一类幂函数的c-差分性质及其(−1)-差分谱

The c-Differential Properties of a Class of Power Functions and Their(−1)-Differential Spectrum

差分攻击是攻击迭代分组密码最有效的方法之一.密码算法抵抗差分攻击的能力与其采用的密码函数抵抗差分攻击的能力密切相关,而后者可以用差分均匀度来衡量.密码函数的差分均匀度越小,其抵抗差分攻击的能力就越强.为了抵抗差分攻击,分组密码算法中的核心部件S盒(S-boxes)应该具有较低的差分均匀度.同时,具有低差分均匀度的密码函数在编码理论、组合设计等领域中有着广泛的应用.乘法差分攻击作为差分攻击的推广被提出,密码函数抵抗乘法差分攻击的能力用其c-差分均匀度反映.本文主要研究了有限域Fpn上幂函数x^(p^(n)+3)/2的c-差分性质,这里p是奇素数,n是正整数.对于一般的c≠±1,本文给出了这类幂函数的c-差分均匀度的上界,并针对c=−1求解了其c-差分谱.

Differential attack is one of the most effective methods to attack iterative block cipher.The ability of cryptographic algorithms to resist differential attack is closely related to the ability of cryptographic functions to resist differential cryptanalysis,which can be measured by the differential uniformity.The smaller the differential uniformity of cryptographic functions,the stronger their ability to resist differential attack.In order to resist differential attack,the core component S-boxes of block cipher algorithms should have low differential uniformity.Meanwhile,cryptographic functions with low differential uniformity are widely used in areas such as coding theory and combinatorial design.The multiplicative differential attack has been proposed as a generalization of the differential attack,and the ability of cryptographic functions to resist multiplicative differential attack is reflected by their c-differential uniformity.This paper mainly studies the c-differential properties of the power function x^(p^(n)+3)/2 over Fpn,where p is an odd prime and n is a positive integer.The upper bound of the c-differential uniformity of this class of power functions is given for a general c≠±1,and its c-differential spectrum is presented when c=−1.