学术报告：Bent functions: algebraic constructions from the Desarguesian spread

文章来源： | 发布时间：2016-09-13 | 【字号： 小 中 大 】 |

Title: Bent functions: algebraic constructions from the Desarguesian spread

Speaker: Prof. Sihem Mesnager (University of Paris VIII)

Time: 2016年9月13日，上午10:00-11:30

Address: Room 3224

Abstract:

Boolean functions are important objects in discrete mathematics. They play a role in mathematics and in many domains of computer science. We will be mainly interested in their relationships with error correcting codes and private-key cryptography. The talk is devoted to special families of Boolean functions which are viewed as important objects in combinatorics and the information theory framework (namely, cryptography and coding theory) : the so-called bent functions.

Bent functions are maximally nonlinear Boolean functions. They are wonderful creatures introduced by O. Rothaus in the 1960's and initially studied by J. Dillon since 1974. For their own sake as interesting combinatorial objects, but also for their relations to coding theory (e.g. Reed-Muller codes, Kerdock codes, etc.), combinatorics (e.g. Difference sets), design theory, sequence theory, and applications in cryptography (design of stream ciphers and of S-boxes for block ciphers), they have attracted a lot of research for four decades.

Spreads are important mathematical objects. In this talk we give a survey of the main results in bent functions derived from the Desarguesian spread. Emphasis will be made on bent functions which are constant, linear and affine on elements of the Desarguesian spread.

Sihem Mesnager's Short Bio:

Sihem Mesnager received his PhD from the University of Pierre and Marie Curie (Paris VI). She is currently a professor with Telecom ParisTech and associate professor in Mathematics at University of Paris VIII. Her research interests include cryptography, Boolean functions, coding theory, Commutative algebra and computational algebraic geometry. She has published more 70 papers in international journals and proceedings of international conferences. She also wrote two books on bent functions and error correcting codes, respectively.

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