Results: This paper presents the R/Bioconductor package minet (version 1.1.6) which provides a set of functions to infer mutual information networks from a dataset. Once fed with a microarray dataset, the package returns a network where nodes denote genes, edges model statistical dependencies between genes and the weight of an edge quantifies the statistical evidence of a specific (e.g transcriptional) gene-to-gene interaction. Four different entropy estimators are made available in the package minet (empirical, Miller-Madow, Schurmann-Grassberger and shrink) as well as four different inference methods, namely relevance networks, ARACNE, CLR and MRNET. Also, the package integrates accuracy assessment tools, like F-scores, PR-curves and ROC-curves in order to compare the inferred network with a reference one. Conclusion:The package minet provides a series of tools for inferring transcriptional networks from microarray data. It is freely available from the Comprehensive R Archive Network (CRAN) as well as from the Bioconductor website.

The paper presents MRNET, an original method for inferring genetic networks from microarray data. The method is based on maximum relevance/minimum redundancy (MRMR), an effective information-theoretic technique for feature selection in supervised learning. The MRMR principle consists in selecting among the least redundant variables the ones that have the highest mutual information with the target. MRNET extends this feature selection principle to networks in order to infer gene-dependence relationships from microarray data. The paper assesses MRNET by benchmarking it against RELNET, CLR, and ARACNE, three state-of-the-art information-theoretic methods for large (up to several thousands of genes) network inference. Experimental results on thirty synthetically generated microarray datasets show that MRNET is competitive with these methods.

This paper investigates the power of SAT solvers in cryptanalysis. The contributions are twofold and are relevant to both theory and practice. First, we introduce an efficient, generic and automated method for generating SAT instances encoding a wide range of cryptographic computations. This method can be used to automate the first step of algebraic attacks, i.e. the generation of a system of algebraic equations. Second, we illustrate the limits of SAT solvers when attacking cryptographic algorithms, with the aim of finding weak keys in block ciphers and preimages in hash functions. SAT solvers allowed us to find, or prove the absence of, weak-key classes under both differential and linear attacks of full-round block ciphers based on the International Data Encryption Algorithm (IDEA), namely, WIDEA-n for n ∈ {4, 8}, and MESH-64(8). In summary: (i) we have found several classes of weak keys for WIDEA-n and (ii) proved that a particular class of weak keys does not exist in MESH-64(8). SAT solvers provided answers to two complementary open problems (presented in Fast Software Encryption 2009): the existence and non-existence of such weak keys. Although these problems were supposed to be difficult to answer, SAT solvers provided an efficient solution. We also report on experimental results about the performance of a modern SAT solver as the encoded cryptanalytic tasks become increasingly hard. The tasks correspond to preimage attacks on reduced MD4 algorithm.

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