%0 Journal Article %T A New Ring-Based SPHF and PAKE Protocol On Ideal Lattices %J The ISC International Journal of Information Security %I Iranian Society of Cryptology %Z 2008-2045 %A Ebrahimi Atani, Reza %A Ebrahimi Atani, Shahabaddin %A Hassani Karbasi, Amir %D 2019 %\ 01/30/2019 %V 11 %N 1 %P 75-86 %! A New Ring-Based SPHF and PAKE Protocol On Ideal Lattices %K Lattice Based cryptography %K Ring-LWE %K SPHF %K PAKE %R 10.22042/isecure.2018.109810.398 %X \emph{ 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, \emph { 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 \emph { ring-based } smooth projectice 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 the first efficient password-based authenticated key exchange ` ` ( Ring - PAKE ) " protocol over \emph{ rings } whose security relies on ideal lattice assumptions. %U https://www.isecure-journal.com/article_80508_39337c5ceba48a5deb5f33524c5e1831.pdf