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 ecient 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.