Biblio

Recent advances in the automated analysis of cryptographic protocols have aroused new interest in the practical application of unification modulo theories, especially theories that describe the algebraic properties of cryptosystems. However, this application requires unification algorithms that can be easily implemented and easily extended to combinations of different theories of interest. In practice this has meant that most tools use a version of a technique known as variant unification. This requires, among other things, that the theory be decomposable into a set of axioms B and a set of rewrite rules R such that R has the finite variant property with respect to B. Most theories that arise in cryptographic protocols have decompositions suitable for variant unification, but there is one major exception: the theory that describes encryption that is homomorphic over an Abelian group.

In this paper we address this problem by studying various approximations of homomorphic encryption over an Abelian group. We construct a hierarchy of increasingly richer theories, taking advantage of new results that allow us to automatically verify that their decompositions have the finite variant property. This new verification procedure also allows us to construct a rough metric of the complexity of a theory with respect to variant unification, or variant complexity. We specify different versions of protocols using the different theories, and analyze them in the Maude-NPA cryptographic protocol analysis tool to assess their behavior. This gives us greater understanding of how the theories behave in actual application, and suggests possible techniques for improving performance.

The Maude-NRL Protocol Analyzer (Maude-NPA) is a tool for reasoning about the security of cryptographic protocols in which the cryptosystems satisfy different equational properties. It tries to find secrecy or authentication attacks by searching backwards from an insecure attack state pattern that may contain logical variables, in such a way that logical variables become properly instantiated in order to find an initial state. The execution mechanism for this logical reachability is narrowing modulo an equational theory. Although Maude-NPA also possesses a forwards semantics naturally derivable from the backwards semantics, it is not suitable for state space exploration or protocol simulation.

In this paper we define an executable forwards semantics for Maude-NPA, instead of its usual backwards one, and restrict it to the case of concrete states, that is, to terms without logical variables. This case corresponds to standard rewriting modulo an equational theory. We prove soundness and completeness of the backwards narrowing-based semantics with respect to the rewriting-based forwards semantics. We show its effectiveness as an analysis method that complements the backwards analysis with new prototyping, simulation, and explicit-state model checking features by providing some experimental results.

The Maude-NRL Protocol Analyzer (Maude-NPA) is a tool for reasoning about the security of cryptographic protocols in which the cryptosystems satisfy different equational properties. It tries to find secrecy or authentication attacks by searching backwards from an insecure attack state pattern that may contain logical variables, in such a way that logical variables become properly instantiated in order to find an initial state. The execution mechanism for this logical reachability is narrowing modulo an equational theory. Although Maude-NPA also possesses a forwards semantics naturally derivable from the backwards semantics, it is not suitable for state space exploration or protocol simulation. In this paper we define an executable forwards semantics for Maude-NPA, instead of its usual backwards one, and restrict it to the case of concrete states, that is, to terms without logical variables. This case corresponds to standard rewriting modulo an equational theory. We prove soundness and completeness of the backwards narrowing-based semantics with respect to the rewriting-based forwards semantics. We show its effectiveness as an analysis method that complements the backwards analysis with new prototyping, simulation, and explicit-state model checking features by providing some experimental results.