JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (10): 47-51.doi: 10.6040/j.issn.1671-9352.0.2014.409

Previous Articles     Next Articles

Constructions of bent-negabent Boolean functions

ZHUO Ze-peng, CHONG Jin-feng, WEI Shi-min   

  1. School of Mathematical Science, Huaibei Normal University, Huaibei 235000, Anhui, China
  • Received:2014-09-12 Revised:2015-07-22 Online:2015-10-20 Published:2015-10-21

PDF (PC)

432

Abstract: A new method to construct negabent function was provided. Based on it, a construction of bent-negabent function was obtained. And then, the special Boolean function by concatenation was investigated. A necessary conditions for this Boolean function to be a negabent function was presented. Finally, the direct sum construction of bent-negabent function is given.

Key words: negabent function, bent function, Boolean function

CLC Number: 

  • TN918.1
[1] ROTHAUS O S. On bent functions[J]. Journal of Combinatorial Theory, 1976, 20:300-305.
[2] CARLET C. Two new classes of bent functions[C]// Proceedings of EUROCRYPT 1993. Berlin: Springer-Verlag, 1994, 765:77-101.
[3] CARLET C. On the secondary constructions of resilient and bent functions[J]. Progress in Computer Science and Applied logic, 2004, 23:3-28
[4] CLIMENT J, GARCIA F, REQUENA V. On the construction of bent functions of n+2 variables from bent function of n variables[J]. Advances in Mathematics of Communications, 2008, 2(4):421-431.
[5] PARKERMG, POTT A. On Boolean functions which are bent and negabent[C]// Proceedings of International Workshop on Sequences, Subsequences, and Consequences. Berlin: Springer-Verlag, 2007: 9-23.
[6] SCHMIDT K U, PARKER M G, POTT A. Negabent functions in the Maiorana-McFarland class[C]// Proceedings of the 5th International Conference on Sequences and Their Applications (SETA 2008). Berlin: Springer-Verlag, 2008: 390-402.
[7] SARKAR S. On the symmetric negabent Boolean functions[C]// Proceedings of the 10th International Conference on Cryptology in India. Berlin: Springer-Verlag, 2009: 136-143.
[8] STANICA P, GANGOPADHYAY S, CHATURVEDI A, et al. Nega-Hadamard transform, bent and negabent functions[C]// Proceedings of the 6th International Conference on Sequences and Their Applications. Heidelberg: Springer-Verlag, 2010: 359-372.
[9] GANGOPADHYAY S, CHATURVEDI A. A new class of bent-negabent Boolean functions[EB/OL]. [2014-07-025].http://eprint.iacr.org/2010/597.pdf.
[10] SARKAR S. Characterizing negabent Boolean functions over finite fields[C]// Proceedings of the 7th International Conference Sequences and Their Applications(SETA 2012). Berlin: Springer-Verlag, 2012: 77-88.
[11] STANICA P, GANGOPADHYAY S, CHATURVEDI A, et al. Investigations on bent and negabent functions via the nega-Hadamard transforms[J]. IEEE Transformations on Information Theory, 2012, 58(6):4064-4072.
[12] SU Wei, POTT A, TANG Xiaohu. Characterization of negabent functions and construction of bent-negabent functions with maximum algebraic degree[J]. IEEE Transformations on Information Theory, 2013, 59(6):3387-3395.
[13] 卓泽朋, 崇金凤, 魏仕民. Nega-Hadamard变换和negabent函数[J]. 山东大学学报:理学版,2013, 48(7):29-32.ZHUO Zepeng, CHONG Jinfeng, WEI Shimin. On Nega-Hadamard transform and negabent functions [J]. Journal of Shandong University: Natural Science, 2013, 48(7):29-32.
[1] YUAN Hong-bo, YANG Xiao-yuan, WEI Yue-chuan, LIU Long-fei, FAN Cun-yang. Matrix description and properties of global avalanche characteristics [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(11): 89-94.
[2] ZHUO Ze-peng, CHONG Jin-feng, WEI Shi-min. On Nega-Hadamard transform and negabent functions [J]. J4, 2013, 48(7): 29-32.
[3] FU Li. Basic properties of uniform logic formulas and  distribution of their truth degrees [J]. J4, 2010, 45(11): 59-62.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd