Novel Smooth Hash Proof Systems Based on Lattices

摘要

As a basic and important primitive, hash proof system can be used to construct many cryptographic schemes and protocols. Therefore, it is significant to instantiate more efficient hash proof systems from various assumptions. Although there are many hash proof systems based on various classical assumptions, only a handful of efficient hash proof systems are known based on post-quantum assumptions. In this paper, we present several new hash proof systems based on the standard learning with errors (LWE) problem, which is at least as hard as standard worst-case lattice problems. Comparing with other existing constructions based on lattices, our main advantages are 2-fold: much simpler and more efficient. And our constructions can be easily extended to be identity-based ones and updatable ones. Throughout the paper, our main idea is to base hash proof systems on a new subset indistinguishability problem related to LWE, and employ the property of smooth parameter of q-ary orthogonal lattices to ensure smoothness.