Adaptive Pseudo-free Groups and Applications

  • Dario Catalano
  • Dario Fiore
  • Bogdan Warinschi
Conference paper

DOI: 10.1007/978-3-642-20465-4_13

Volume 6632 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Catalano D., Fiore D., Warinschi B. (2011) Adaptive Pseudo-free Groups and Applications. In: Paterson K.G. (eds) Advances in Cryptology – EUROCRYPT 2011. EUROCRYPT 2011. Lecture Notes in Computer Science, vol 6632. Springer, Berlin, Heidelberg

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.

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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