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Threshold Phenomena in Random Lattices and Efficient Reduction Algorithms

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Algorithms - ESA’ 99 (ESA 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1643))

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Abstract

Two new lattice reduction algorithms are presented and analyzed. These algorithms, called the Schmidt reduction and the Gram reduction, are obtained by relaxing some of the constraints of the classical LLL algorithm. By analyzing the worst case behavior and the average case behavior in a tractable model, we prove that the new algorithms still produce “good” reduced basis while requiring fewer iterations on average. In addition, we provide empirical tests on random lattices coming from applications, that confirm our theoretical results about the relative behavior of the different reduction algorithms.

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Author information

Authors and Affiliations

  1. GREYC - Université de Caen, F-14032, Caen Cedex, France

    Ali Akhavi

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  1. Ali Akhavi
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Editor information

Editors and Affiliations

  1. Department of Applied Mathematics and DIMATIA Centre, Charles University, Malostranská nám. 25, CZ-11800, Prague 1, Czech Republic

    Jaroslav Nešetřil

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© 1999 Springer-Verlag Berlin Heidelberg

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Akhavi, A. (1999). Threshold Phenomena in Random Lattices and Efficient Reduction Algorithms. In: Nešetřil, J. (eds) Algorithms - ESA’ 99. ESA 1999. Lecture Notes in Computer Science, vol 1643. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48481-7_41

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  • DOI: https://doi.org/10.1007/3-540-48481-7_41

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66251-8

  • Online ISBN: 978-3-540-48481-3

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