NTRU over rings beyond $${\mathbb{Z}}$$

  • Authors:
  • Monica Nevins;Camelia Karimianpour;Ali Miri

  • Affiliations:
  • Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada;Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada;School of Information Technology and Engineering (SITE), and Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada

  • Venue:
  • Designs, Codes and Cryptography
  • Year:
  • 2010

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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.