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Designs, Codes and Cryptography

, Volume 56, Issue 1, pp 65–78 | Cite as

NTRU over rings beyond \({\mathbb{Z}}\)

  • Monica Nevins
  • Camelia KarimianPour
  • Ali Miri
Article

Abstract

The NTRU cryptosystem is constructed on the base ring \({\mathbb{Z}}\) . We give suitability conditions on rings to serve as alternate base rings. We present an example of an NTRU-like cryptosystem based on the Eisenstein integers \({\mathbb{Z}[\zeta_3]}\) , which has a denser lattice structure than \({\mathbb{Z}}\) for the same dimension, and which furthermore presents a more difficult lattice problem for lattice attacks, for the same level of decryption failure security.

Keywords

Public-key cryptography Lattice NTRU 

Mathematics Subject Classification (2000)

Primary 11T71 Secondary 13G 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of OttawaOttawaCanada
  2. 2.School of Information Technology and Engineering (SITE), and Department of Mathematics and StatisticsUniversity of OttawaOttawaCanada

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