关键词: 有限域, 逻辑函数, 广义bent函数, 完全非线性函数

Abstract:

A weak definition of generalized bent function over finite fields is presented. And then the relation between Perfect nonlinear functions and generalized bent functions is studied. We prove that a q-ary logic function over （ ）is a perfect nonlinear function iff is a generalized bent function for each non-zero element in . The difference between several versions of generalized bent function’s definitions over finite fields is discussed. Relations between spectrum of and that of its component functions are also presented. Furthermore we prove that is nonlinear perfect function over iff its component function is - dimension vector generalized bent function.

Key words: finite fields, logical function, generalized bent function, perfect nonlinear function