Password-Authenticated Key Exchange(PAKE) protocol has a wide application prospect in the coming post-quantum era. Scaling down the number of communication rounds is capable of effectively improving the execution efficiency, and this is a rather important direction for optimizing PAKE protocols over lattices. Up to now, there are mainly two technical routes in the existing literature guiding the construction of low-round PAKE schemes over lattices. One is based on Non-Interactive Zero-Knowledge(NIZK) proofs, but how to implement NIZK proofs in the standard model over lattices is still an open question for these derivative schemes; the other one is nominally designed as Indistinguishability under Adaptive Chosen-Ciphertext Attack(IND-CCA2) secure based protocol, nevertheless it applies only an Indistinguishability under Chosen-Ciphertext Attack(IND-CCA1) secure based Public Key Encryption(PKE) scheme in implementation, which relies on the introduction of signature/verification algorithms or other techniques to ensure its security in implementation. Moreover, these two methods will introduce extra computation and communication costs. Therefore, taking advantage of the additive homomorphic property of the Learning with Errors(LWE) problem, this paper proposes an IND-CCA2 secure word-independent Smooth Projective Hash Function(SPHF) over lattices, which also supports the construction of one-round PAKE protocols. And this paper identifies the exact values of parameters of the PKE scheme that the proposed SPHF predicates on, ultimately eliminate the influence of the incomplete additive homomorphic property of the LWE problem on the correctness of the SPHF. As far as we know, so mentioned function is the first IND-CCA2 secure word-independent SPHF over lattices. Besides, the proposed SPHF possesses independent research value and great application potential in multiple practice fields such as witness encryption, zero-knowledge proof, oblivious transmission and so on. On this basis, this paper innovatively designs an efficient provably secure PAKE protocol. This protocol is resistant to quantum attack; it only requires one-round communication, achieving the optimal communication round; it is based on the standard model, thus capable of avoiding the potential security threats of utilizing random oracles, especially in situations where the utilize of random oracles may cause lattice-based PAKE protocols to suffer offline password guessing attacks and quantum attacks. In practical applications, the proposed protocol does not reflect dependence on the utilization of NIZK proofs, signature/verification algorithms or other techniques to ensure its security, which will effectively improve the execution efficiency. In addition, this paper utilizes a dataset containing 4.74 million unique username-password pairs of Renren to verify that the PAKE security analysis model based on the CDF-Zipf law is indubitable feasible to more accurately evaluate the security guarantee that a real PAKE protocol can provide. Finally, in the standard model and based on this more realistic security analysis model, this paper provides a strict proof of the security of above mentioned protocol. Controlled experimental results show that the proposed PAKE protocol has the most optimal efficiency and the lowest communication cost compared with other related protocols, which drops in line with our expectations. © 2022, Science Press. All right reserved.
