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Hard Instances of the Constrained Discrete Logarithm Problem

  • Ilya Mironov
  • Anton Mityagin
  • Kobbi Nissim
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4076)

Abstract

The discrete logarithm problem (DLP) generalizes to the constrained DLP, where the secret exponent x belongs to a set known to the attacker. The complexity of generic algorithms for solving the constrained DLP depends on the choice of the set. Motivated by cryptographic applications, we study explicit construction of sets for which the constrained DLP is hard. We draw on earlier results due to Erdös et al. and Schnorr, develop geometric tools such as generalized Menelaus’ theorem for proving lower bounds on the complexity of the constrained DLP, and construct explicit sets with provable non-trivial lower bounds.

Keywords

Bipartite Graph Generic Algorithm Generic Complexity Discrete Logarithm Discrete Logarithm Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Ilya Mironov
    • 1
  • Anton Mityagin
    • 2
  • Kobbi Nissim
    • 3
  1. 1.SVC-5Microsoft CorpUSA
  2. 2.Department of Computer Science and EngineeringUniversity of CaliforniaLa JollaUSA
  3. 3. Ramat-GanIsrael

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