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The Convergence of Slide-Type Reductions

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Public-Key Cryptography – PKC 2021 (PKC 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12710))

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Abstract

In this work, we apply the dynamical systems analysis of Hanrot et al. (CRYPTO’11) to a class of lattice block reduction algorithms that includes (natural variants of) slide reduction and block-Rankin reduction. This implies sharper bounds on the polynomial running times (in the query model) for these algorithms and opens the door to faster practical variants of slide reduction. We give heuristic arguments showing that such variants can indeed speed up slide reduction significantly in practice. This is confirmed by experimental evidence, which also shows that our variants are competitive with state-of-the-art reduction algorithms.

Supported by the European Research Council, ERC consolidator grant (682815 - TOCNeT).

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Notes

  1. 1.

    The restriction that \(d \mid n\) is lifted in [ALNS20] by combining it with the algorithm of [MW16].

  2. 2.

    Technically, LLL reduction also requires size-reduction and usually contains a slack factor in the inequality to guarantee termination in polynomial time. Neither of these additional requirements are important for this work, so we ignore it here for simplicity.

  3. 3.

    Code available at: http://pub.ist.ac.at/~mwalter/publication/hkz_slide/hkz_slide.zip.

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Acknowledgment

This work was initiated in discussions with Léo Ducas, when the author was visiting the Simons Institute for the Theory of Computation during the program “Lattices: Algorithms, Complexity, and Cryptography”. We thank Thomas Espitau for pointing out a bug in a proof in an earlier version of this manuscript.

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  1. IST Austria, Klosterneuburg, Austria

    Michael Walter

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  1. Michael Walter
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Correspondence to Michael Walter .

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  1. Texas A&M University, College Station, TX, USA

    Juan A. Garay

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Walter, M. (2021). The Convergence of Slide-Type Reductions. In: Garay, J.A. (eds) Public-Key Cryptography – PKC 2021. PKC 2021. Lecture Notes in Computer Science(), vol 12710. Springer, Cham. https://doi.org/10.1007/978-3-030-75245-3_3

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  • DOI: https://doi.org/10.1007/978-3-030-75245-3_3

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