Document Type : Research Article


1 University of Guilan, Rasht, Iran

2 Department of Mathematics, University of Guilan, Rasht, Iran

3 Dep. Math. University Campus 2, University of Guilan


\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.


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