## Equational cryptographic reasoning in the Maude-NRL Protocol Analyzer (2006)

Venue: | In Proc. of the First International Workshop on Security and Rewriting Techniques (SecReT 2006), Electronic Notes in Theoretical Computer Science. Elsevier Sciences Publisher |

Citations: | 5 - 3 self |

### BibTeX

@INPROCEEDINGS{Escobar06equationalcryptographic,

author = {Santiago Escobar and Joe Hendrix and Catherine Meadows and José Meseguer},

title = {Equational cryptographic reasoning in the Maude-NRL Protocol Analyzer},

booktitle = {In Proc. of the First International Workshop on Security and Rewriting Techniques (SecReT 2006), Electronic Notes in Theoretical Computer Science. Elsevier Sciences Publisher},

year = {2006}

}

### OpenURL

### Abstract

Abstract. The Maude-NRL Protocol Analyzer (Maude-NPA) is a tool and inference system for reasoning about the security of cryptographic protocols in which the cryptosystems satisfy different equational properties. It both extends and provides a formal framework for the original NRL Protocol Analyzer, which limited itself to an equational theory ∆ of convergent rewrite rules. In this paper we extend our framework to include theories of the form ∆ ⊎ B, where B is the theory of associativity and commutativity and ∆ is convergent modulo B. Order-sorted B-unification plays a crucial role; to obtain this functionality we describe a sort propagation algorithm that filters out unsorted B-unifiers provided by the CiME unification tool. We show how extensions of some of the state reduction techniques of the original NRL Protocol Analyzer can be applied in this context. We illustrate the ideas and capabilities of the Maude-NPA with an example involving the Diffie-Hellman key agreement protocol. 1

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Citation Context ...inference system for reasoning about the security of cryptographic protocols in which the cryptosystems satisfy different equational properties. It is the next generation of the NRL Protocol Analyzer =-=[21]-=-, a tool that supported limited equational reasoning and was successfully applied to the analysis of many different protocols. In Maude-NPA we improved on the original NPA in two ways. First of all, i... |

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Citation Context ...the work in this area has concentrated on problems of secrecy and static equivalence in bounded session protocols, which have been proved to be decidable for an important class of equational theories =-=[23,7,1,9,6,12]-=-. For unbounded sessions, however, the problem is less well understood and has been recently studied in [5,4]. In [17] and [7] tree-automata based approximations are applied to associative-commutative... |

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Citation Context ...the work in this area has concentrated on problems of secrecy and static equivalence in bounded session protocols, which have been proved to be decidable for an important class of equational theories =-=[23,7,1,9,6,12]-=-. For unbounded sessions, however, the problem is less well understood and has been recently studied in [5,4]. In [17] and [7] tree-automata based approximations are applied to associative-commutative... |

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Citation Context ...tive-commutative theories such as exponentiation and exclusive-or. Probably the most closely related work to ours in this area is the unification algorithms for exponentiation in Narendan and Meadows =-=[20]-=- and Kapur, Narendran, and Wang [19]. The theory we use in this paper is an order-sorted version of a fragment of the theories for which unification algorithms are developed there. In this work, howev... |

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Citation Context ... corresponding unsorted theories is non-terminating, whereas narrowing with the order-sorted theories does terminate. The current support of order-sorted unification in the Maude-NPA leverages CiME’s =-=[11]-=- rich library of composable unsorted unification algorithms, including any combination of associativity, commutativity and identity axioms (except associativity without commutativity). The Maude-NPA t... |

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Citation Context ...a tool that supported limited equational reasoning and was successfully applied to the analysis of many different protocols. In Maude-NPA we improved on the original NPA in two ways. First of all, in =-=[15]-=- we formalized the inference system of NPA, providing the first formal description of the tool, in terms of rewriting logic and narrowing. We also provided proofs of soundness and completeness. More r... |

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Citation Context ...n proved to be decidable for an important class of equational theories [23,7,1,9,6,12]. For unbounded sessions, however, the problem is less well understood and has been recently studied in [5,4]. In =-=[17]-=- and [7] tree-automata based approximations are applied to associative-commutative theories to develop abstract approximations. These techniques have been implemented in tools (for Diffie-Hellman theo... |

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Citation Context ...ponentiation and exclusive-or. Probably the most closely related work to ours in this area is the unification algorithms for exponentiation in Narendan and Meadows [20] and Kapur, Narendran, and Wang =-=[19]-=-. The theory we use in this paper is an order-sorted version of a fragment of the theories for which unification algorithms are developed there. In this work, however, we use a hybrid approach that we... |

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Citation Context ...have the typing exp : Gen × NeNonceSet → Exp. In particular, exp(W, Y ∗ Z) is a constructor term as claimed. 9The next key observation is that ∆ is confluent, terminating, and coherent modulo B (see =-=[18]-=- for these notions). Coherence modulo B is particularly easy to check, since the associative-commutative multiplication symbol in B does not appear in ∆’s lefthand side exp(exp(W, Y ), Z). We can then... |

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Citation Context ...h have been proved to be decidable for an important class of equational theories [23,7,1,9,6,12]. For unbounded sessions, however, the problem is less well understood and has been recently studied in =-=[5,4]-=-. In [17] and [7] tree-automata based approximations are applied to associative-commutative theories to develop abstract approximations. These techniques have been implemented in tools (for Diffie-Hel... |

1 |
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Citation Context ...m. This is then combined with rewrite theories that are terminating and confluent with respect to the AC theory. Some other work that is closely related to ours is the work of Comon-Lundh and Delaune =-=[10]-=- on the finite variant property, in which techniques are developed for achieving termination even when narrowing by itself does not terminate. Although this paper does not make use of their results, w... |