A Symbolic Characterisation of Open Bisimulation for the Spi Calculus

Open hedged bisimulation was proposed as a generalisation to the spi calculus of the pi calculus'open bisimulation. In this paper, we extend previous work on open hedged bisimulation. We show that open hedged bisimilarity is closed under respectful substitutions and give a symbolic characterisation of open hedged bisimulation. The latter result is an important step towards mechanisation of open hedged bisimilarity

Equivalences and calculi for formal verification of cryptographic protocols

Security protocols are essential to the proper functioning of any distributed system running over an insecure network but often have flaws that can be exploited even without breaking the cryptography. Formal cryptography, the assumption that the cryptographic primitives are flawless, facilitates the construction of formal models and verification tools. Such models are often based on process calculi, small formal languages for modelling communicating systems. The spi calculus, a process calculus for the modelling and formal verification of cryptographic protocols, is an extension of the pi calculus with cryptography. In the spi calculus, security properties can be formulated as equations on process terms, so no external formalism is needed. Moreover, the contextual nature of observational process equivalences takes into account any attacker/environment that can be expressed in the calculus. We set out to address the problem of automatic verification of observational equivalence in an extension of the spi calculus: A channel-passing calculus with a more general expression language. As a first step, we study existing non-contextual proof techniques for a particular canonical contextual equivalence. In contrast to standard process calculi, reasoning on cryptographic processes must take into account the partial knowledge of the environment about transmitted messages. In the setting of the spi calculus, several notions of environment-sensitive bisimulation has been developed to treat this environment knowledge. We exhibit distinguishing examples between several of these notions, including ones previously believed to coincide. We then give a general framework for comparison of environment-sensitive relations, based on a comparison of the corresponding kinds of environment and notions of environment consistency. Within this framework we perform an exhaustive comparison of the different bisimulations, where every possible relation that is not proven is disproven. For the second step, we consider the question of which expression languages are suitable. Extending the expression language to account for more sophisticated cryptographic primitives or other kinds of data terms quickly leads to decidability issues. Two important problems in this area are the knowledge problem and an indistinguishability problem called static equivalence. It is known that decidability of static equivalence implies decidability of knowledge in many cases; we exhibit an expression language where knowledge is decidable but static equivalence is not. We then define a class of constructor-destructor expression languages and prove that environment consistency over any such language directly corresponds to static equivalence in a particular extension thereof. We proceed to place some loose constraints on deterministic expression evaluation, and redefine the spi calculus in this more general setting. Once we have chosen an expression language, we encounter a third problem, which is inherent in the operational semantics of message-passing process calculi: The possibility to receive arbitrary messages gives rise to infinite branching on process input. To mitigate this problem, we define a symbolic semantics, where the substitution of received messages for input variables never takes place. Instead, input variables are only subject to logical constraints. We then use this symbolic semantics to define a symbolic bisimulation that is sound and complete with respect to its concrete counterpart, extending the possibilities for automated bisimulation checkers

A Fully Abstract Symbolic Semantics for Psi-Calculi

We present a symbolic transition system and bisimulation equivalence for psi-calculi, and show that it is fully abstract with respect to bisimulation congruence in the non-symbolic semantics. A psi-calculus is an extension of the pi-calculus with nominal data types for data structures and for logical assertions representing facts about data. These can be transmitted between processes and their names can be statically scoped using the standard pi-calculus mechanism to allow for scope migrations. Psi-calculi can be more general than other proposed extensions of the pi-calculus such as the applied pi-calculus, the spi-calculus, the fusion calculus, or the concurrent constraint pi-calculus. Symbolic semantics are necessary for an efficient implementation of the calculus in automated tools exploring state spaces, and the full abstraction property means the semantics of a process does not change from the original

Theory and tool support for the formal verification of cryptographic protocols

Cryptographic protocols are an essential component of network communications. Despite their relatively small size compared to other distributed algorithms, they are known to be error-prone. This is due to the obligation to behave robustly in the context of unknown hostile attackers who might want to act against the security objectives of the jointly interacting entities. The need for techniques to verify the correctness of cryptographic protocols has stimulated the development of new frameworks and tools during the last decades. Among the various models is the spi calculus: a process calculus which is an extension of the pi calculus that incorporates cryptographic primitives. Process calculi such as the spi calculus offer the possibility to describe in a precise and concise way distributed algorithms such as cryptographic protocols. Moreover, spi calculus offers an elegant way to formalise some security properties of cryptographic protocols via behavioural equivalences. At the time this thesis began, this approach lacked tool support. Inspired by the situation in the pi calculus, we propose a new notion of behavioural equivalence for the spi calculus that is close to an algorithm. Besides, we propose a "coq" formalisation of our results that not only validates our theoretical developments but also will eventually be the basis of a certified tool that would automate equivalence checking of spi calculus terms. To complete the toolchain, we propose a formal semantics for an informal notation to describe cryptographic protocols, so called protocol narrations. We give a rigorous procedure to translate protocol narrations into spi calculus terms; this constitutes the foundations of our automatic translation tool "spyer"

On Bisimulations for the Spi Calculus

The spi calculus is an extension of the pi calculus with cryptographic primitives, designed for the verification of cryptographic protocols. Due to the extension, the naive adaptation of labeled bisimulations for the pi calculus is too strong to be useful for the purpose of verification. Instead, as a viable alternative, several "environment-sensitive" bisimulations have been proposed.In this report we formally study the differences between these bisimulations

Compositional analysis of protocol equivalence in the applied pi-calculus using quasi-open bisimilarity

This paper shows that quasi-open bisimilarity is the coarsest bisimilarity congruence for the applied -calculus. Furthermore, we show that this equivalence is suited to security and privacy problems expressed as an equivalence problem in the following senses: (1) being a bisimilarity is a safe choice since it does not miss attacks based on rich strategies; (2) being a congruence it enables a compositional approach to proving certain equivalence problems such as unlinkability; and (3) being the coarsest such bisimilarity congruence it can establish proofs of some privacy properties where finer equivalences fail to do so

Compositional Analysis of Protocol Equivalence in the Applied pi-Calculus Using Quasi-open Bisimilarity

This paper shows that quasi-open bisimilarity is the coarsest bisimilarity congruence for the applied pi-calculus. Furthermore, we show that this equivalence is suited to security and privacy problems expressed as an equivalence problem in the following senses: (1) being a bisimilarity is a safe choice since it does not miss attacks based on rich strategies; (2) being a congruence it enables a compositional approach to proving certain equivalence problems such as unlinkability; and (3) being the coarsest such bisimilarity congruence it can establish proofs of some privacy properties where finer equivalences fail to do so