Abstract. We show how to aggressively add uninferred constraints, in a controlled manner, to formulas for finding Van der Waerden numbers during search. We show that doing so can improve the performance of standard SAT solvers on these formulas by orders of magnitude. We obtain a new and much greater lower bound for one of the Van der Waerden numbers, specifically a bound of 1132 for W (2, 6). We believe this bound to actually be the number we seek. The structure of propositional formulas for solving Van der Waerden numbers is similar to that of formulas arising from Bounded Model Checking. Therefore, we view this as a preliminary investigation into solving hard formulas in the area of Formal Verification. 1

Abstract. In classical approaches to knowledge representation, reasoners are assumed to derive all the logical consequences of their knowledge base. As a result, reasoning in the first-order case is only semi-decidable. Even in the restricted case of finite universes of discourse, reasoning remains inherently intractable, as the reasoner has to deal with two independent sources of complexity: unbounded chaining and unbounded quantification. The purpose of this study is to handle these difficulties in a logic-oriented framework based on the paradigm of approximate reasoning. The logic is semantically founded on the notion of resource, an accuracy measure, which controls at the same time the two barriers of complexity. Moreover, a stepwise technique is included for improving approximations. Finally, both sound approximations and complete ones are covered. Based on the logic, we develop an approximation algorithm with a simple modification of classical instance-based theorem provers. The procedure yields approximate proofs whose precision increases as the reasoner has more resources at her disposal. The algorithm is interruptible, improvable, dual, and can be exploited for anytime computation. Moreover, the algorithm is flexible enough to be used with a wide range of propositional satisfiability methods.

Parallel heuristic search algorithms are widely used in artificial intelligence. This paper describes novel parallel variants of two standard sequential search algorithms, the standard Davis Putnam algorithm (DP); and the same algorithm extended with conflict-directed backjumping (CBJ). Encouraging preliminary results for the GpH parallel dialect of the non-strict functional programming language Haskell suggest that modest real speedup can be achieved for the most interesting hard search cases.

Abstract. Algebraic side-channel attacks have been recently introduced as a powerful cryptanalysis technique against block ciphers. These attacks represent both a target algorithm and its physical information leakages as an overdefined system of equations that the adversary tries to solve. They were first applied to PRESENT because of its simple algebraic structure. In this paper, we investigate the extent to which they can be exploited against the AES Rijndael and discuss their practical specificities. We show experimentally that most of the intuitions that hold for PRESENT can also be observed for an unprotected implementation of Rijndael in an 8-bit controller. Namely, algebraic side-channel attacks can recover the AES master key with the observation of a single encrypted plaintext and they easily deal with unknown plaintexts/ciphertexts in this context. Because these attacks can take advantage of the physical information corresponding to all the cipher rounds, they imply that one cannot trade speed for code size (or gate count) without affecting the physical security of a leaking device. In other words, more intermediate computations inevitably leads to more exploitable leakages. We analyze the consequences of this observation on two different masking schemes and discuss its impact on other countermeasures. Our results exhibit that algebraic techniques lead to a new understanding of implementation weaknesses that is different than classical side-channel attacks. 1