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有限域中的循环矩阵在密码学方面的相关问题 被引量：2

Nonsingular circulant matrices over finite fields
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摘要 利用有限域上循环矩阵的性质,使用2种不同方法去解决有限域上可逆循环矩阵的个数问题.最后给出有限域上可逆循环矩阵个数的计算公式,并对多变量密码学中的循环矩阵的应用进行简要分析,这对矩阵理论研究和相关密码学的分析有促进作用. Study on the number of nonsingular circulant matrices over finite fields is significant in both maticx theory and practice.We characterize the properties of circulant matrices over finite fields and find two different ways to solve the problem.Finally,we give the formula to figure out the number of the nonsingular circulant matrices over finite fields in all circumstances and analyze some applications of circulant matrices in MPKC.
作者 赵岩 林东岱
机构地区 中国科学院软件研究所 中国科学院研究生院
出处 《中国科学院研究生院学报》 CAS CSCD 北大核心 2012年第6期805-814,共10页 Journal of the Graduate School of the Chinese Academy of Sciences
基金 国家973项目(2011CB302400) 国家自然科学基金(60970152)资助
关键词 循环矩阵 可逆 有限域 密码学 circulant matrices nonsingularity finite fields cryptography
分类号 TN918.1 [电子电信—通信与信息系统]
  • 相关文献

参考文献11

  • 1Davis P J. Circulant matrices[ M]. John Wiley and Sons, 1979.
  • 2Stuart J L, Weaver J R. Matrices that commute with a permutations alatrix[J].Linear Algebra and Its Applieations, 1991 : 255-265.
  • 3Stallings W. Cryptography and network security: principles and practices l MI. 4th ed. Prentice Hail, 2006: 96-115.
  • 4Dickson L E. The analytic representation of substitution on a power of a prime number of letters with a discussion of the linear group[ C ]//JAnn of Math,1896-1989,11 (1) :65-120.
  • 5Singh R P, Sarma B K, Saikia A. Public key cryptography using permutation P-polynomials over finite fields[ EB/OL]. (2009-06-24) [ 2011-02-12] . http ://eprint. iacr. org/2009/208.
  • 6Lancaster P, Tismenetsky M. The theory of matrices[ M ]. 2nd ed. Academic Press, INC, 1985.
  • 7Geller D, Kra 1, Popescu S, et al. On circulant matrices-preprint[ R/OL]. Stony brook university[2011-02-05 ]. http://www, ares. org/ notices/201203 / rtx 120300368 p. pdf.
  • 8Peter M N, Cheryl E P. Cyclic matrices over finite fields[J]. J London Math Soc,1995,52(2) :263-284.
  • 9韩海清,张焕国.轮换矩阵密码学性质[J].武汉大学学报（理学版）,2010,56(6):673-677. 被引量：3
  • 10林东岱代数学基础及有限域[M].北京:高等教育出版社,2006:46-50.

二级参考文献12

  • 1周炜.有限域上可逆循环阵的计数[J].纯粹数学与应用数学,1996,12(2):107-108. 被引量：2
  • 2Dacemen J, Rijmen V. AES Proposal Rijndael [EB/ OL]. [2008-10-05]. http://www, east. kuleuven, ac. be/ rijjmen/rijndael.
  • 3Heys H M,Tavares S E. The design of product ciphers resistant to differential and linear cryptanalysis [J]. Journal of Cryptology, 1996,9( 1 ) : 1-19.
  • 4Heys H M, Tavares S E. The design of substitutionpermutation networks resistant to differential and linear cryptanalysis [J]. Proceedings of 2nd ACM Conference on Computer and Communications Security, Fair fax, Virginia , 1994 : 148-155.
  • 5Daemen J, Rijmen V. AES Proposal=RIJNDAEL[EB/ OL]. [2008-01-30]. http:/ / www. nist. gov. / aes.
  • 6Mac Williams F J, Sloane N J A. The Theory of Error-Correcting Codes [M]. New York.. North-Holland Publishing Company, 1977.
  • 7Stuar J L, Weacer J R. Diaonally scaled permutations and circulant matrices[J].Linear Algebra Appl, 1994, 212/213:397-411.
  • 8Davis P J. Circulant Matrices [M]. New York: Wiley- Interscience Publication, 1979.
  • 9Wang K. On the generalizations of circulants[J].Linear Algebra Appl, 1979,25 : 197-216.
  • 10McElliece R J. Finite Fields for Computer Scientists and Engineers [M]. Holland.. Kluwer Academic Plenum Publishers, 1987 : 123- 149.

共引文献2

同被引文献31

  • 1Rothaus S. On Bent functions[ J]. Comb. Theory, 1976, 20A: 300-305.
  • 2Wolfmann J. Bent functions and coding theory[M]. Springer Netherlands, 1999: 393-418.
  • 3Olsen J D, Seholtz R A, Welch L R. Bent function sequences[J]. IEEE Trans. on Inf. Theory, 1982, 28(6) : 858-864.
  • 4Sebcrry J, Zhang X M. Constructions of Bent functions from two known Bent functions[J].. Australasian Journal of Combinato- ties, 1994, 9: 21-35.
  • 5Nyberg K. Constructions of Bent functions and difference sets[ C]//EUROCRYPT'90. 1991: 151-160.
  • 6Kumar P V, Scholtz R A, Welch L R. Generalized bent functions and their properties[ J]. Journal of Combinatorial Theory, Series A, 1985, 40(1) : 90-107.
  • 7Khoo K, Gong G, Stinson D R. A New Characterization of Semi-bent and Bent Functions on Finite Fields[ J]. Designs, Codes and Cryptography, 2006, 38 (2) : 279-295.
  • 8Ma W, Lee M. A new family of generalized bent functions[ C]//SETA'04. 2004: 24-28.
  • 9Li S, Hu L, Zeng X. Constructions of p-ary quadratic Bent functions[ J]. Acta Applicandae Mathematicae, 2008, 100 (3) : 227 -245.
  • 10Yu N Y, Gong G. Constructions of quadratic bent functions in polynomial forms[ J]. Information Theory~ IEEE Transactions on, 2006, 52(7): 3291-3299.

引证文献2

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中国科学院研究生院学报
2012年 第6期

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