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Recursive Lattice Reduction

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Security and Cryptography for Networks (SCN 2010)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 6280))

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Abstract

Lattice reduction is known to be a very powerful tool in modern cryptanalysis. In the literature, there are many lattice reduction algorithms that have been proposed with various time complexity (from quadratic to subexponential). These algorithms can be utilized to find a short vector of a lattice with a small norm. Over time, shorter vector will be found by incorporating these methods. In this paper, we take a different approach by presenting a methodology that can be applied to any lattice reduction algorithms, with the implication that enables us to find a shorter vector (i.e. a smaller solution) while requiring shorter computation time. Instead of applying a lattice reduction algorithm to a complete lattice, we work on a sublattice with a smaller dimension chosen in the function of the lattice reduction algorithm that is being used. This way, the lattice reduction algorithm will be fully utilized and hence, it will produce a better solution. Furthermore, as the dimension of the lattice becomes smaller, the time complexity will be better. Hence, our methodology provides us with a new direction to build a lattice that is resistant to lattice reduction attacks. Moreover, based on this methodology, we also propose a recursive method for producing an optimal approach for lattice reduction with optimal computational time, regardless of the lattice reduction algorithm used. We evaluate our technique by applying it to break the lattice challenge by producing the shortest vector known so far. Our results outperform the existing known results and hence, our results achieve the record in the lattice challenge problem.

This work is partially supported by The Department of Prime Minister and Cabinet’s Research Support for Counter-Terrorism: PR06-0006.

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  1. Centre for Computer and Information Security Research School of Computer Science and Software Engineering, University of Wollongong, Australia

    Thomas Plantard & Willy Susilo

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  1. Thomas Plantard
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  2. Willy Susilo
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  1. AT&T Labs Research, Florham Park, NJ, USA

    Juan A. Garay

  2. Dipartimento di Informatica ed Applicazioni, Università di Salerno, via Ponte don Melillo, 84084, Fisciano, (SA), Italy

    Roberto De Prisco

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Plantard, T., Susilo, W. (2010). Recursive Lattice Reduction. In: Garay, J.A., De Prisco, R. (eds) Security and Cryptography for Networks. SCN 2010. Lecture Notes in Computer Science, vol 6280. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15317-4_21

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  • DOI: https://doi.org/10.1007/978-3-642-15317-4_21

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