstract: The traditional encryption scheme does not take into account the situation in which the adversary eavesdrops on the ciphertext to force the sender or receiver to hand over the public key,random number,plaintext,or secret key used in the encryption.Therefore,the concept of deniable encryption was proposed in 1997 to solve the information leakage caused by the coercion problem.At present,only several complete deniable encryption schemes have been proposed and implemented.However,the schemes are not practical due to the problems of low encryption efficiency and high expansion rate.By constructing a “translucent set”,a practical bi-deniable anti-quantum encryption scheme is proposed in this paper.The scheme uses the difficult problem of Module Learning With Errors (MLWE) based on polynomial ring to construct two ciphertext distributions that adversaries can’tdistinguish.The indistinguishability of two ciphertext distributions is verified by chi-square statistical experiments.The schemes’ security can be reduced to the Shortest Independent Vectors Problem (SIVP).Meanwhile,the correctness,security,deniable,expansion rate and complexity of the scheme are theoretically analyzed.And the experimental results obtained through C++are consistent with the theoretical analysis.Experimental results show that the bit error rate is about 1×10^<sup>－23,the ciphertext expansion rate 5.0,and the encryption efficiency is about 670 KB/s.Therefore,it has practical application prospects in many scena-rios,such as electronic election and electronic bidding.

Key words: Anti-quantum attack, Deniable encryption, Lattice encryption, Symmetric encryption, Translucent set