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On the Optimality of Lattices for the Coppersmith Technique

  • Yoshinori Aono
  • Manindra Agrawal
  • Takakazu Satoh
  • Osamu Watanabe
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7372)

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].

Keywords

Lattice Coppersmith technique Univariate equation Impossibility result RSA 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Yoshinori Aono
    • 1
  • Manindra Agrawal
    • 2
  • Takakazu Satoh
    • 3
  • Osamu Watanabe
    • 4
  1. 1.National Institute of Information and Communications TechnologyTokyoJapan
  2. 2.Department of Computer Science and EngineeringIndian Institute of TechnologyKanpurIndia
  3. 3.Department of MathematicsTokyo Institute of TechnologyTokyoJapan
  4. 4.Department of Mathematical and Computing SciencesTokyo Institute of TechnologyTokyoJapan

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