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Petri nets with name creation for transient secure association

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Abstract

Transient secure association has been widely accepted as a possible alternative to traditional authentication in the context of Ubiquitous Computing. Two components in a distributed system with transient secure association may share a master-slave relationship, which creates a hierarchical but dynamic structure of components. In this paper we develop several formal models for distributed systems with transient secure association, with incremental expressive power, all based on Petri nets. The first model, that we call transient secure association (TSA) systems, considers finitely many components. Then we consider a small extension of TSA systems, in which slaves are initialized whenever a master-slave relation is broken. Last, we define unbounded TSA (uTSA) systems, for which the number of components is not bounded. For each of the defined formalisms, we establish a link to a known class of Petri nets, thus inheriting the corresponding (un)decidability results from them.

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Notes

  1. Other standard approaches rely on infinite sets of initial states.

  2. Not to be confused with any equivalence or preorder in Van Glabbeek’s spectrum [13].

  3. We call it weak isomorphism even if, as defined, it is not a symmetric relation.

  4. Multiset subtraction is only used in that case in the paper.

  5. We define it in this way to follow our generic definition of Petri nets, though it is clearly equivalent to the definition using total functions to \(\mathbb {N}\).

  6. Actually, home space is only decidable for linear sets of final markings, as is the case of the set of final markings of our example.

  7. Without that assumption, we just need to define \(init(N_i)\) accordingly.

  8. Other “creating” policies can be envisaged, as creating components that are initially imprinted by the creating one.

  9. Actually, we could add some control states that sequentialize the simulating net so that, in particular, no other transition can be fired during the simulation of a killing. We have preferred not to do so for simplicity of our construction.

  10. This class was called asynchronous \(\nu \)-PN in [18].

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Acknowledgments

The author would like to thank the anonymous referees for their valuable comments, that have increased the quality of this paper. This work is partially supported by the Spanish projects DESAFIOS10 TIN2009-14599-C03-01, STRONGSOFT TIN2012-39391-C04-04 and the Comunidad de Madrid program PROMETIDOS S2009/TIC-1465.

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  1. Facultad de Informática, Universidad Complutense de Madrid, C/Prof. José García Santesmases, 9, 28040 , Madrid, Spain

    Fernando Rosa-Velardo

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Rosa-Velardo, F. Petri nets with name creation for transient secure association. Acta Informatica 50, 403–436 (2013). https://doi.org/10.1007/s00236-013-0188-0

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