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May-Ozerov Algorithm for Nearest-Neighbor Problem over \({\mathbb {F}}_{q}\) and Its Application to Information Set Decoding

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Innovative Security Solutions for Information Technology and Communications (SECITC 2016)

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Abstract

May and Ozerov proposed an algorithm for the nearest-neighbor problem of vectors over the binary field at EUROCRYPT 2015. They applied their algorithm to the decoding problem of random linear codes over the binary field and confirmed the performance improvement. We describe a generalization of their algorithm for vectors over the finite field \(\mathbb {F}_{q}\) with arbitrary prime power q. We also apply the generalized algorithm to the decoding problem of random linear codes over \(\mathbb {F}_{q}\). It is observed by our numerical analysis of asymptotic time complexity that the May-Ozerov nearest-neighbor algorithm may not contribute to the performance improvement of the Stern information set decoding over \(\mathbb {F}_{q}\) with \(q\ge 3\).

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Acknowledgments

This work was supported in part by JSPS KAKENHI Grant Numbers JP25330152 and JP16H02828.

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Authors and Affiliations

  1. Faculty of Engineering, University of Fukui, Fukui, Japan

    Shoichi Hirose

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  1. Shoichi Hirose
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Correspondence to Shoichi Hirose .

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Editors and Affiliations

  1. Military Technical Academy , Bucharest, Romania

    Ion Bica

  2. NEC Laboratories Europe , Heidelberg, Germany

    Reza Reyhanitabar

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Hirose, S. (2016). May-Ozerov Algorithm for Nearest-Neighbor Problem over \({\mathbb {F}}_{q}\) and Its Application to Information Set Decoding. In: Bica, I., Reyhanitabar, R. (eds) Innovative Security Solutions for Information Technology and Communications. SECITC 2016. Lecture Notes in Computer Science(), vol 10006. Springer, Cham. https://doi.org/10.1007/978-3-319-47238-6_8

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  • DOI: https://doi.org/10.1007/978-3-319-47238-6_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-47237-9

  • Online ISBN: 978-3-319-47238-6

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