DU Jiao, FU Shaojing, QU Longjiang, LI Chao, PANG Shanqi. The Existence of a Class of Balanced Multi-output Rotation Symmetric Boolean Functions[J]. Chinese Journal of Electronics, 2018, 27(5): 995-1001. doi: 10.1049/cje.2018.04.005
Citation: DU Jiao, FU Shaojing, QU Longjiang, LI Chao, PANG Shanqi. The Existence of a Class of Balanced Multi-output Rotation Symmetric Boolean Functions[J]. Chinese Journal of Electronics, 2018, 27(5): 995-1001. doi: 10.1049/cje.2018.04.005

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

doi: 10.1049/cje.2018.04.005
Funds:  This work is 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), and Ph.D research startup foundation of Henan Normal University (No.5101019170133).
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  • Corresponding author: LI Chao (corresponding author) received the B.S. degree in mathematics in 1987 from the University of Information Engineering of China, the M.S. degree in mathematics in 1990 from the University of Science and Technology of China, and the Ph.D. degree in engineering in 2002 from the National University of Defense Technology of China. Since December 2001, he has been a professor with the Department of Mathematics and System Science, National University of Defense Technology. His research fields include coding theory, cryptography and sequences. (Email:lichao nudt@sina.com)
  • Received Date: 2016-06-08
  • Rev Recd Date: 2017-06-30
  • Publish Date: 2018-09-10
  • A new characterization of balanced rotation symmetric (n,m)-functions is presented. Based on the characterization, the nonexistence of balanced rotation symmetric (pr, m)-functions is determined, where p is an odd prime and m ≥ 2. And there exist balanced rotation symmetric (2r, m)-functions for 2 ≤ m ≤ 2r-r. With the help of these results, we also prove that there exist rotation symmetric resilient (2r, m)-functions for 2 ≤ m ≤ 2r-r-1.
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