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具有特定非零Walsh谱值个数的布尔函数的研究及构造 被引量：2

THE RESEARCH AND CONSTRUCTION OF BOOLEAN FUNCTIONS WITH GIVEN NUMBER OF NON-ZERO WALSH SPECTRUM VALUES
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摘要 布尔函数与其变元的相关性与流密码的相关攻击有紧密联系.Walsh变换则是研究布尔函数相关特性的主要工具。本文研究了非零Walsh谱值个数k=9,10的布尔函数,证明了k=9的函数的不存在性,并构造了所有k=10的函数。 The correlation of a Boolean function with its variables is closely related to the correlation attack on stream ciphers. The Walsh transformation is the main tool to study the correlation of a Boolean function. The paper studies the functions with k(the number of non-zero walsh spectrum values)=9,10. It is proved that there are no functions with k=9, and we construct all functions with k=10.
作者 马智 王也青 裴定一
机构地区 信息安全国家重点实验室(中国科学院研究生院)
出处 《应用数学学报》 CSCD 北大核心 2003年第4期622-628,共7页 Acta Mathematicae Applicatae Sinica
关键词 布尔函数 WALSH变换 相关性 流密码 Boolean functions, correlation, Walsh transformation, stream cipher
分类号 TN918.1 [电子电信—通信与信息系统] O153.2 [理学—基础数学]
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参考文献5

  • 1[1]Pei Dingyi, Qin Wenliang. The Correlation of a Boolean Function with Its Variables, Progress in Cryptology -Indocrypt'2000. Lecture Notes in Computer Science 1977, Springer, 2000, 1-8
  • 2[2]Chepyzhov V, Smeets B. On a Fast Correlation Attack on Certain Stream Cipher. Advance in Cryptology-Eurocrypt'91, 1991, 176-185
  • 3[3]Golic J. On the Security of Shift Register Based Keystream Generators, Anderson R, editor, Fast Software Encryption, Cambridge Security Workshop, Springer-Verlag, 1994, 90-100
  • 4[4]Golic J, Mihaljevic M. A Generalized Correlation Attack on a Class of Stream Cipher Based on the Levenshtein Distance. J. of Cryptology, 1991, 3:201-212
  • 5[5]Rueppel R A, Stream Cipher, Simmons G J, editor, Contemporary Cryptology: the Science of Information Integrity, 1992, 65-134

同被引文献8

  • 1Pei D Y, Qin W L. The Correlation of a Boolean Function with Its Variables, Progress in CryptologyIndocrypt'2000. Lecture Notes in Computer Science 1977, Berlin: Springer-Verlag, 2000, 1-8
  • 2Rueppel R A, Stream Cipher, Simmons G J, editor, Contemporary Cryptology: The Scienceof Information Integrity, 1992, 65-134
  • 3Chepyzhov V, Smeets B. On a Fast Correlation Attack on Certain Stream Cipher. Advance in Cryptology-Eurocrypt'91. Berlin: Springer-Verlag, 1991, 176-185
  • 4Golic J. On the Security of Shift Register Based Keystream Generators. Anderson R, editor, Fast Software Encryption, Cambridge Security Workshop. Berlin: Springer-Verlag, 1994, 90-100
  • 5Golic J, Mihaljevic M. A Generalized Correlation Attack on a Class of Stream Cipher Based on the Levenshtein Distance. New York: Springer-Verlag: J. of Cryptology, 1991, 3, 201-212
  • 6Rueppel R A.Stream cipher[A].Simmons G J.Contemporary cryptology:the Science of Information Integrity[C].1992.65～134.
  • 7Zeng Xiang-yong,Hu Lei.A composition construction of bent-like boolean function from quadratic polynomials[J/OL].http:∥eprint iacr.org2003204.pdf.
  • 8Cohen E. Linear and quadratic equations in a Galois field with applications to geometry[J].Duke Math,1965,32:631～641.

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应用数学学报
2003年 第4期

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