基于旋转矩阵的加密解密算法
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摘要
利用舍入误差分析的方法及计算机浮点运算的特性,构造一种基于旋转矩阵的加密解密算法,并提出了保证算法有效的充分条件.应用实例验证了算法的可行性.
Using the method of round-off error analysis and the characteristics of computer-floating-point operation,we constructed a new kind of encryption and decryption algorithm based on rotation matrix. Then we proposed sufficient conditions for the validity of the algorithm. Finally,we used some numerical examples to verify the feasibility of the algorithm.
Using the method of round-off error analysis and the characteristics of computer-floating-point operation,we constructed a new kind of encryption and decryption algorithm based on rotation matrix. Then we proposed sufficient conditions for the validity of the algorithm. Finally,we used some numerical examples to verify the feasibility of the algorithm.
引文
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[7]冯果忱,黄明游,刘停战,等.数值分析:上册[M].北京:高等教育出版社,2011:4-16;31-32.(FENG Guochen,HUANG Mingyou,LIU Tingzhan,et al.Numerical Analysis:Ⅰ[M].Beijing:Higher Education Press,2011:4-16;31-32.)
[8]杨晓元,苏光伟,张敏情.基于Kerckhoffs原则的图像隐秘算法[J].武汉大学学报(理学版),2009,55(1):67-70.(YANG Xiaoyuan,SU Guangwei,ZHANG Minqing.Image Steganography Scheme Based on Kerckhoffs’Principle[J].Journal of Wuhan University(Science Edition),2009,55(1):67-70.)
[9]杜现昆,原永久,牛凤文,等.高等代数[M].北京:高等教育出版社,2012:45.(DU Xiankun,YUAN Yongjiu,NIU Fengwen,et al.Advanced Algebra[M].Beijing:Higher Education Press,2012:45.)
[2]高献伟,周玉坤,路而红,等.DES算法硬件实现的研究[J].北京电子科技学院学报,2001,9(1):11-16.(GAO Xianwei,ZHOU Yukun,LU Erhong,et al.Research on Hardware Implementation of DES Algorithm[J].Journal of Beijing Electronic Science and Technology Institute,2001,9(1):11-16.)
[3]Diffie W,Hellman M E.New Directions in Cryptography[J].IEEE Transactions on Information Theory,1976,22(6):644-654.
[4]GU Lize,ZHENG Shihui.Conjugacy Systems Based on Nonabelian Factorization Problems and Their Applications in Cryptography[J/OL].Journal of Applied Mathematics,2014-04-28.http://dx.doi.org/10.1155/2014/630607.
[5]Rivest R L,Shamir A,Adleman L.A Method for Obtaining Digital Signatures and Public Key Cryptosystems[J].Communications of the ACM,1978,21(2):120-126.
[6]张焕国,刘金会,贾建卫,等.矩阵分解在密码中应用研究[J].密码学报,2014,1(4):341-357.(ZHANG Huanguo,LIU Jinhui,JIA Jianwei,et al.A Survey on Applications of Matrix Decomposition in Cryptography[J].Journal of Cryptologic Research,2014,1(4):341-357.)
[7]冯果忱,黄明游,刘停战,等.数值分析:上册[M].北京:高等教育出版社,2011:4-16;31-32.(FENG Guochen,HUANG Mingyou,LIU Tingzhan,et al.Numerical Analysis:Ⅰ[M].Beijing:Higher Education Press,2011:4-16;31-32.)
[8]杨晓元,苏光伟,张敏情.基于Kerckhoffs原则的图像隐秘算法[J].武汉大学学报(理学版),2009,55(1):67-70.(YANG Xiaoyuan,SU Guangwei,ZHANG Minqing.Image Steganography Scheme Based on Kerckhoffs’Principle[J].Journal of Wuhan University(Science Edition),2009,55(1):67-70.)
[9]杜现昆,原永久,牛凤文,等.高等代数[M].北京:高等教育出版社,2012:45.(DU Xiankun,YUAN Yongjiu,NIU Fengwen,et al.Advanced Algebra[M].Beijing:Higher Education Press,2012:45.)