Sufficient Conditions for Intractability over Black-Box Groups: Generic Lower Bounds for Generalized DL and DH Problems

  • Andy Rupp
  • Gregor Leander
  • Endre Bangerter
  • Alexander W. Dent
  • Ahmad-Reza Sadeghi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5350)

Abstract

The generic group model is a valuable methodology for analyzing the computational hardness of number-theoretic problems used in cryptography. Although generic hardness proofs exhibit many similarities, still the computational intractability of every newly introduced problem needs to be proven from scratch, a task that can easily become complicated and cumbersome when done rigorously. In this paper we make the first steps towards overcoming this problem by identifying criteria which guarantee the hardness of a problem in an extended generic model where algorithms are allowed to perform any operation representable by a polynomial function.

Keywords

Generic Group Model Straight-Line Programs Hardness Conditions Lower Bounds 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Andy Rupp
    • 1
  • Gregor Leander
    • 1
  • Endre Bangerter
    • 2
  • Alexander W. Dent
    • 3
  • Ahmad-Reza Sadeghi
    • 1
  1. 1.Horst Görtz Institute for IT-SecurityGermany
  2. 2.Bern University of Applied SciencesSwitzerland
  3. 3.Royal HollowayUniversity of LondonUnited Kingdom

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