Sonia Santiago

State space reduction in the Maude-NRL Protocol Analyzer

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 supported equational reasoning in a more limited way. Maude-NPA supports a wide variety of algebraic properties that includes many crypto-systems of interest such as, for example, one-time pads and Diffie-Hellman. Maude-NPA, like the original NPA, looks for attacks by searching backwards from an insecure attack state, and assumes an unbounded number of sessions. Because of the unbounded number of sessions and the support for different equational theories, it is necessary to develop ways of reducing the search space and avoiding infinite search paths. In order for the techniques to prove useful, they need not only to speed up the search, but should not violate completeness, so that failure to find attacks still guarantees security. In this paper we describe some state space reduction techniques that we have implemented in Maude-NPA. We also provide completeness proofs, and experimental evaluations of their effect on the performance of Maude-NPA.

A Formal Definition of Protocol Indistinguishability and Its Verification Using Maude-NPA

Intuitively, two protocols \({\mathcal P}_1\) and \({\mathcal P}_2\) are indistinguishable if an attacker cannot tell the difference between interactions with \({\mathcal P}_1\) and with \({\mathcal P}_2\). In this paper we: (i) propose an intuitive notion of indistinguishability in Maude-NPA; (ii) formalize such a notion in terms of state unreachability conditions on their synchronous product; (iii) prove theorems showing how —assuming the protocol’s algebraic theory has a finite variant (FV) decomposition– these conditions can be checked by the Maude-NPA tool; and (iv) illustrate our approach with concrete examples. This provides for the first time a framework for automatic analysis of indistinguishability modulo as wide a class of algebraic properties as FV, which includes many associative-commutative theories of interest to cryptographic protocol analysis.

Effective Symbolic Protocol Analysis via Equational Irreducibility Conditions

We address a problem that arises in cryptographic protocol analysis when the equational properties of the cryptosystem are taken into account: in many situations it is necessary to guarantee that certain terms generated during a state exploration are in normal form with respect to the equational theory. We give a tool-independent methodology for state exploration, based on unification and narrowing, that generates states that obey these irreducibility constraints, called contextual symbolic reachability analysis, prove its soundness and completeness, and describe its implementation in the Maude-NPA protocol analysis tool. Contextual symbolic reachability analysis also introduces a new type of unification mechanism, which we call asymmetric unification, in which any solution must leave the right side of the solution irreducible. We also present experiments showing the effectiveness of our methodology.

Sequential protocol composition in maude-NPA

Protocols do not work alone, but together, one protocol relying on another to provide needed services. Many of the problems in cryptographic protocols arise when such composition is done incorrectly or is not well understood. In this paper we discuss an extension to the Maude-NPA syntax and operational semantics to support dynamic sequential composition of protocols, so that protocols can be specified separately and composed when desired. This allows one to reason about many different compositions with minimal changes to the specification. Moreover, we show that, by a simple protocol transformation, we are able to analyze and verify this dynamic composition in the current Maude-NPA tool. We prove soundness and completeness of the protocol transformation with respect to the extended operational semantics, and illustrate our results on some examples.

Asymmetric unification: a new unification paradigm for cryptographic protocol analysis

We present a new paradigm for unification arising out of a technique commonly used in cryptographic protocol analysis tools that employ unification modulo equational theories. This paradigm relies on: (i) a decomposition of an equational theory into (R,E) where R is confluent, terminating, and coherent modulo E, and (ii) on reducing unification problems to a set of problems

A Graphical User Interface for Maude-NPA

s =_{}^{?} t

A rewriting-based forwards semantics for Maude-NPA

under the constraint that t remains R/E-irreducible. We call this method asymmetric unification. We first present a general-purpose generic asymmetric unification algorithm. and then outline an approach for converting special-purpose conventional unification algorithms to asymmetric ones, demonstrating it for exclusive-or with uninterpreted function symbols. We demonstrate how asymmetric unification can improve performanceby running the algorithm on a set of benchmark problems. We also give results on the complexity and decidability of asymmetric unification.

Analysis of the IBM CCA Security API Protocols in Maude-NPA

This paper presents a graphical user interface (GUI) for the Maude-NPA, a crypto protocol analysis tool that takes into account algebraic properties of cryptosystems not supported by other tools, such as cancellation of encryption and decryption, Abelian groups (including exclusive or), and modular exponentiation. Maude-NPA has a theoretical basis in rewriting logic, unification and narrowing, and performs backwards search from a final attack state to determine whether or not it is reachable from an initial state. The GUI animates the Maude-NPA verification process, displaying the complete search tree and allowing users to display graphical representations of final and intermediate nodes of the search tree. One of the most interesting points of this work is that our GUI has been developed using the framework for declarative graphical interaction associated to Maude that includes IOP, IMaude and JLambda. This framework facilitates the interaction and the interoperation between formal reasoning tools (Maude-NPA in our case) and allows Maude to communicate easily with other tools.

Strand spaces with choice via a process algebra semantics

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.

Analysis of the PKCS#11 API Using the Maude-NPA Tool

Standards for cryptographic protocols have long been attractive candidates for formal verification. It is important that such standards be correct, and cryptographic protocols are tricky to design and subject to non-intuitive attacks even when the underlying cryptosystems are secure. Thus a number of general-purpose cryptographic protocol analysis tools have been developed and applied to protocol standards. However, there is one class of standards, security application programming interfaces (security APIs), to which few of these tools have been applied. Instead, most work has concentrated on developing special-purpose tools and algorithms for specific classes of security APIs. However, there can be much advantage gained from having general-purpose tools that could be applied to a wide class of problems, including security APIs.