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Understanding Adaptivity: Random Systems Revisited

  • Dimitar Jetchev
  • Onur Özen
  • Martijn Stam
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7658)

Abstract

We develop a conceptual approach for probabilistic analysis of adaptive adversaries via Maurer’s methodology of random systems (Eurocrypt’02). We first consider a well-known comparison theorem of Maurer according to which, under certain hypotheses, adaptivity does not help for achieving a certain event. This theorem has subsequently been misinterpreted, leading to a misrepresentation with one of Maurer’s hypotheses being omitted in various applications. In particular, the only proof of (a misrepresentation of) the theorem available in the literature contained a flaw. We clarify the theorem by pointing out a simple example illustrating why the hypothesis of Maurer is necessary for the comparison statement to hold and provide a correct proof. Furthermore, we prove several technical statements applicable in more general settings where adaptivity might be helpful, which can be seen as the random system analogue of the game-playing arguments recently proved by Jetchev, Özen and Stam (TCC’12).

Keywords

Hash Function Random Permutation Full Version Monotone Condition Conditional Probability Distribution 
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

© International Association for Cryptologic Research 2012

Authors and Affiliations

  • Dimitar Jetchev
    • 1
  • Onur Özen
    • 1
  • Martijn Stam
    • 2
  1. 1.EPFL IC IIF LACALLausanneSwitzerland
  2. 2.Department of Computer ScienceUniversity of BristolBristolUK

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