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Southwest Jiaotong University School of Mathematics

信息与计算科学系

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挪威科学院院士Tor Helleseth教授学术报告

来源:   作者:数学与信息交叉团队     日期:2019-10-28 21:52:20   点击数:  

挪威科学院院士Tor Helleseth教授学术报告

数学与信息交叉前沿系列讲座

报告时间:30 October 20193:00-4:00pm

报告地点:Room X7503#

主持人(Chair) 周正春教授

报告题目: Quadrinomial APN functions

Abstract:

An almost perfect nonlinear (APN) function f(x) is a mapping from the finite field GF(2n) with 2n elements to itself that has the property that f(x+a) + f(a) = b has at most 2 solutions x for any nonzero a and any b in the finite field. APN functions have many applications in cryptography to construct optimal S-boxes, in coding theory to construct optimal error-correcting codes, and in discrete mathematics. Many basic constructions of APN functions are known but there are still many open and challenging problems.

This talk will provide an introduction and an overview over known results of APN functions as well as some recent new constructions of infinite classes of APN functions. These are generalisations of sporadic binomial APN functions constructed by Edel and pott in 2006. An open question has been to generalise these to an infinite family. We present a generalisation to quadrinomial APN functions. Some of the remaining open problems in this area will also be discussed.

Speaker’s Short Biography

Tor Helleseth教授是挪威科学院院士,Bergen大学终身教授,IEEE Fellow,中国外国专家局“高端外国专家项目”特聘专家,信息科学领域的国际著名学者,一直致力于基础理论和应用研究,在编码理论、信息安全、组合数学等领域都做出了开创性和奠基性的工作。