A B S T R A C T Smooth Projective Hash Functions (SPHFs) as a specific pattern of zero knowledge proof system are fundamental tools to build many efficient 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 first lattice-based PAKE using the Learning With Errors (LWE) problem. In this work, we present a new efficient ring-based smooth

more »

... 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 efficient password-based authenticated key exchange "(Ring-PAKE)" protocol over rings whose security relies on ideal lattice assumptions.