一种完全非线性函数的构造

J4 ›› 2011, Vol. 46 ›› Issue (3): 26-30.

一种完全非线性函数的构造

郭腓望,张习勇,韩文报

信息工程大学信息工程学院, 河南郑州 450002

收稿日期:2010-09-18 发布日期:2011-04-21
作者简介:郭腓望(1985- ),男,硕士,主要研究方向为密码学.Email:peace-cream@126.com
基金资助:
国家自然科学基金资助项目(60803154)

A construction of perfect nonlinear functions

GUO Fei-wang, ZHANG Xi-yong, HAN Wen-bao

Institute of Information Engineering, Information Engineering University, Zhengzhou 450002, Henan, China

Received:2010-09-18 Published:2011-04-21

摘要/Abstract

摘要：

完全非线性(perfect nonlinear,PN)函数在密码学和代数组合等领域中具有重要的应用价值。从已有的两个基本完全非线性函数出发,通过确定一类有限域上线性化多项式方程的解,构造了奇数特征有限域上一类2次完全非线性函数,证明了该函数不等价于形式为x²的完全非线性函数,并通过一个实例分析了它与完全非线性函数x^ps+1的等价性问题。

关键词: PN函数;APN函数;CCZ等价;EA等价;线性置换

Abstract:

Perfect nonlinear functions are widely used in cryptography and algebra combinatorics. By using two known perfect nonlinear functions, a quadratic perfect nonlinear function over finite fields of odd characteristic was constructed based on determining the root of a linearized function.This quadratic function was proved to be inequivalent to x², and then an example was used to analyzed its inequivalence to x^ps+1.

Key words: perfect nonlinear function; almost perfect nonlinear function; CCZ-equivalence;EA-equivalence; linearized permutation

郭腓望,张习勇,韩文报. 一种完全非线性函数的构造[J]. J4, 2011, 46(3): 26-30.

GUO Fei-wang, ZHANG Xi-yong, HAN Wen-bao. A construction of perfect nonlinear functions[J]. J4, 2011, 46(3): 26-30.

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