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Archive : Discrete Mathematics

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Lauren De Meyer, University of Leuven, BelgiumLauren De Meyer, University of Leuven, BelgiumEWG 336<br><br>Title: Classification of Balanced Quadratic Functions <br><br> Abstract: S-boxes, typically the only nonlinear part of a block cipher, are the heart of symmetric cryptographic primitives. They significantly impact the cryptographic strength and the implementation characteristics of an algorithm. Due to their simplicity, quadratic vectorial Boolean functions are preferred when efficient implementations for a variety of applications are of concern. Many characteristics of a function stay invariant under affine equivalence. So far, all 6-bit Boolean functions, 3- and 4-bit permutations and 5-bit quadratic permutations have been classified up to affine equivalence. In this work, we propose a highly efficient algorithm to classify n × m functions for n ≥ m. Our algorithm enables for the first time a complete classification of 6-bit quadratic permutations as well as all balanced quadratic functions for n ≤ 6. These functions can be valuable for new cryptographic algorithm designs with efficient multi-party computation or side-channel analysis resistance as goal. In addition, we provide a second tool for finding decompositions of length two. We demonstrate its use by decomposing existing higher degree S-boxes and constructing new S-boxes with good cryptographic and implementation properties.12/3/2018 7:00:00 PM12/3/2018 8:00:00 PMFalse
Morgan Rodgers, California State University, Fresno Morgan Rodgers, California State University, FresnoEWG 336<br><br>Title: Intriguing sets in distance regular graphs. <br><br> To view the abstract click here: <a href=""> View Abstract</a>11/26/2018 7:00:00 PM11/26/2018 8:00:00 PMFalse
Dr. G. Eric Moorhouse, University of WyomingDr. G. Eric Moorhouse, University of WyomingEWG 336<br><br>Title: Double Covers <br><br> Abstract: Double covers appear in a variety of contexts, in topology, graph theory, group theory, geometry and association schemes. While higher index covers (r-fold covers for arbitrary positive r) are generally important, double covers play a distinguished role; for example double covers are necessarily Galois covers, a fact that does not hold for higher index r. In some instances, double covers provide interesting constructions of with desirable properties; and in others, they yield isomorphism invariants used in classification and even some nonexistence results. I will survey some of these settings in which double covers have played a particularly useful role.11/12/2018 7:00:00 PM11/12/2018 8:00:00 PMFalse
Dr. Peter Sin, University of FloridaDr. Peter Sin, University of FloridaEWG 336<br><br>Title: Spreads, Ovoids, Opposites and Irreducible Group Representations <br><br> Abstract: A spread in a polar space is set of disjoint generators (maximal totally isotropic subspaces) that cover the set of points. Dually, an ovoid is set of points such that each generator contains exactly one point from the set. These definitions can be extended to Generalized Polygons, using the concept of oppositeness. I will discuss recent work (with Ihringer and Xiang) on the bounds from representation theory on the size of a partial spreads and partial ovoids. In particular, we show that ovoids cannot exist in the finite Tits octagon.11/5/2018 7:00:00 PM11/5/2018 8:00:00 PMFalse

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