Construction and Count of 1-Resilient Rotation Symmetric Boolean Functions on <i>4p</i> Variables

PANG Shanqi; XU Wenju; DU Jiao; WANG Ying

doi:10.1049/cje.2017.05.003

Volume 26 Issue 6

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Article Navigation > Chinese Journal of Electronics > 2017 > 26(6): 1276-1283

PANG Shanqi, XU Wenju, DU Jiao, et al., “Construction and Count of 1-Resilient Rotation Symmetric Boolean Functions on 4p Variables,” Chinese Journal of Electronics, vol. 26, no. 6, pp. 1276-1283, 2017, doi: 10.1049/cje.2017.05.003

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PANG Shanqi, XU Wenju, DU Jiao, et al., “Construction and Count of 1-Resilient Rotation Symmetric Boolean Functions on 4p Variables,” Chinese Journal of Electronics, vol. 26, no. 6, pp. 1276-1283, 2017, doi: 10.1049/cje.2017.05.003

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Construction and Count of 1-Resilient Rotation Symmetric Boolean Functions on 4p Variables

doi: 10.1049/cje.2017.05.003

College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China

Funds: This work is supported by National Natural Science Foundation of China (No.11571094, No.U1404601, No.11471104, No.61402154, No.11501181), Program for Innovative Research Team (in Science and Technology) in University of Henan Province (No.14IRTSTHN023), Ph.D. Research Startup Foundation of Henan Normal University (No.5101019170133), and the Basic and Cutting-edge Technology Research Projects of Science and Technology Department of Henan Province (No.132300410430).

More Information

Corresponding author: DU Jiao (corresponding author) was born in Hubei, China, in 1978. He received the M.S. degree in mathematics from Henan Normal University, Xinxiang, China, and the Ph.D. Degree in cryptography from Beijing University of Posts and Telecommunications, Beijing, China, in 2008 and 2013 respectively. (Email:jiaodudj@126.com)
Received Date: 2016-01-06
Rev Recd Date: 2016-03-28
Publish Date: 2017-11-10

Abstract

Abstract

This paper studies the properties of orbit matrix and gives a formula to compute the number of these orbit matrices on 4p variables, where p is an odd prime. It has been demonstrated that the construction of 1-resilient Rotation symmetric Boolean functions (RSBFs) on 4p variables is equivalent to solving an equation system. By the proposed method, all 1-resilient RSBFs on 12 variables can be constructed. We present a counting formula for the total number of all 1-resilient RSBFs on 4p variables. As application of our method, some 1-resilient RSBFs on 12 variables are presented.
- Cryptography,
- Rotation symmetric Boolean functions,
- Orbit matrix,
- Resilient functions

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References(23)

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