We present a framework suited to the analysis of cryptographic protocols that make use of time in their execution. We provide a process algebra syntax that makes time information available to processes, and a transition semantics that takes account of fundamental properties of time. Additional properties can be added by the user if desirable. This timed protocol framework can be implemented either as a simulation tool or as a symbolic analysis tool in which time references are represented by logical variables, and in which the properties of time are implemented as constraints on those time logical variables. These constraints are carried along the symbolic execution of the protocol. The satisfiability of these constraints can be evaluated as the analysis proceeds, so attacks that violate the laws of physics can be rejected as impossible. We demonstrate the feasibility of our approach by using the Maude-NPA protocol analyzer together with an SMT solver that is used to evaluate the satisfiability of timing constraints. We provide a sound and complete protocol transformation from our timed process algebra to the Maude-NPA syntax and semantics, and we prove its soundness and completeness. We then use the tool to analyze Mafia fraud and distance hijacking attacks on a suite of distance-bounding protocols.

In this paper, we perform an automated analysis of two devices developed by Yubico: YubiKey, designed to authenticate a user to network-based services, and YubiHSM, Yubico's hardware security module. Both are analyzed using the Maude-NPA cryptographic protocol analyzer. Although previous work has been done applying automated tools to these devices, to the best of our knowledge there has been no completely automated analysis to date. This is not surprising, because both YubiKey and YubiHSM, which make use of cryptographic APIs, involve a number of complex features: (i) discrete time in the form of Lamport clocks, (ii) a mutable memory for storing previously seen keys or nonces, (iii) event-based properties that require an analysis of sequences of actions, and (iv) reasoning modulo exclusive-or. In this work, we have been able to both prove properties of YubiKey and find the known attacks on the YubiHSM, in a completely automated way beyond the capabilities of previous work in the literature.

Equational unification of two terms consists of finding a substitution that, when applied to both terms, makes them equal modulo some equational properties. A narrowing-based equational unification algorithm relying on the concept of the variants of a term is available in the most recent version of Maude, version 3.0, which provides quite sophisticated unification features. A variant of a term t is a pair consisting of a substitution σ and the canonical form of tσ . Variant-based unification is decidable when the equational theory satisfies the finite variant property. However, this unification procedure does not take into account constructor symbols and, thus, may compute many more unifiers than the necessary or may not be able to stop immediately. In this paper, we integrate the notion of constructor symbol into the variant-based unification algorithm. Our experiments on positive and negative unification problems show an impressive speedup.

Maude-NPA is an analysis tool for cryptographic security protocols that takes into account the algebraic properties of the cryptosystem. Maude-NPA can reason about a wide range of cryptographic properties. However, some algebraic properties, and protocols using them, have been beyond Maude-NPA capabilities, either because the cryptographic properties cannot be expressed using its equational unification features or because the state space is unmanageable. In this paper, we provide a protocol transformation that can safely get rid of cryptographic properties under some conditions. The time and space difference between verifying the protocol with all the crypto properties and verifying the protocol with a minimal set of the crypto properties is remarkable. We also provide, for the first time, an encoding of the theory of bilinear pairing into Maude-NPA that goes beyond the encoding of bilinear pairing available in the Tamarin tool.

We present a framework suited to the analysis of cryptographic protocols that make use of time in their execution. We provide a process algebra syntax that makes time information available to processes, and a transition semantics that takes account of fundamental properties of time. Additional properties can be added by the user if desirable. This timed protocol framework can be implemented either as a simulation tool or as a symbolic analysis tool in which time references are represented by logical variables, and in which the properties of time are implemented as constraints on those time logical variables. These constraints are carried along the symbolic execution of the protocol. The satisfiability of these constraints can be evaluated as the analysis proceeds, so attacks that violate the laws of physics can be rejected as impossible. We demonstrate the feasibility of our approach by using the Maude-NPA protocol analyzer together with an SMT solver that is used to evaluate the satisfiability of timing constraints. We provide a sound and complete protocol transformation from our timed process algebra to the Maude-NPA syntax and semantics, and we prove its soundness and completeness. We then use the tool to analyze Mafia fraud and distance hijacking attacks on a suite of distance-bounding protocols.