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

DU Jiao; PANG Shanqi; WEN Qiaoyan; LIAO Xin

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Article Navigation > Chinese Journal of Electronics > 2014 > 23(4): 816-820

DU Jiao, PANG Shanqi, WEN Qiaoyan, et al., “Construction and Count of 1-Resilient Rotation Symmetric Boolean Functions on pr Variables,” Chinese Journal of Electronics, vol. 23, no. 4, pp. 816-820, 2014,

Citation:

DU Jiao, PANG Shanqi, WEN Qiaoyan, et al., “Construction and Count of 1-Resilient Rotation Symmetric Boolean Functions on p^r Variables,” Chinese Journal of Electronics, vol. 23, no. 4, pp. 816-820, 2014,

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

1.
College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China;
2.
State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China;
3.
College of Information Science and Engineering, Hunan University, Changsha 410082, China

Funds: This work is supported by National Natural Science Foundation of China (No.11171093, No.11471104, No.61402154, No.61402162, No.61300181, No.61272057, No.61202434, No.61170270, No.61100203, No.61121061), the Fundamental Research Funds for the Central Universities (No.BUPT2011YB01, No.2012RC0612), the Natural Science Research Program of the Education Department of Henan Province (No.2011B110010), Innovative Research Team (in Science and Technology) in University of Henan Province (No.14IRTSTHN023), Specialized Research Fund for the Doctoral Program of Higher Education (No.20130161120004) and Hunan Provincial Natural Science Foundation of China (No.14JJ7024).

Received Date: 2013-07-01
Rev Recd Date: 2013-12-01
Publish Date: 2014-10-05

Abstract

Abstract

Construction and count of 1-resilient Rotation symmetric Boolean functions (RSBFs) on p^r variables are demonstrated. It is proved that constructions of 1-resilient RSBFs on p^r variables are equivalent to solving an equation system. An accurate enumeration formula of all 1-resilient RSBFs on p^r variables is also proposed. Some examples are given, and the exact numbers of 1-resilient RSBFs on 8 and 9 variables are obtained respectively.
- Cryptography,
- Rotation symmetric,
- Support table,
- Correlation-immune,
- Resilient functions

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References(29)

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