A Survey of Symbolic Methods in Computational Analysis of Cryptographic Systems

Since the 1980s, two approaches have been developed for analyzing security protocols. One of the approaches relies on a computational model that considers issues of complexity and probability. This approach captures a strong notion of security, guaranteed against all probabilistic polynomial-time attacks. The other approach relies on a symbolic model of protocol executions in which cryptographic primitives are treated as black boxes. Since the seminal work of Dolev and Yao, it has been realized that this latter approach enables significantly simpler and often automated proofs. However, the guarantees that it offers have been quite unclear. For more than twenty years the two approaches have coexisted but evolved mostly independently. Recently, significant research efforts attempt to develop paradigms for cryptographic systems analysis that combines the best of both worlds. There are two broad directions that have been followed. {\em Computational soundness} aims to establish sufficient conditions under which results obtained using symbolic models imply security under computational models. The {\em direct approach} aims to apply the principles and the techniques developed in the context of symbolic models directly to computational ones. In this paper we survey existing results along both of these directions. Our goal is to provide a rather complete summary that could act as a quick reference for researchers who want to contribute to the field, want to make use of existing results, or just want to get a better picture of what results already exist

How to prove security of communication protocols? A discussion on the soundness of formal models w.r.t. computational ones.

Security protocols are short programs that aim at securing communication over a public network. Their design is known to be error-prone with flaws found years later. That is why they deserve a careful security analysis, with rigorous proofs. Two main lines of research have been (independently) developed to analyse the security of protocols. On the one hand, formal methods provide with symbolic models and often automatic proofs. On the other hand, cryptographic models propose a tighter modeling but proofs are more difficult to write and to check. An approach developed during the last decade consists in bridging the two approaches, showing that symbolic models are sound w.r.t. symbolic ones, yielding strong security guarantees using automatic tools. These results have been developed for several cryptographic primitives (e.g. symmetric and asymmetric encryption, signatures, hash) and security properties. While proving soundness of symbolic models is a very promising approach, several technical details are often not satisfactory. Focusing on symmetric encryption, we describe the difficulties and limitations of the available results

Symbolic Analysis of Identity-Based Protocols

International audienceWe show how the Tamarin tool can be used to model and reason about security protocols using identity-based cryptography, including identity-based encryption and signatures. Although such protocols involve rather different primitives than conventional public-key cryptography , we illustrate how suitable abstractions and Tamarin's support for equational theories can be used to model and analyze realistic industry protocols, either finding flaws or gaining confidence in their security with respect to different classes of adversaries. Technically, we propose two models of identity-based cryptography. First, we formalize an abstract model, based on simple equations, in which verification of realistic protocols is feasible. Second, we formalize a more precise model, leveraging Tamarin's support for bilinear pairing and exclusive-or. This model is much closer to practical realizations of identity-based cryptography, but deduction is substantially more complex. Along the way, we point out the limits of precise modeling and highlight challenges in providing support for equational reasoning. We evaluate our models on an industrial protocol case study, where we find and fix flaws

Unifying Simulatability Definitions in Cryptographic Systems under Different Timing Assumptions

AbstractThe cryptographic concept of simulatability has become a salient technique for faithfully analyzing and proving security properties of arbitrary cryptographic protocols. We investigate the relationship between simulatability in synchronous and asynchronous frameworks by means of the formal models of Pfitzmann et al., which are seminal in using this concept in order to bridge the gap between the formal-methods and the cryptographic community. We show that the synchronous model can be seen as a special case of the asynchronous one with respect to simulatability, i.e., we present an embedding from the synchronous model into the asynchronous one that we show to preserve simulatability. We show that this result allows for carrying over lemmas and theorems that rely on simulatability from the asynchronous model to its synchronous counterpart without any additional work, hence future work on enhancing simulatability-based models can concentrate on the more general asynchronous case

Real-or-Random Key Secrecy of the Otway-Rees Protocol via a Symbolic Security Proof

AbstractWe present the first cryptographically sound security proof of the well-known Otway-Rees protocol. More precisely, we show that the protocol is secure against arbitrary active attacks including concurrent protocol runs if it is implemented using provably secure cryptographic primitives. We prove secrecy of the exchanged keys with respect to the accepted cryptographic definition of real-or-random secrecy, i.e., indistinguishability of exchanged keys and random ones, given the view of a general cryptographic attacker. Although we achieve security under cryptographic definitions, our proof is performed in a deterministic setting corresponding to a slightly extended Dolev-Yao model; in particular, it does not have to deal with probabilistic aspects of cryptography and is hence in the scope of current proof tools. The reason is that we exploit a recently proposed ideal cryptographic library, which has a provably secure cryptographic implementation, as well as recent results on linking symbolic and cryptographic key secrecy. Besides establishing the cryptographic security of the Otway-Rees protocol, our result also exemplifies the potential of this cryptographic library and the recent secrecy preservation theorem for symbolic yet cryptographically sound proofs of security