Two-Round Three-Party PAKE Protocol over Lattices

Password-based authenticated key exchange (PAKE) enables the participants of the protocol to negotiate a secure session key on the open network only by remembering a low-entropy password. However, with the rapid development of quantum computing technology, the PAKE protocol, which is based on traditional problems such as large integer decomposition and discrete logarithm, is no longer secure. The lattice cryptosystem is a typical anti-quantum cryptography. Then with the rapid development of big data, cloud computing and supercomputers, more and more large-scale communication systems begin to appear. The existing two-party PAKE based on lattices is no longer suitable for today's large-scale communication system, and the existing single three-party PAKE based on lattices also have some problems, such as low implementation efficiency, unable to realize key exchange and so on. Therefore, by using the non-adaptive smooth projection hash function (SPHF) on the lattice, a two-round three-party PAKE protocol based on lattices with provable security is proposed. This protocol can resist quantum attacks and does not need zero knowledge proof. And the key ex-change is realized in two rounds of communication, thus reducing the number of communication rounds. Compared with other similar methods, the protocol proposed in this paper has higher execution efficiency and lower computing cost, and is more suitable for large-scale communication systems.