2021/05/18 by Li, Kangquan, Zhou, Yue, Li, Chunlei +1
#FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.2105.08464
In this paper, we present two new infinite classes of APN functions over \gf22m and \gf23m, respectively. The first one is with bivariate form and obtained by adding special terms, ∑(aix2iy2i,bix2iy2i), to a known class of APN functions by Göloǧlu over \gf2m2. The second one is of the form L(z)2m+1+vz2m+1 over \gf23m, which is a generalization of one family of APN functions by Bracken et al. [Cryptogr. Commun. 3 (1): 43-53, 2011]. The calculation of the CCZ-invariants Γ-ranks of our APN classes over \gf28 or \gf29 indicates that they are CCZ-inequivalent to all known infinite families of APN functions. Moreover, by using the code isomorphism, we see that our first APN family covers an APN function over \gf28 obtained through the switching method by Edel and Pott in [Adv. Math. Commun. 3 (1): 59-81, 2009].