GMM型高维输出严格几乎最优弹性密码函数构造  

Constructions of GMM Type Strictly Almost Optimal Resilient Boolean Functions with High-Dimentional Vectorial Outputs

作　　者：张卫国[1] 胡姚达 董雪雯 ZHANG Wei-Guo;HU Yao-Da;DONG Xue-Wen(State Key Laboratory of Integrated Services Networks,Xidian University,Xi’an 710071,China;Wuhan Marine Communication Research Institute,Wuhan 430200,China)

机构地区：[1]西安电子科技大学综合业务网理论及关键技术实验室,西安710071 [2]武汉船舶通信研究所,武汉430200

出　　处：《密码学报》2023年第2期246-263,共18页Journal of Cryptologic Research

基　　金：国家自然科学基金(61972303,62272360)。

摘　　要：在流密码的设计中,非线性组合部件应选用具有高非线性度的弹性密码函数.高非线性度可以保障密码系统不易遭受最佳仿射逼近攻击,而弹性可以使系统能够抵抗相关攻击.使用高维向量输出的弹性函数,可以增加密码系统的加解密速度,但难以提高函数的非线性度.本文基于三类向量阵列,给出两个GMM型弹性函数的构造方案.所构造的函数具有严格几乎最优非线性度和较高的向量输出维数,很好地实现了非线性度、弹性阶和向量输出维数三者之间的折中.采用本文的函数构造方案,对某些给定的n,m,t,可以构造出一系列具有目前已知最高非线性度的(n,m,t)弹性函数.In the design of a stream cipher,the algebraic form of the nonlinear combining subsystem should be a resilient function with high nonlinearity.High nonlinearity ensures the cipher against best affine approximation attacks,while resiliency offers protection against correlation attacks.By using vectorial resilient functions as the combining functions,the speed of the encryption and decryption of the cipher can be increased,and yet it is difficult to improve the nonlinearity of the resilient functions.In this paper,we give two constructions of generalized Maiorana-McFarland(GMM)type strictly almost optimal resilient functions with higher-dimensional vectorial outputs based on three kinds of vector arrays.A good tradeoff is gained among the parameters of nonlinearity,resiliency order and vector-output dimension.It is shown that(n;m;t)resilient functions with currently best known nonlinearity can be constructed for some given n,m and t.

关 键 词：对称密码 多输出布尔函数 弹性 非线性度 不相交码 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]