137
Views
8
CrossRef citations to date
0
Altmetric
Original Articles

New secondary constructions of differentially 4-uniform permutations over

, &
Pages 1670-1693 | Received 21 Jun 2015, Accepted 04 Jul 2016, Published online: 07 Sep 2016

References

  • E. Biham and A. Shamir, Differential cryptanalysis of DES-like cryptosystems, J. Cryptol. 4(1) (1991), pp. 3–72. doi: 10.1007/BF00630563
  • C. Bracken, E. Byrne, N. Markin, and G. McGuire, New families of quadratic almost perfect nonlinear trinomials and multinomials, Finite Fields Appl. 14(3) (2008), pp. 703–714. doi: 10.1016/j.ffa.2007.11.002
  • C. Bracken, E. Byrne, N. Markin, and G. McGuire, A few more quadratic APN functions, Cryptogr. Commun. 3(1) (2011), pp. 43–53. doi: 10.1007/s12095-010-0038-7
  • C. Bracken and G. Leander, A highly nonlinear differentially 4-uniform power mapping that permutes fields of even degree, Finite Fields Appl. 16(4) (2010), pp. 231–242. doi: 10.1016/j.ffa.2010.03.001
  • C. Bracken, C.H. Tan, and Y. Tan, Binomial differentially 4-uniform permutations with high nonlinearity, Finite Fields Appl. 18(3) (2012), pp. 537–546. doi: 10.1016/j.ffa.2011.11.006
  • L. Budaghyan and C. Carlet, Classes of quadratic APN trinomials and hexanomials and related structures, IEEE Trans. Inform. Theory 54(5) (2008), pp. 2354–2357. doi: 10.1109/TIT.2008.920246
  • L. Budaghyan, C. Carlet, and G. Leander, Two classes of quadratic APN binomials inequivalent to power functions, IEEE Trans. Inform. Theory 54(9) (2008), pp. 4218–4229. doi: 10.1109/TIT.2008.928275
  • L. Budaghyan, C. Carlet, and G. Leander, Constructing new APN functions from known ones, Finite Fields Appl. 15(2) (2009), pp. 150–159. doi: 10.1016/j.ffa.2008.10.001
  • L. Budaghyan, C. Carlet, and A. Pott, New class of almost bent and almost perfect nonlinear polynomials, IEEE Trans. Inform. Theory 52(3) (2006), pp. 1141–1152. doi: 10.1109/TIT.2005.864481
  • C. Carlet, On known and new differentially uniform functions, ACISP, 2011, pp. 1–15.
  • C. Carlet, P. Charpin, and V. Zinoviev, Codes, bent functions and permutations suitable for DES-like cryptsystems, Des. Codes Cryptogr. 15(2) (1998), pp. 125–156. doi: 10.1023/A:1008344232130
  • C. Carlet, D. Tang, X.H. Tang, and Q.Y Liao, New construction of differentially 4-uniform bijections, Proceedings of INSCRYPT 2013, 9th International Conference, Guangzhou, China, 27–30 November 2013, LNCS 8567, 2014, pp. 22–38.
  • J.F Dillon, APN polynomials and related codes, Workshop in Banff International Research Station, Alberta, Canada, 2006.
  • J.F Dillon, APN polynomials: An update, Conference Finite Fields and their Applications Fq9, Dublin, Ireland, 2009.
  • Y. Edel and A. Pott, A new almost perfect nonlinear function which is not quadratic, Adv. Math. Commun. 3(1) (2009), pp. 59–81. doi: 10.3934/amc.2009.3.59
  • R. Gold, Maximal recursive sequences with 3-valued recursive cross-correlation functions (corresp.), IEEE Trans. Inform. Theory 14(1) (1968), pp. 154–156. doi: 10.1109/TIT.1968.1054106
  • T. Kasami, The weight enumerators for several classes of subcodes of the 2nd order binary reed-muller codes, Inform. Control 18(4) (1971), pp. 369–394. doi: 10.1016/S0019-9958(71)90473-6
  • L. Knudsen, Truncated and higher order differentials, Lecture Notes in Comput. Sci. 1008 (1995), FSE 1994, pp. 196–211.
  • G. Lachaud and J. Wolfmann, The weights of the orthogonals of the extended quadratic binary Goppa codes, IEEE Trans. Inform. Theory 36(3) (1990), pp. 686–692. doi: 10.1109/18.54892
  • Y.Q. Li and M.S. Wang, Constructing differentially 4-uniform permutations over F22m from quadratic APN permutations over F22m+1, Des. Codes. Cryptogr. 72 (2014), pp. 249–264. doi: 10.1007/s10623-012-9760-9.
  • Y.Q. Li, M.S. Wang, and Y.Y. Yu, Constructing differentially 4-uniform permutations over F22k from the inverse function revisted, preprint, eprint.iacr/2013/731.
  • L. Matsui, Linear Cryptanalysis Method for DES Cipher, Advances in Cryptology – EUROCRYPT' 93, Springer, Berlin Heidelberg, 1994, pp. 386–397.
  • K. Nyberg, Differentially uniform mappings for cryptography, Advances in Cryptology – EUROCRYPT' 93 (Lofthus, 1993), LNCS 765, 1994, pp. 55–64.
  • K. Nyberg and L. Knudsen, Provable security against differential cryptanalysis, Proc. Advance in Cryptology – CRYPTO' 92, LNCS 740, 1993, pp. 566–574.
  • J. Peng, C.H. Tan, and Q.C. Wang, A new construction of differentially 4-uniformity permutations over F22k, preprint (2014). Available at arXiv:1407.4884v1[cs.IT].
  • J. Peng, C.H. Tan, and Q.C. Wang, A new family of differentially 4-uniform permutations over F22k for odd k, Sci. Chi. Math. 59 (2016), pp. 1221–1234. doi: 10.1007/s11425-016-5122-9.
  • L.J. Qu, Y. Tan, C. Li, and G. Gong, More constructions of differentially 4-uniform permutations on F22k, Des. Codes Cryptogr. 78 (2016), pp. 391–408, to appear. Available at http://arxiv.org/abs/1309.7423.
  • L.J. Qu, Y. Tan, C.H. Tan, and C. Li, Constructing differentially 4-uniform permutations over F22k via the switching method, IEEE Trans. Inform. Theory 59(7) (2013), pp. 4675–4686. doi: 10.1109/TIT.2013.2252420
  • D. Tang, C. Carlet, and X. Tang, Differentially 4-uniform bijections by permuting the inverse function, Des. Codes. Cryptogr. 77 (2015), pp. 117–141. doi: 10.1007/s10623-014-9992-y.
  • Y. Yu, M.S. Wang, and Y.Q. Li, Constructing low differential uniformity functions from known ones, Chinese Journal of Electronics 22 (2013), pp. 495–499.
  • Z.B. Zha, L. Hu, and S.W. Sun, Constructing new differentially 4-uniform permutations from the inverse function, Finite Fields Applications 25 (2014), pp. 64–78. doi: 10.1016/j.ffa.2013.08.003
  • Z.B. Zha, L. Hu, S.W. Sun, and J.Y. Shan, Further results on differentially 4-uniform permutations over F22m, Sci.China Math. 58 (2015), pp. 1577–1588. doi: 10.1007/s11425-015-4996-2.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.