Construction and Counting of Resilient 2-Rotation Symmetric Boolean Functions with 2p Variables

doi:10.13190/jbupt.201205.36.duj

JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM ›› 2012, Vol. 35 ›› Issue (5): 36-40.doi: 10.13190/jbupt.201205.36.duj

• Papers • Previous Articles Next Articles

Construction and Counting of Resilient 2-Rotation Symmetric Boolean Functions with 2p Variables

DU Jiao, WEN Qiao-yan, ZHANG Jie, PANG Shan-qi, LIAO Xin

1. State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications2. Department of Mathematics and Information Science, Xinxiang University3. School of Science, Beijing University of Posts and Telecommunications4. College of Mathematics and Information Science, Henan Normal University

Received:2012-03-12 Revised:2012-05-10 Online:2012-10-28 Published:2012-07-06
Contact: Jiao DU E-mail:jiaodudj@126.com

Abstract

Abstract:

By using the method of matrix analysis, the orbit of the resilient 2-rotation symmetric Boolean functions with 2p variables is investigated, where p≥3and p is prime. Some properties about characteristic matrix of them are given. A necessary and sufficient condition for 2-rotation symmetric Boolean functions(RSBFs) with 4 or 2p variables being resilient is derived. Construction and counting of this class functions are equivalent to solving three equation systems. Construction and counting of all the resilient 2-RSBFs with 2p variables are determined by this way.

Key words: resilient Boolean function, rotation symmetry, characteristic matrix, counting

CLC Number:

TN918.1

DU Jiao, WEN Qiao-yan, ZHANG Jie, PANG Shan-qi, LIAO Xin. Construction and Counting of Resilient 2-Rotation Symmetric Boolean Functions with 2p Variables[J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2012, 35(5): 36-40.

References

[1] Siegenthaler T. Correlation-immunity of no-nlinear combining functions for cryptographic applications[J]. IEEE Transactions on Information Theory, 1984, 30(5): 776-780.
[2] Filiol E. Fontaine C. Highly nonlinear balanced Boolean functions with good correlation immunity//Advances in Cryptology-EUROCRYPT 98. Berlin:Springer-Verlag, 1998.
[3] Courtois N, Meier W. Algebraic attacks on stream ciphers with linear feedback//Berlin: Biham Eed. Advances in Cryptology Eurocrypt 2003. LNCS: Springer-Verlag, 2003: 346-359.
[4] Canteaut A. Open problems related to algebraic attacks on stream ciphers//WCC2005. Berlin: Springer,2006: 120-134.
[5] 杜蛟,温巧燕,张劼,等. 5元1阶弹性函数的代数免疫阶[J]. 通信学报, 2011, 32(4): 17-24. Du Jiao, Wen Qiaoyan, Zhang Jie, et al. On the algebraic immunity for 1^st-resilience Boolean functions with five variables[J]. Journalon Communication, 2011, 32(4): 17-24.
[6] Pieprzyk J, Qu Chenxin. Fast hashing and rotation symmetric functions[J]. Journal Universal Computer Science, 1999, 5(1): 20-31.
[7] Cusick W, Stanica P, Maitra S. Fast evaluation, weight and nonlinearity of rotation symmetric functions[J]. Discrete Mathematics, 2002, 258(1-3): 289-301.
[8] Stanica P, Maitra S, Clark J. Results on rotation symmetric bent and correlation immune Boolean functions//Fast Software Encryption Workshop (FSE 2004), LNCS301//New Delhi: Springer-Verlag, 2004: 161-177.
[9] Kavut S,Maitra S, Yucel M D. Search for Boolean functions with excellent profiles in the rotation symmetric class [J]. IEEE Transactions on Information Theory, 2007, 53(5): 1743-1751.
[10] Fu Shaojing, Li Chao, Qu Longjiang. On the number of rotation symmetric Boolean functions [J]. Science China Information Sciences, 2010, 53(3): 537-545.
[11] 张鹏,付绍静,屈龙江,等. 平衡旋转对称布尔函数的计数[J]. 应用科学学报, 2012, 30(1): 45-51. Zhang Peng, Fu Shaojing, Qu Longjiang, et al.Enumeration of balanced rotation-symmetric Boolean functions[J]. Journal of Applied Sciences, 2012, 30(1):45-51.
[12] Kavut S,Maitra S, Yucel M D. Generalized rotation symmetric and dihedral symmetric 9-variable Boolean functions with nonlinearity 242. http://eprint.iacr.org/2007/308.pdf
[13] 李泉,高光谱,刘文芬. k-阶旋转对称函数性质分析与轨道计数[J]. 通信学报, 2012, 33(1): 114-119. Li Quan, Gao Guangpu, Liu Wenfen. Analysis of properties and counting of orbits for k-rotation symmetric Boolean functions[J]. Journal on Communication, 2012, 33(1): 114-119.
[14] 温巧燕,钮心忻,杨义先. 现代密码学中的布尔函数[M]. 北京:科学出版社, 2000.
[15] 庞善起,杜蛟,席金彦. 相关免疫函数阶的判别方法[J]. 应用数学学报, 2009, 32(3): 445-453. Pang Shanqi, Du Jiao, Xi Jinyan. Some methods for judging the order of correlation-immune functions[J]. Acta Mathematicae Applicacatae Sinica, 2009, 32(3): 445-453.

Construction and Counting of Resilient 2-Rotation Symmetric Boolean Functions with 2p Variables

PDF

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 6

Recommended Articles

Metrics

Comments

[1]	LIU Xi-wen, CHEN Hai-ming. A Human Action Counting and Recognition Method Based on CSI [J]. Journal of Beijing University of Posts and Telecommunications, 2020, 43(5): 105-111.
[2]	XU Peng, YANG Jing-yuan. 4A Enabler in PaaS Platform Supporting Recommendation Applications [J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2015, 38(s1): 98-102.
[3]	. EnergyEfficient Cooperative Spectrum Sensing  in Cognitive Radio Networks [J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2010, 33(4): 93-96.
[4]	WANG Meng-jie. Research and Implement on Service Accounting of Next Generation Internet [J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2008, 31(3): 119-122.
[5]	ZHANG Jinyu1,MENG Luoming2,QIU Xuesong2. A Real Time Accounting Management with Constant Price for IPDiffServ Network [J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2005, 28(3): 68-71.
[6]	CHENG Lu, MENG Luo-ming, QIU Xue-song. Classification and Definition Method of IP Charging and Accounting Parameters for NGOSS [J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2004, 27(6): 6-10.