The Existence of a Class of Balanced Multi-output Rotation Symmetric Boolean Functions  

作　　者：DU Jiao FU Shaojing QU Longjiang LI Chao PANG Shanqi 

机构地区：[1]College of Mathematics and Information Science,Henan Normal University [2]Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control,Henan Normal University [3]College of Computer Science,National University of Defense Technology [4]College of Liberal Arts and Science,National University of Defense Technology

出　　处：《Chinese Journal of Electronics》2018年第5期995-1001,共7页电子学报（英文版）

基　　金：supported by National Key R&D Program of China(No.2017YFB0802000);National Natural Science Foundation of China(No.61672530,No.61722213,No.61572026,No.U1404601,No.11501181);Ph.D research startup foundation of Henan Normal University(No.5101019170133)

摘　　要：A new characterization of balanced rotation symmetric(n, m)-functions is presented. Based on the characterization, the nonexistence of balanced rotation symmetric(p^r, m)-functions is determined, where p is an odd prime and m ≥ 2. And there exist balanced rotation symmetric(2~r, m)-functions for 2 ≤ m ≤ 2~r-r. With the help of these results, we also prove that there exist rotation symmetric resilient(2~r, m)-functions for 2 ≤ m ≤ 2~r-r-1.A new characterization of balanced rotation symmetric（n, m）-functions is presented. Based on the characterization, the nonexistence of balanced rotation symmetric（p^r, m）-functions is determined, where p is an odd prime and m ≥ 2. And there exist balanced rotation symmetric（2^r, m）-functions for 2 ≤ m ≤ 2^r-r. With the help of these results, we also prove that there exist rotation symmetric resilient（2^r, m）-functions for 2 ≤ m ≤ 2^r-r-1.

关 键 词：CRYPTOGRAPHY Rotation symmetric Orbit matrix Correlation immune Resilient functions 

分 类 号：TN918.1[电子电信—通信与信息系统]