A Bayesian model is based on a pair of probability distributions, known as the prior and sampling distributions. A wide range of fundamental machine learning tasks, including regression, classification, clustering, and many others, can all be seen as Bayesian models. We propose a new probabilistic programming abstraction, a typed Bayesian model, which is based on a pair of probabilistic expressions for the prior and sampling distributions. A sampler for a model is an algorithm to compute synthetic data from its sampling distribution, while a learner for a model is an algorithm for probabilistic inference on the model. Models, samplers, and learners form a generic programming pattern for model-based inference. They support the uniform expression of common tasks including model testing, and generic compositions such as mixture models, evidence-based model averaging, and mixtures of experts. A formal semantics supports reasoning about model equivalence and implementation correctness. By developing a series of examples and three learner implementations based on exact inference, factor graphs, and Markov chain Monte Carlo, we demonstrate the broad applicability of this new programming pattern.

We verify cryptographic protocols coded in C for correspondence properties with respect to the computational model of cryptography. The first step uses symbolic execution to extract a process calculus model from a C implementation of the protocol. The new contribution is the second step in which we translate the extracted model to a CryptoVerif protocol description, such that successful verification with CryptoVerif implies the security of the original C implementation. We implement our method and apply it to verify several protocols out of reach of previous work in the symbolic model (using ProVerif), either due to the use of XOR and Diffie-Hellman commitments, or due to the lack of an appropriate computational soundness result. We analyse only a single execution path, so our tool is limited to code following a fixed protocol narration. This is the first security analysis of C code to target a verifier for the computational model. We successfully verify over 3000 LOC. One example (about 1000 LOC) is independently written and currently in testing phase for industrial deployment; during its analysis we uncovered a vulnerability now fixed by its author.

Consider the problem of verifying security properties of a cryptographic protocol coded in C. We propose an automatic solution that needs neither a pre-existing protocol description nor manual annotation of source code. First, symbolically execute the C program to obtain symbolic descriptions for the network messages sent by the protocol. Second, apply algebraic rewriting to obtain a process calculus description. Third, run an existing protocol analyser (ProVerif) to prove security properties or find attacks. We formalise our algorithm and appeal to existing results for ProVerif to establish computational soundness under suitable circumstances. We analyse only a single execution path, so our results are limited to protocols with no significant branching. The results in this paper provide the first computationally sound verification of weak secrecy and authentication for (single execution paths of) C code.