New constructions of public-key encryption schemes from conjugacy search problems

Authors:
Lihua Wang;Licheng Wang;Zhenfu Cao;Eiji Okamoto;Jun Shao
Affiliations:
Information Security Research Center, National Institute of Information and Communications Technology, Tokyo, Japan;Information Security Center, State Key Laboratory of Networking and Switching Techn., Beijing Univ. of Posts and Telecommunications Beijing, P.R. China and Inf. Security Research Center, National ...;Trusted Digital Technology Laboratory, Shanghai Jiao Tong University, Shanghai, P.R. China;Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba, Japan;College of Computer and Information Engineering, Zhejiang Gongshang University, Hangzhou, P.R. China
Venue:
Inscrypt'10 Proceedings of the 6th international conference on Information security and cryptology
Year:
2010

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Abstract

We propose new public-key encryption schemes based on the conjugacy search problems (CSP) over noncommutative monoids. Under the newly developed cryptographic assumptions, our basic construction is proven IND-CPA secure in the standard model. Then, we describe two extensions: The first is proven IND-CCA secure in the random oracle model, while the second achieves the IND-CCA security in the standard model. Finally, our proposal is instantiated by using the monoid of matrices over truncated multivariable polynomials over rings. Meanwhile, we also give a discussion on the possibility to instantiate our schemes with braid groups.