A Spatial-Epistemic Logic for Reasoning about Security Protocols

Reasoning about security properties involves reasoning about where the information of a system is located, and how it evolves over time. While most security analysis techniques need to cope with some notions of information locality and knowledge propagation, usually they do not provide a general language for expressing arbitrary properties involving local knowledge and knowledge transfer. Building on this observation, we introduce a framework for security protocol analysis based on dynamic spatial logic specifications. Our computational model is a variant of existing pi-calculi, while specifications are expressed in a dynamic spatial logic extended with an epistemic operator. We present the syntax and semantics of the model and logic, and discuss the expressiveness of the approach, showing it complete for passive attackers. We also prove that generic Dolev-Yao attackers may be mechanically determined for any deterministic finite protocol, and discuss how this result may be used to reason about security properties of open systems. We also present a model-checking algorithm for our logic, which has been implemented as an extension to the SLMC system.Comment: In Proceedings SecCo 2010, arXiv:1102.516

Closed nominal rewriting and efficiently computable nominal algebra equality

We analyse the relationship between nominal algebra and nominal rewriting, giving a new and concise presentation of equational deduction in nominal theories. With some new results, we characterise a subclass of equational theories for which nominal rewriting provides a complete procedure to check nominal algebra equality. This subclass includes specifications of the lambda-calculus and first-order logic.Comment: In Proceedings LFMTP 2010, arXiv:1009.218

Computing Knowledge in Equational Extensions of Subterm Convergent Theories

International audienceWe study decision procedures for two knowledge problems critical to the verification of security protocols, namely the intruder deduction and the static equivalence problems. These problems can be related to particular forms of context matching and context unification. Both problems are defined with respect to an equational theory and are known to be decidable when the equational theory is given by a subterm convergent term rewrite system. In this work we extend this to consider a subterm convergent term rewrite system defined modulo an equational theory, like Commutativity. We present two pairs of solutions for these important problems. The first solves the deduction and static equivalence problems in systems modulo shallow theories such as Commutativity. The second provides a general procedure that solves the deduction and static equivalence problems in subterm convergent systems modulo syntactic permutative theories, provided a finite measure is ensured. Several examples of such theories are also given

A theory of normed simulations

In existing simulation proof techniques, a single step in a lower-level specification may be simulated by an extended execution fragment in a higher-level one. As a result, it is cumbersome to mechanize these techniques using general purpose theorem provers. Moreover, it is undecidable whether a given relation is a simulation, even if tautology checking is decidable for the underlying specification logic. This paper introduces various types of normed simulations. In a normed simulation, each step in a lower-level specification can be simulated by at most one step in the higher-level one, for any related pair of states. In earlier work we demonstrated that normed simulations are quite useful as a vehicle for the formalization of refinement proofs via theorem provers. Here we show that normed simulations also have pleasant theoretical properties: (1) under some reasonable assumptions, it is decidable whether a given relation is a normed forward simulation, provided tautology checking is decidable for the underlying logic; (2) at the semantic level, normed forward and backward simulations together form a complete proof method for establishing behavior inclusion, provided that the higher-level specification has finite invisible nondeterminism.Comment: 31 pages, 10figure

New Equations for Neutral Terms: A Sound and Complete Decision Procedure, Formalized

The definitional equality of an intensional type theory is its test of type compatibility. Today's systems rely on ordinary evaluation semantics to compare expressions in types, frustrating users with type errors arising when evaluation fails to identify two `obviously' equal terms. If only the machine could decide a richer theory! We propose a way to decide theories which supplement evaluation with `$\nu$-rules', rearranging the neutral parts of normal forms, and report a successful initial experiment. We study a simple -calculus with primitive fold, map and append operations on lists and develop in Agda a sound and complete decision procedure for an equational theory enriched with monoid, functor and fusion laws

Computation of distances for regular and context-free probabilistic languages

Several mathematical distances between probabilistic languages have been investigated in the literature, motivated by applications in language modeling, computational biology, syntactic pattern matching and machine learning. In most cases, only pairs of probabilistic regular languages were considered. In this paper we extend the previous results to pairs of languages generated by a probabilistic context-free grammar and a probabilistic finite automaton.PostprintPeer reviewe

Verification of Agent-Based Artifact Systems

Artifact systems are a novel paradigm for specifying and implementing business processes described in terms of interacting modules called artifacts. Artifacts consist of data and lifecycles, accounting respectively for the relational structure of the artifacts' states and their possible evolutions over time. In this paper we put forward artifact-centric multi-agent systems, a novel formalisation of artifact systems in the context of multi-agent systems operating on them. Differently from the usual process-based models of services, the semantics we give explicitly accounts for the data structures on which artifact systems are defined. We study the model checking problem for artifact-centric multi-agent systems against specifications written in a quantified version of temporal-epistemic logic expressing the knowledge of the agents in the exchange. We begin by noting that the problem is undecidable in general. We then identify two noteworthy restrictions, one syntactical and one semantical, that enable us to find bisimilar finite abstractions and therefore reduce the model checking problem to the instance on finite models. Under these assumptions we show that the model checking problem for these systems is EXPSPACE-complete. We then introduce artifact-centric programs, compact and declarative representations of the programs governing both the artifact system and the agents. We show that, while these in principle generate infinite-state systems, under natural conditions their verification problem can be solved on finite abstractions that can be effectively computed from the programs. Finally we exemplify the theoretical results of the paper through a mainstream procurement scenario from the artifact systems literature

Automating Security Analysis: Symbolic Equivalence of Constraint Systems

We consider security properties of cryptographic protocols, that are either trace properties (such as confidentiality or authenticity) or equivalence properties (such as anonymity or strong secrecy). Infinite sets of possible traces are symbolically represented using deducibility constraints. We give a new algorithm that decides the trace equivalence for the traces that are represented using such constraints, in the case of signatures, symmetric and asymmetric encryptions. Our algorithm is implemented and performs well on typical benchmarks. This is the first implemented algorithm, deciding symbolic trace equivalence

Type Safety of Rewrite Rules in Dependent Types

The expressiveness of dependent type theory can be extended by identifying types modulo some additional computation rules. But, for preserving the decidability of type-checking or the logical consistency of the system, one must make sure that those user-defined rewriting rules preserve typing. In this paper, we give a new method to check that property using Knuth-Bendix completion