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Australasian Conference on Information Security and Privacy

ACISP 2008: Information Security and Privacy pp 433–446Cite as

A Tree-Based Approach for Computing Double-Base Chains

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 5107))

Abstract

We introduce a tree-based method to find short Double-Base chains. As compared to the classical greedy approach, this new method is not only simpler to implement and faster, experimentally it also returns shorter chains on average. The complexity analysis shows that the average length of a chain returned by this tree-based approach is \(\frac{\log_2 n }{4.6419}\cdotp\) This tends to suggest that the average length of DB-chains generated by the greedy approach is not O(logn/loglogn). We also discuss generalizations of this method, namely to compute Step Multi-Base Representation chains involving more than 2 bases and extended DB-chains having nontrivial coefficients.

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Author information

Authors and Affiliations

  1. Department of Computing, Macquarie University, Australia

    Christophe Doche

  2. Institut Camille Jordan, CNRS UMR 5208, Université Lyon 1, 69622, Villeurbanne Cedex, France

    Laurent Habsieger

Authors
  1. Christophe Doche
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  2. Laurent Habsieger
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Editor information

Yi Mu Willy Susilo Jennifer Seberry

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Doche, C., Habsieger, L. (2008). A Tree-Based Approach for Computing Double-Base Chains. In: Mu, Y., Susilo, W., Seberry, J. (eds) Information Security and Privacy. ACISP 2008. Lecture Notes in Computer Science, vol 5107. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70500-0_32

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  • DOI: https://doi.org/10.1007/978-3-540-70500-0_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-69971-2

  • Online ISBN: 978-3-540-70500-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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