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Adaptive Pseudo-free Groups and Applications

  • Dario Catalano
  • Dario Fiore
  • Bogdan Warinschi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6632)

Abstract

In this paper we explore a powerful extension of the notion of pseudo-free groups, proposed by Rivest at TCC 2004. We identify, motivate, and study pseudo-freeness in face of adaptive adversaries who may learn solutions to other non-trivial equations before having to solve a new non-trivial equation.

We present a novel, carefully crafted definition of adaptive pseudo-freeness that walks a fine line between being too weak and being unsatisfiable. We show that groups that satisfy our definition yield, via a generic construction, digital and network coding signature schemes.

Finally, we obtain concrete constructions of such schemes in the RSA group by showing this group to be adaptive pseudo-free. In particular, we demonstrate the generality of our framework for signatures by showing that most existing schemes are instantiations of our generic construction.

Keywords

Signature Scheme Random Oracle Univariate Equation Computational Group Digital Signature Scheme 
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 2011

Authors and Affiliations

  • Dario Catalano
    • 1
  • Dario Fiore
    • 2
  • Bogdan Warinschi
    • 3
  1. 1.Dipartimento di Matematica e InformaticaUniversità di CataniaItaly
  2. 2.École Normale SupérieureCNRS - INRIAParisFrance
  3. 3.Dept. Computer ScienceUniversity of BristolUK

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