关键词: 理想格, 可证明安全, 口令认证, 密钥协商, 环上误差学习问题

Abstract: The key agreement protocol based on standard lattice has longer key and higher ciphertext expansion rate,and the way of lattice representation needs larger space,while the ideal lattice has shorter key length and higher running efficiency.Therefore,combined with Ring Learning with Error(RLWE) problem,an anonymous password authentication key agreement protocol based on the ideal lattice is proposed.Users use low entropy passwords to authenticate and share session keys through servers,so as to avoid users’ long-term key security being threatened in the process of identity authentication.The analysis results show that,compared with the traditional 2PAKE and 3PAKE protocols,the proposed protocol has higher efficiency and shorter key length,which can resist quantum attacks and is suitable for large-scale network communication.

Key words: ideal lattice, provably secure, password authentication, key agreement, Ring Learning with Error(RLWE) problem