环Z2l上广义Bent函数的稳定性

文献「４」为研究密钥流序列的线性复杂度稳定性和使一些流密码能抗ＢＡＡ（最佳仿射逼近）攻击，提出Ｂｅｎｔ函数稳定性概念，文献「７」研究了素域Ｚｐ上广义Ｂｅｎｔ函数的稳定性及其构造，并指出当ｍ是合数时，ｍ值广义Ｂｅｎｔ函数并不都有稳定性，本文进一步在环Ｚ２＾ｌ（ｌ〉１）上提出了广义Ｂｅｎｔ函数稳定性的概念，综合应用谱、概率和代数数论的方法考察了稳定的概率意义，给出了稳定函数的概率判别条件，提供了构造稳

THE STABILITY OF GENERALIZED BENT FUNCTIONS OVER Z2l

Ding and Xiao 4] showed the stability of bent functions on purpose to study the stability of linear complexity of key sequences and to make stream ciphers against BAA(the best affine approximation).Wang et al.7] discussed the stability of generalized bent functions over Zp (p prime) and pointed out m-ary generalized bent funcitons are not always stable when m is a composite integer.This paper introduces the concept of stability of generalized bent functions over Z2l(l>1) and examines probability characterization of "stability" with the method of spectrum,probability and algebraic number theory.Probability criterion and a typical construction method of these stable functions are presented.The stability of generalized bent functions over Zpl(p prime) can be investigated in the same manner.