Cryptology ePrint Archive: Report 2015/1170

Characterizing NTRU-Variants Using Group Ring and Evaluating their Lattice Security

Takanori Yasuda and Xavier Dahan and Kouichi Sakurai

Abstract: The encryption scheme NTRU is designed over a quotient ring of a polynomial ring. Basically, if the ring is changed to any other ring, NTRU-like cryptosystem is constructible.

In this paper, we propose a variant of NTRU using group ring, which is called GR-NTRU. GR-NTRU includes NTRU as a special case. Moreover, we analyze and compare the security of GR-NTRU for several concrete groups. It is easy to investigate the algebraic structure of group ring by using group representation theory. We apply this fact to the security analysis of GR-NTRU. We show that the original NTRU and multivariate NTRU are most secure among several GR-NTRUs which we investigated.

Category / Keywords: public-key cryptography / Lattice-based cryptography, NTRU, group ring, group representation theory

Date: received 4 Dec 2015

Contact author: yasuda at isit or jp

Available format(s): PDF | BibTeX Citation

Version: 20151205:043019 (All versions of this report)

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