Automated Security Proofs with Sequences of Games

This paper presents the first automatic technique for proving not only protocols but also primitives in the exact security computational model. Automatic proofs of cryptographic protocols were up to now reserved to the Dolev-Yao model, which however makes quite strong assumptions on the primitives. On the other hand, with the proofs by reductions, in the complexity theoretic framework, more subtle security assumptions can be considered, but security analyses are manual. A process calculus is thus defined in order to take into account the probabilistic semantics of the computational model. It is already rich enough to describe all the usual security notions of both symmetric and asymmetric cryptography, as well as the basic computational assumptions. As an example, we illustrate the use of the new tool with the proof of a quite famous asymmetric primitive: unforgeability under chosen-message attacks (UF-CMA) of the Full-Domain Hash signature scheme under the (trapdoor)-one-wayness of some permutations

On formal verification of arithmetic-based cryptographic primitives

Cryptographic primitives are fundamental for information security: they are used as basic components for cryptographic protocols or public-key cryptosystems. In many cases, their security proofs consist in showing that they are reducible to computationally hard problems. Those reductions can be subtle and tedious, and thus not easily checkable. On top of the proof assistant Coq, we had implemented in previous work a toolbox for writing and checking game-based security proofs of cryptographic primitives. In this paper we describe its extension with number-theoretic capabilities so that it is now possible to write and check arithmetic-based cryptographic primitives in our toolbox. We illustrate our work by machine checking the game-based proofs of unpredictability of the pseudo-random bit generator of Blum, Blum and Shub, and semantic security of the public-key cryptographic scheme of Goldwasser and Micali.Comment: 13 page

Formally based semi-automatic implementation of an open security protocol

International audienceThis paper presents an experiment in which an implementation of the client side of the SSH Transport Layer Protocol (SSH-TLP) was semi-automatically derived according to a model-driven development paradigm that leverages formal methods in order to obtain high correctness assurance. The approach used in the experiment starts with the formalization of the protocol at an abstract level. This model is then formally proved to fulfill the desired secrecy and authentication properties by using the ProVerif prover. Finally, a sound Java implementation is semi-automatically derived from the verified model using an enhanced version of the Spi2Java framework. The resulting implementation correctly interoperates with third party servers, and its execution time is comparable with that of other manually developed Java SSH-TLP client implementations. This case study demonstrates that the adopted model-driven approach is viable even for a real security protocol, despite the complexity of the models needed in order to achieve an interoperable implementation

Formal Verification of Security Protocol Implementations: A Survey

Automated formal verification of security protocols has been mostly focused on analyzing high-level abstract models which, however, are significantly different from real protocol implementations written in programming languages. Recently, some researchers have started investigating techniques that bring automated formal proofs closer to real implementations. This paper surveys these attempts, focusing on approaches that target the application code that implements protocol logic, rather than the libraries that implement cryptography. According to these approaches, libraries are assumed to correctly implement some models. The aim is to derive formal proofs that, under this assumption, give assurance about the application code that implements the protocol logic. The two main approaches of model extraction and code generation are presented, along with the main techniques adopted for each approac

Formal security proofs with minimal fuss: Implicit computational complexity at work

International audienceWe show how implicit computational complexity can be used in order to increase confidence in game-based security proofs in cryptography. For this purpose we extend CSLR, a probabilistic lambda-calculus with a type system that guarantees the existence of a probabilistic polynomial-time bound on computations. This allows us to define cryptographic constructions, feasible adversaries, security notions, computational assumptions, game transformations, and game-based security proofs in a unified framework. We also show that the standard practice of cryptographers, ignoring that polynomial-time Turing machines cannot generate all uniform distributions, is actually sound. We illustrate our calculus on cryptographic constructions for public-key encryption and pseudorandom bit generation

Computationally Sound Mechanized Proofs for Basic and Public-key Kerberos

We present a computationally sound mechanized analysis of Kerberos 5, both with and without its public-key extension PKINIT. We prove authentication and key secrecy properties using the prover CryptoVerif, which works directly in the computational model; these are the first mechanical proofs of a full industrial protocol at the computational level. We also generalize the notion of key usability and use CryptoVerif to prove that this definition is satisfied by keys in Kerberos

Another Look at Automated Theorem-Proving. II

I continue the discussion initiated in part I of whether or not computer-assisted proofs are a promising approach to preventing errors in reductionist security arguments. I examine some recent papers that describe automated security proofs for hashed ElGamal encryption, Boneh-Franklin identity-based encryption, and OAEP

From Computationally-proved Protocol Specifications to Implementations

International audienceno abstrac

Mechanizing Game-Based Proofs of Security Protocols

Proceedings of the summer school MOD 2011International audienceAfter a short introduction to the field of security protocol verification, we present the automatic protocol verifier CryptoVerif. In contrast to most previous protocol verifiers, CryptoVerif does not rely on the Dolev-Yao model, but on the computational model. It produces proofs presented as sequences of games, like those manually done by cryptographers; these games are formalized in a probabilistic process calculus. CryptoVerif provides a generic method for specifying security properties of the cryptographic primitives. It can prove secrecy and correspondence properties (including authentication). It produces proofs valid for any number of sessions, in the presence of an active adversary. It also provides an explicit formula for the probability of success of an attack against the protocol, as a function of the probability of breaking each primitive and of the number of sessions