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三类Semi-Bent函数的构造 被引量：1

Constructions of Three Classes of Semi-Bent Functions
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摘要 Semi-bent函数是一种具有高非线性度的布尔函数,它们在密码和通信领域中都有重要的应用价值.本文构造了三类由迹函数表示的semi-bent函数.证明了当限制某些参数的取值范围时,这些新构造函数的semi-bent性与Kloosterman和密切相关.并且证明了每一类新构造的含有n个变元的semi-bent函数,都存在一个semi-bent函数的子类,它们的代数次数是n/2.利用Kloosterman和的零点,也给出了小域上semi-bent函数的例子. Semi-bent functions are a kind of Boolean functions with high nonlinearity.They have important applications in cryptography and communications.This paper gives three classes of semi-bent functions represented by trace.It is shown that the semi-bentness of the new functions is closely related to Kloosterman sums when the values of some parameters are restricted.It is also proved there exists a subclass of semi-bent functions with degree n/2 in each class of the new semi-bent functions on n variables.Several examples of the semi-bent functions in a small field are given by using the zeros of some Kloosterman sums.
作者 何业锋 马文平
机构地区 西安电子科技大学计算机网络与信息安全教育部重点实验室 西安邮电学院通信与信息工程学院
出处 《电子学报》 EI CAS CSCD 北大核心 2011年第1期233-236,共4页 Acta Electronica Sinica
基金 国家自然科学基金(No.60773002) 国家863高技术研究发展计划(No.2007AA01Z472) 大唐移动通信资助基金
关键词 布尔函数 semi-bent函数 HADAMARD变换 KLOOSTERMAN和 Boolean function semi-bent function Hadamard transform Kloosterman sums
分类号 TN918.1 [电子电信—通信与信息系统]
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参考文献11

  • 1K Khoo, G. Gong, D R Stinson. A new characterization of semi-bent and bent functions on finite fields [ J ]. Designs, Codes and Cryptography, 2006,38 (2) : 279 - 295.
  • 2P Charpin, E Pasalic, C Tavemier. On bent and semi-bent quadratic Boolean functions [J].IEEE Transactions on Information Theory,2005,51 (12) :4286 - 4298.
  • 3李超,屈龙江.Bent函数和弹性函数的最小距离[J].电子学报,2008,36(1):136-140. 被引量：4
  • 4M Matsui. Linear cryptanalysis method for DES cipher [ A ]. Proceedings of Workshop on the theory and application of cryptographic techniques on Advances in cryptology[ C]. Springer- Verlag New York, 1994.386 - 397.
  • 5R Gold. Maximal recursive sequences with 3-valued recursive cross-correlation functions[ J]. IEEE Transactions on Information Theory, 1968, IT - 14( 1 ) : 154 - 156.
  • 6S Boztas,P V Kumar. Binary sequences with Gold-like correlation but large linear span[ J]. IEEE Transactions on Information Theory, 1994,40(2) :532 - 537.
  • 7K Khoo,G.Gong,D R Stinson. A new family of gold-like sequences[A]. Proceedings of IEEE International Symposium on Information Theory[ C]. Switzerland: Lausanne, 2002. 181.
  • 8SUN Guanghong,WU Chuankun.Construction of Semi-Bent Boolean Functions in Even Number of Variables[J].Chinese Journal of Electronics,2009,18(2):231-237. 被引量：6
  • 9I Shparlinski. On the values of Kloosterman sums [ J]. IEEE Transactions on Information Theory, 2009, 55 ( 6 ) : 2599 - 2601.
  • 10H Dobbertin, G Leander, A Canteaut, et al. Construction of bent functions via Niho power functions[ J ].Journal of Combinatorial Theory ,Series A,2006, 113(5) : 779 - 798.

二级参考文献9

  • 1Chor B, Goldreich O, et al. Extraction problem or t-resilient functions[ A] .26th IEEE Symp Foundations of Computer Science[ C]. 1985.26.396 - 407.
  • 2M Fedorova, Y V Tarannikov. On the constructing of highly nonlinear resilient Boolean functions by means of special matrices[ A ]. In Progress in Cryptology INDOCRYPT 2001 [ C ]. volume 2247 in LNCS, Springer Verlag,2001.254- 266.
  • 3X Guo-Zhen, J Massey. A spectral characterization of correlation immune combining functions[J], IEEE, Transactions on Information Theory, 1988,34(3) : 569 - 571.
  • 4S Maity, S Maitra, Minimum distance between bent and 1-resilient Boolean functions[A]. In Fast Software Encryption-FSE 2004[C]. volume 3017 in LNCS, Springer Verlag, 2004.143 - 160.
  • 5S Maitra, E Pasalic. Further constructions of resilient Boolean functions with very high nonlinearity[ J]. IEEE Transactions on Information Theory,2002,48(7) : 1825 - 1834.
  • 6S Maity, T Johansson. Construction of cryptographically important boolean functions[ A] .In INDOCRYPT 2002[ C]. Volume 2551 in LNCS, Springer Vedag, 2002.234 - 245.
  • 7O S Rothaus. On bent functions [ J ]. Journal of Combinatorial Theory, Series A, 1976,20: 300 - 305.
  • 8P Sarkar, S Maitra. Nonlinearity bounds and constrctions of resilient Boolean functions [ A ]. In Advances in Cryptology-CRYPTO 2000[C]. volume 1880 in LNCS, Springer Verlag, 2000.515 - 532.
  • 9Y V Tarannikov. On resilient Boolean functions with maximum possible nonlinearity [ A ]. In Progress in Cryptology-INDOCRYPT 2000[C] .volume 1977 in LNCS, Springer Verlag, 2000.19 - 30.

共引文献8

同被引文献18

  • 1MEIER W, PASALIC E, CARLET C. Algebraic attacks and decomposition of Boolean functions[A]. Advances in Cryptology-Eurocrypt 2004[C]. Berlin, Germany, 2004. 474-491.
  • 2CLAUDE C. Relating three nonlinearity parameters of vectorial functions and building APN functions from bent functions[J]. Des Codes Cryptogr, 2011, 59(1-3):89-109.
  • 3ZHENG Y, ZHANG X M. On Plateaued functions[J]. IEEE Transactions on Information Theory, 2001, 47 (3): 1215-1223.
  • 4CARLET C, PROUF E. On Plateaued functions and their constructions[A]. Fast Software Encryption 2003[C]. Lund, Sweden, 2887. 54-73.
  • 5YING D H, ZHAO Y Q, FENG D G. Correlation functions of mulioutput m-valued logical functions and relation between correlation functions and spectra[J]. Zhengzhou Univ NatSci.Ed, 2007,39(2):21-24.
  • 6MACWILLIAMS F J, SLOANE N J. The Theory of Error-Correcting Codes[M]. North Holland: Elsevier, 1977.
  • 7FEINSILVER P, KOCIK J, Krawtchouk matrices from classical and quantum random walks[J]. Contemporary Mathematics, 2007, 287(2001): 83-96.
  • 8CARLET C. Partially-bent functions[J]. Des Codes Cryptogr, 1993, 3(2):135-145.
  • 9丁存生,肖国镇.流密码学及其应用[M].国防工业出版社,1994.
  • 10KRASIKOV I, LITSYN S. On integral zeros of krawtchouk polynomials[J]. Journal of Combinatorial Theory, 1996, 74(1):71-99.

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2011年 第1期

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