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报告题目: On Perfect Nonlinear Functions
演讲人： Professor Ling San
Nanyang Technological University
时间： 2008年5月21日（星期三）下午3：00-4：00
地点： 闵行校区教4-303
摘 要
Interest in highly nonlinear functions arises from applications in cryptography, coding theory and sequences. There are at least two ways of defining and measuring the nonlinearity of a function f from an abelian group (A,+) to another abelian group (B,+), one of which is the following: the nonlinearity P_f of f is defined by
P_f= max_{0\neq a in A}max_{b in B}|{x: x in A, f(x+a)-f(x)=b}|/|A|.
The smaller the value of P_f, the higher the corresponding nonlinearity of f. Clearly, P_f\geq 1/|B|. A function f from A to B is called a perfect nonlinear function if P_f=1/|B|. In particular, a function f: A B is a perfect nonlinear function if and only if for every a in A\{0} and every b in B, we have |{x: x in A, f(x+a)-f(x)=b}| =|A|/|B|.
In this talk, we will attempt to give a brief survey of what is known about perfect nonlinear functions, including some recent developments that further strengthen their links with number theory. If time permits, we shall also give an example of possible applications of perfect nonlinear functions.
主讲人简介：Ling San (林杉)，新加坡南洋理工大学（Nanyang Technological University）数学系教授，Chairman of the School of Physical and Mathematical Sciences。1990年美国加州大学贝克莱分校获博士学位。1992年起在国立新加坡大学(National University of Singapore)、南洋理工大学任教。主要研究密码学与编码理论，已发表论文64篇，出版专著2部。
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