Perfect nonlinear binomials and their semifields

Finite Fields and Their Applications - Tập 15 - Trang 125-133 - 2009
Zhengbang Zha1, Gohar M. Kyureghyan2, Xueli Wang3
1College of Mathematics and Econometrics, Hunan University, Changsha, 410082, China
2Department of Mathematics, Otto-von-Guericke University of Magdeburg, Universitätplatz 2, 39106 Magdeburg, Germany
3School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China

Tài liệu tham khảo

J. Bierbrauer, A family of crooked functions, Des. Codes Cryptogr., doi:10.1007/s10623-008-9227-1 Bracken, 2008, New families of quadratic almost perfect nonlinear trinomials and multinomials, Finite Fields Appl., 14, 703, 10.1016/j.ffa.2007.11.002 Bracken Budaghyan, 2008, Two classes of quadratic APN binomials inequivalent to power functions, IEEE Trans. Inform. Theory, 54, 4218, 10.1109/TIT.2008.928275 Budaghyan, 2008, New Perfect Nonlinear Multinomials Over Fp2k for Any Odd Prime p, vol. 5203 Carlet, 1998, Codes, bent functions and permutations suitable for DES-like cryptosystems, Des. Codes Cryptogr., 15, 125, 10.1023/A:1008344232130 Coulter, 2008, Commutative presemifields and semifields, Adv. Math., 217, 282, 10.1016/j.aim.2007.07.007 Coulter, 1997, Planar functions and planes of Lenz-Barlotti class II, Des. Codes Cryptogr., 10, 167, 10.1023/A:1008292303803 Dembowski, 1968, Planes of order n with collineation groups of order n2, Math. Z., 103, 239, 10.1007/BF01111042 Ding, 2006, A new family of skew Paley–Hadamard difference sets, J. Combin. Theory Ser. A, 113, 1526, 10.1016/j.jcta.2005.10.006 Edel, 2006, A new APN function which is not equivalent to a power mapping, IEEE Trans. Inform. Theory, 52, 744, 10.1109/TIT.2005.862128 Helleseth, 1997, Some power mappings with low differential uniformity, Appl. Algebra Engrg. Comm. Comput., 8, 363, 10.1007/s002000050073 Kyureghyan, 2008, Some Theorems on Planar Mappings, vol. 5130 Nyberg, 1994, Differentially uniform mappings for cryptography, vol. 765, 134 Zh. Zha, X. Wang, New families of perfect nonlinear functions, 2008, submitted for publication