Tree automata with one memory set constraints and cryptographic protocols

  • Authors:
  • Hubert Comon;Véronique Cortier

  • Affiliations:
  • Department of Computer Science, Gates 4B, Stanford University, CA and Laboratoire Spécification et Vérification, CNRS and Ecole Normale Supérieure de Cachan, 61 Avenue du Prési ...;Laboratoire Spécification et Vérification, CNRS and Ecole Normale Supérieure de Cachan, 61 Avenue du Président Wilson, 94235 Cachan cedex, France

  • Venue:
  • Theoretical Computer Science - Automata, languages and programming
  • Year:
  • 2005

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Abstract

We introduce a class of tree automata that perform tests on a memory that is updated using function symbol application and projection. The language emptiness problem for this class of tree automata is shown to be in DEXPTIME.We also introduce a class of set constraints with equality tests and prove its decidability by completion techniques and a reduction to tree automata with one memory.Finally, we show how to apply these results to cryptographic protocols. We introduce a class of cryptographic protocols and show the decidability of secrecy for an arbitrary number of agents and an arbitrary number of (concurrent or successive) sessions, provided that only a bounded number of new data is generated. The hypothesis on the protocol (a restricted copying ability) is shown to be necessary: without this hypothesis, we prove that secrecy is undecidable, even for protocols without nonces.