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 cryptographyNTRUgroup ringgroup representation theory
Contact author(s)
yasuda @ isit or jp
History
2015-12-05: received
Short URL
https://ia.cr/2015/1170
License
Creative Commons Attribution
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},
      note = {\url{https://eprint.iacr.org/2015/1170}},
      url = {https://eprint.iacr.org/2015/1170}
}
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