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On the Optimality of Lattices for the Coppersmith Technique

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Information Security and Privacy (ACISP 2012)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7372))

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Abstract

We investigate the Coppersmith technique [7] for finding solutions of a univariate modular equation within a range given by range parameter U. This paper provides a way to analyze a general type of limitation of the lattice construction. Our analysis bounds the possible range of U from above that is asymptotically equal to the bound given by the original result of Coppersmith. To show our result, we establish a framework for the technique by following the reformulation of Howgrave-Graham [14], and derive a condition for the technique to work. We then provide a way to analyze a bound of U for achieving the condition. Technically, we show that (i) the original result of Coppersmith achieves an optimal bound for U when constructing a lattice in a standard way. We then show evidence supporting that (ii) a non-standard lattice construction is generally difficult. We also report on computer experiments demonstrating the tightness of our analysis. Some of the detailed arguments are omitted due to the space limit; see the full-version [1].

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Author information

Authors and Affiliations

  1. National Institute of Information and Communications Technology, Tokyo, Japan

    Yoshinori Aono

  2. Department of Computer Science and Engineering, Indian Institute of Technology, Kanpur, India

    Manindra Agrawal

  3. Department of Mathematics, Tokyo Institute of Technology, Tokyo, Japan

    Takakazu Satoh

  4. Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo, Japan

    Osamu Watanabe

Authors
  1. Yoshinori Aono
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  2. Manindra Agrawal
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  3. Takakazu Satoh
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  4. Osamu Watanabe
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Editor information

Editors and Affiliations

  1. School of Computer Science and Software Engineering, University of Wollongong, Northfields Avenue, NSW, 2522, Wollongong, Australia

    Willy Susilo

  2. School of Computer Science and Software Engineering, University of Wollongong, Northfields Avenue, 2522, Wollongong, NSW, Australia

    Yi Mu

  3. School of Computer Science and Software Engineering, University of Wollongong, Northfields Avenue, 2522, Wollongong, NSW, Australia

    Jennifer Seberry

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Aono, Y., Agrawal, M., Satoh, T., Watanabe, O. (2012). On the Optimality of Lattices for the Coppersmith Technique. In: Susilo, W., Mu, Y., Seberry, J. (eds) Information Security and Privacy. ACISP 2012. Lecture Notes in Computer Science, vol 7372. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31448-3_28

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  • DOI: https://doi.org/10.1007/978-3-642-31448-3_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31447-6

  • Online ISBN: 978-3-642-31448-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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