Efficient module learning with errors?based post?quantum password?authenticated key exchange

Password-authenticated key exchange (PAKE) is a cryptographic primitive that can establish secure remote communications between the client and server, especially with advantage of amplifying memorable passwords into strong session keys. However, arrival quantum computing era has brought new challenges to traditional PAKE protocols. Thus, designing an efficient post-quantum scheme becomes open research question. In this paper, authors construct quantum-safe protocol, which horizontal extension password-authenticated (PAK) protocol in field module lattices. Subsequently, accompany proposed rigorous security proof random oracle model two adaptions: applying CDF-Zipf characterise ability adversary using pairing errors assumption simplify proof. Taking flexibility learning (MLWE) problem, elaborately select three parameter sets meet different application scenarios. Specifically, authors’ Recommended-PAKE implementation achieves 177-bit generous margin cope later improvement cryptanalysis. The performance results indicate MLWE-PAKE quite practical: compared latest Yang-PAK, Recommended-PAK reduces communication cost running time by 36.8% 13.8%, respectively.