YU Yuyin, WANG Mingsheng, LI Yongqiang, “Constructing Differentially 4 Uniform Permutations from Known Ones,” Chinese Journal of Electronics, vol. 22, no. 3, pp. 495-499, 2013,
Citation: YU Yuyin, WANG Mingsheng, LI Yongqiang, “Constructing Differentially 4 Uniform Permutations from Known Ones,” Chinese Journal of Electronics, vol. 22, no. 3, pp. 495-499, 2013,

Constructing Differentially 4 Uniform Permutations from Known Ones

Funds:  This work is supported by the National Natural Science Foundation of China (No.60970134, No.11171323, No.61173134), the IIE's Cryptography Research Project (No.Y2Z0011102), the Strategic Priority Research Program of the Chinese Academy of Sciences (No.XDA06010701).
  • Received Date: 2012-04-01
  • Rev Recd Date: 2012-09-01
  • Publish Date: 2013-06-15
  • Low differential uniformity functions provide good resistance to differential attacks. The AES (Advanced encryption standard) uses a differentially 4 uniform function (the inverse function) as its S-box. We give a further study of the inverse function in this paper. It is observed that after exchanging two values of a low differential uniformity function, its differential property still keeps good. Especially, for the inverse function over F2n (n even), various possible differential uniformities are completely determined after its two values are exchanged. As a consequence, we get some highly nonlinear permutations with differential uniformity 4 which are not CCZequivalent (Carlet Charpin-Zinoviev equivalent) to the inverse function on F2n.
  • loading
  • C. Carlet, P. Charpin and V. Zinoviev, “Codes, bent functions and permutations suitable for DES-like cryptosystems”, Designs, Codes and Cryptography, Vol.15, No.2, pp.125-156. 1998.
    K. Nyberg, “Differentially uniform mappings for cryptography”, Proceedings of EUROCRYPT'93, LNCS 765, pp.55-64, 1994.
    L. Budaghyan, C. Carlet and G. Leander, “Constructing new APN functions from known ones”, Finite Fields and Their Applications,Vol.15, No.2, pp.150-159, 2009.
    L. Budaghyan, C. Carlet, G. Leander, “Two classes of quadratic APN binomials inequivalent to power functions”, IEEE Trans. Inform. Theory, Vol.54, No.9, pp.4218-4229, 2008.
    C. Bracken, G. Leander, “A highly nonlinear differentially 4 uniform power mapping that permutes fields of even degree”, Finite Fields and Their Applications, Vol.16, No.4, pp.231-242, 2010.
    K. Browning, J.F. Dillon, R.E. Kibler and M.McQuistan, “APN polynomials and related codes”, Special volume of Journal of Combinatorics, Information and System Sciences, honoring the 75-th birthday of Prof. D.K. Ray-Chaudhuri, Vol.34, No.1-4, pp.135-159, 2009.
    C. Carlet, “Relating three nonlinearity parameters of vectorial functions and building APN functions from bent functions”, Designs, Codes and Cryptography, Vol.59, No.1-3, pp.89-109, 2011.
    J.F. Dillon, “APN polynomials: an update (ppt)”, Fq9, The 9th International Conference on Finite Fields and Applications, Dublin, Ireland, 2009.
    Y. Edel, A. Pott, “A new almost perfect nonlinear function which is not quadratic”, Adv. Math. Commun., Vol.3, pp.5981, 2009.
    R. Gold, “Maximal recursive sequences with 3-valued recursive cross-correlation functions”, IEEE Trans. Inform. Theory, Vol.14, No.1, pp.154-156, 1968.
    T. Kasami, “The weight enumerators for several classes of subcodes of the second order binary Reed-Muller codes”, Inform. Control, Vol.18, pp.369-394, 1971.
    C. Carlet, “On known and new differentially uniform functions”, ACISP 2011, LNCS 6812, Springer-Verlag Berlin Heidelberg, pp.1-15, 2011.
    T.P. Berger, A. Canteaut, P. Charpin and Y. Laigle-Chapuy, “On almost perfect nonlinear functions over F2n”, IEEE Trans. Inform. Theory, Vol.52, No.9, pp.4160-4170, 2006.
    R. Lidl, H. Niederreiter, Finite Fields, Cambridge, U.K.: Cambridge Univ. Press, pp.56, 1983.
  • 加载中


    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 (674) PDF downloads(1398) Cited by()
    Proportional views


    DownLoad:  Full-Size Img  PowerPoint