A New RingBased SPHF and PAKE Protocol On Ideal Lattices

Smooth Projective Hash Functions (SPHFs) as a speci c pattern of zero knowledge proof system are fundamental tools to build many eficient cryptographic schemes and protocols. As an application of SPHFs, Password-Based Authenticated Key Exchange (PAKE) protocol is well-studied area in the last few years. In 2009, Katz and Vaikuntanathan described the rst lattice-based PAKE using the Learning With Errors (LWE) problem. In this work, we present a new e cient ring-based smooth projective hash function \(Ring-SPHF) using Lyubashevsky, Peikert, and Regev s dual-style cryptosystem based on the Learning With Errors over Rings (Ring-LWE) problem. Then, using our ring-SPHF, we propose an eficient password-based authenticated key exchange \(Ring-PAKE) protocol over rings whose security relies on ideal lattice assumptions.