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On the orders of transformation matrices (mod n) and two types of generalized Arnold transformation matrices 被引量：5

On the orders of transformation matrices (mod n) and two types of generalized Arnold transformation matrices
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摘要 In this paper, we analyze the structure of the orders of matrices (mod n), and present the relation between the orders of matrices over finite fields and their Jordan normal forms. Then we generalize 2-dimensional Arnold transformation matrix to two types of n-dimensional Arnold transformation matrices: A-type Arnold transformation matrix and B-type transformation matrix, and analyze their orders and other properties based on our earlier results about the orders of matrices.
作者 YANGLizhen CHENKefei
机构地区 DepartmentofComputerScienceandEngineering
出处 《Science in China(Series F)》 2004年第5期655-668,共14页 中国科学（F辑英文版）
关键词 SCRAMBLING Jordan normal form information hiding. scrambling, Jordan normal form, information hiding.
分类号 TP309.2 [自动化与计算机技术—计算机系统结构] TP301.6 [自动化与计算机技术—计算机系统结构]
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参考文献10

  • 1[1]Pfitzmann, A. (ed.), Information Hiding: Third International Workshop, LNCS 1768, Berlin: Springer, 2000.
  • 2[2]Qi Dongxu, Zhou Jiancheng, Han Xiaocheng, A new scrambling transformation and its application to image information hinding, Science in China, Ser. E (in Chinese), 2000, 30(5): 440-447.
  • 3[3]Arnold, V. I., Arez, A, Ergodic Problems of Classical Mechanics, Mathematical Physics Monograph Series,New York: W A Benjamin, INC, 1968.
  • 4[4]Zhou Jiancheng, Tie Xiaoyun, Arnold transformation of digital image and and its periodic, CHMAGRSPH 2000, Hangzhou, 2000.
  • 5[5]Jacobson, N., Basic Algebra I, second edition, New York: W. H. Freeman and Company, 1985, 92-96.
  • 6[6]Brown, E., Vaughan, T. P., Cycles of directed graphs defined by matrix multiplication (mod n), Discrete Mathematics, 2001, 239: 109-120.
  • 7[7]Jacoboson, N., Lectures in Abstract Algebra, v.2. Linear Algebra, New York: Van Nostrand, 1953.
  • 8[8]Fine, N. J., Binomial coefficients modulo a prime, Amer. Math. Monthly, 1947, 54: 589-592.
  • 9[9]Bell, A. D., Math 731/732: Modern Algebra, University of Wisconsin-Milwaukee, 2000.
  • 10[10]Messey, J. L., On the optimality of SAFER+diffusion, submitted to AES Roundl Conf2. http:∥csrc.nist.gov/encryption/aes/round 1/conf2/papers/massey.pdf.

同被引文献28

引证文献5

二级引证文献18

Science in China(Series F)
2004年 第5期

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