隐性权位比特函数的线性复杂度  

Linear Complexity of Hidden Weighted Bit Functions

作　　者：陈芷如 冯立刚 朱友文 CHEN Zhiru;FENG Ligang;ZHU Youwen(School of Computer Science and Technology,Nanjing University of Aeronautics and Astronautics,Nanjing 211100,China)

机构地区：[1]南京航空航天大学计算机科学与技术学院,南京211100

出　　处：《计算机科学与探索》2023年第8期1974-1980,共7页Journal of Frontiers of Computer Science and Technology

基　　金：国家重点研发计划(2020YFB1005900);国家自然科学基金(62172216);江苏省自然科学基金(BK20211180);广西密码学与信息安全重点实验室研究课题(GCIS202107)。

摘　　要：布尔函数既是分组密码的关键部件,也是设计序列的重要方式,在对称密码的设计与分析中起着重要的作用,关于布尔函数的密码学性质研究一直是密码界研究的热点。隐性权位比特函数(HWBF)因具有平衡性、高非线性度等诸多“好”的密码学特性而备受关注,而它的线性复杂度指标在文献中尚无相关结论。因此,讨论了采用n-元HWBF函数构造周期为2n的二元伪随机序列,从数学理论的角度证明该序列是具有最大线性复杂度的平衡序列。同时,应用数论中的Hasse导数和Lucas同余式,计算出该序列的2-错线性复杂度的取值,其中当n(mod 4)∈{0,1,3}时,该序列的2-错线性复杂度达到最大值。结果表明,该序列是一类具备多种密码学指标的优质序列。Boolean functions are crucial primitive in block cipher and are also used to design pseudorandom sequences.They play a crucial role in the design of symmetric cryptography and its analysis,and the study on the cryptographic properties of Boolean functions is a hotspot in cryptography.The hidden weighted bit functions(HWBF)are paid attention since they have many“good”cryptographic measures.However,there are no results on their linear complexity in the literature.Therefore,this paper discusses a family of binary sequences of period 2n built by using n-variable HWBF(hidden weighted bit functions).It is proven that such sequences are balanced with maximal linear complexity using mathematical method.The 2-error linear complexity of the sequences is also determined in terms of the Hasse derivative and Lucas congruence.When n(mod 4)∈{0,1,3},the values of the 2-error linear complexity are maximal.Results indicate that such sequences are of“good”cryptographic measures.

关 键 词：序列密码 伪随机序列 二元序列 隐性权位比特函数 线性复杂度 K-错线性复杂度 

分 类 号：TP393[自动化与计算机技术—计算机应用技术] TN911[自动化与计算机技术—计算机科学与技术]