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

Takanori Yasuda; Xavier Dahan; Kouichi Sakurai

Paper 2015/1170

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

Takanori Yasuda, 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.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint. MINOR revision.
Keywords: Lattice-based cryptography NTRU group ring group representation theory
Contact author(s): yasuda @ isit or jp
History: 2015-12-05: received
Short URL: https://ia.cr/2015/1170
License: CC BY

BibTeX

@misc{cryptoeprint:2015/1170,
      author = {Takanori Yasuda and Xavier Dahan and Kouichi Sakurai},
      title = {Characterizing {NTRU}-Variants Using Group Ring and Evaluating their Lattice Security},
      howpublished = {Cryptology {ePrint} Archive, Paper 2015/1170},
      year = {2015},
      url = {https://eprint.iacr.org/2015/1170}
}