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ETRU: NTRU over the Eisenstein integers

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Abstract

NTRU is a public-key cryptosystem based on polynomial rings over \(\mathbb Z .\) Replacing \(\mathbb Z \) with the ring of Eisenstein integers yields ETRU. We prove through both theory and implementation that ETRU is faster and has smaller keys for the same or better level of security than does NTRU.

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Notes

  1. The isometric embedding of \(\mathbb Z [\omega ]\) into \(\mathbb C \) was chosen in [25] instead, but it was shown in [17] that as the resulting lattice is not integral, the corresponding LLL and BKZ attacks are significantly slower and less effective for the attacker.

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Acknowledgments

The authors would like to thank the anonymous referees for several helpful comments, including pointers to recent literature on the use of the FFT in NTRU-like rings. The second author would also like to acknowledge the warm hospitality of the Institut de Mathématiques et de Modélisation de Montpellier, Université Montpellier II, France, where this work was completed. The second author’s research is supported by a Discovery Grant from NSERC Canada.

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Authors and Affiliations

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

    Katherine Jarvis & Monica Nevins

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  1. Katherine Jarvis
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  2. Monica Nevins
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Correspondence to Monica Nevins.

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Communicated by A. Winterhof.

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Jarvis, K., Nevins, M. ETRU: NTRU over the Eisenstein integers. Des. Codes Cryptogr. 74, 219–242 (2015). https://doi.org/10.1007/s10623-013-9850-3

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