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

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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.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada

    Monica Nevins & Camelia KarimianPour

  2. School of Information Technology and Engineering (SITE), and Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada

    Ali Miri

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  1. Monica Nevins
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  2. Camelia KarimianPour
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  3. Ali Miri
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Correspondence to Monica Nevins.

Additional information

Communicated by S. Galbraith.

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Nevins, M., KarimianPour, C. & Miri, A. NTRU over rings beyond \({\mathbb{Z}}\) . Des. Codes Cryptogr. 56, 65–78 (2010). https://doi.org/10.1007/s10623-009-9342-7

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  • DOI: https://doi.org/10.1007/s10623-009-9342-7

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