Advanced Search
Volume 31 Issue 6
Jun.  2009
Turn off MathJax
Article Contents
Zheng Hao-ran, Zhang Hai-mo, Cui Ting, Du Xiao-qiang. A New Method for Construction of Orthomorphic Permutations[J]. Journal of Electronics & Information Technology, 2009, 31(6): 1438-1441. doi: 10.3724/SP.J.1146.2008.00528
Citation: Zheng Hao-ran, Zhang Hai-mo, Cui Ting, Du Xiao-qiang. A New Method for Construction of Orthomorphic Permutations[J]. Journal of Electronics & Information Technology, 2009, 31(6): 1438-1441. doi: 10.3724/SP.J.1146.2008.00528

A New Method for Construction of Orthomorphic Permutations

doi: 10.3724/SP.J.1146.2008.00528 cstr: 32379.14.SP.J.1146.2008.00528
  • Received Date: 2008-04-28
  • Rev Recd Date: 2008-11-24
  • Publish Date: 2009-06-19
  • Orthomorphic permutations have important application in the design of cryptosystems. Based on the one-to-one corresponding relationship between orthomorphic permutations and transversals of orthomorphic Latin square, the construction issue for orthomorphic permutations is studied, a new construction method is proposed to construct a (n+1)-bit orthomorphic permutation from a n-bit one where n>1. The method extends to obtain a composite transversal of orthomorphic Latin square An+1 by employing a transversal of orthomorphic Latin square An and its supplementary sequence transversal, based on composite transversal of , An+1 transversal of An+1 is constructed. Using the method, 22n (n+1)-bit orthomorphic permutations from a n-bit one can be obtained.
  • loading
  • Mittenthal L. Block substitutions using orthomorphicmappings[J].Advances in Applied Mathematics.1995, 16(1):59-71[2]Dai Zong-duo and Golomb S W. Generating all linearorthomorphisms without repetition[J].Discrete Mathematics.1999, 205(1-3):47-55[3]Huang Gen-xun and Zhu Yue-fei. The lower bound for thenumbers of orthomorphic permutations and a method toconstruct Them[C]. Proceeding of China Crypt2000, Beijing,2000: 27-30.[4]温巧燕, 钮心忻, 杨义先. 现代密码学中的布尔函数[M]. 北京: 科学出版社, 2000: 178-181.Wen Qiao-yan, Niu Xin-xin, and Yang Yi-xian. BooleanFunctions in Modern Cryptography[M]. Beijing: SciencePress, 2000: 178-181.[5]王鹏. 正形置换的一种构造方法[J]. 中南民族学院学报(自然科学版), 2001, 20(1): 50-53.Wang Peng. A method for construction of orthomorphicpermutation[J]. Journal of South-Central University forNationalities(Nat. Sci.), 2001, 20(1): 50-53.[6]李志慧, 李瑞虎, 李学良. 正形置换的构造[J]. 陕西师范大学学报(自然科学版), 2002, 30(4): 18-22.Li Zhi-hui, Li Rui-hu, and Li Xue-1iang. Construction oforthomorphic permutations[J]. Journal of Shanxi NormalUniversity (Natura1 Science Edition), 2002, 30(4): 18-22.[7]亢保元. 密码体制中的正形置换的构造与记数[J].电子与信息学报.2002, 24(9):1294-1296浏览[8]朱华安, 谢端强. 关于密码体制中正形置换的几个结果[J]. 应用科学学报, 2004, 22(2): 132-135.Zhu Hua-an and Xie Duan-qiang. On the construction oforthomorphic permutations in cryptosystems. Journal ofApplied Sciences, 2004, 22(2): 132-135.[9]Harald N and Arne W. Cyclotomic R-orthomorphisms offinite fields[J].Discrete Mathematics.2005, 295(1-3):161-171[10]Zhao Ya-qun and Wang Jue. Walsh spectral characteristicsand the auto-correlation function characteristics of formingorthomor- phic permutations of multi-output functions[J].Wuhan University Journal of Natural Sciences.2006, 11(6):1895-1898[11]常祖领, 柯品惠, 莫骄, 温巧燕. F2n 上的正形置换[J]. 北京邮电大学学报, 2006, 29(1): 115-118.Chang Zu-ling, Ke Pin-hui, Mo Jiao, and Wen Qiao-yan. Onorthomorphisms over F2n[J]. Journal of Beijing University ofPosts and Telecommunications, 2006, 29(1): 115-118.[12]任金萍, 吕述望. 正形置换的枚举与计数[J]. 计算机研究与发展, 2006, 43(6): 1071-1075.Ren Jin-ping and L Shu-wang. Enumerations and countingof orthomorphic permutations[J]. Journal of ComputerResearch and Development, 2006, 43(6): 1071-1075.[13]徐海波, 刘海蛟, 荆继武, 杜皎. 一种正形置换的逐位递增构造方法[J]. 中国科学院研究生院学报, 2006, 23(2): 251-256.Xu Hai-bo, Liu Hai-Jiao, Jing Ji-wu, and Du Jiao. Generatingorthomorphisms bit by bit[J]. Journal of the Graduate Schoolof the Chinese Academy of Sciences, 2006, 23(2): 251-256.[14]周建钦. 关于正形置换的构造[J]. 华中科技大学学报(自然科学版), 2007, 35(2): 40-42.Zhou Jian-qin. On the construction of orthomorphicpermutations[J]. J. Huazhong Univ. of Sci. Tech. (NatureScience Edition), 2007, 35(2): 40-42.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (3916) PDF downloads(913) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return