• DOI:10.48550/arXiv.2209.13456
• Corpus ID: 252545179

More infinite classes of APN-like Power Functions

@article{Qu2022MoreIC,
  title={More infinite classes of APN-like Power Functions},
  author={Longjiang Qu and Kangquan Li},
  journal={ArXiv},
  year={2022},
  volume={abs/2209.13456}
}

• Longjiang Qu, Kangquan Li
• Published 27 September 2022
• Mathematics, Computer Science
• ArXiv

In the literature, there are many APN-like functions that generalize the APN properties or are similar to APN functions, e.g. locally-APN functions, 0-APN functions or those with boomerang uniformity 2. In this paper, we study the problem of constructing infinite classes of APN-like but not APN power functions. For one thing, we find two infinite classes of locally-APN but not APN power functions over F 2 2 m with m even, i.e., F 1 ( x ) = x j (2 m − 1) with gcd( j, 2 m + 1) = 1 and F 2 ( x ) = x j (2 m − 1)+1 with j = 2 m +23 . As far as the authors know, our infinite classes of locally-APN but not APN functions are the only two discovered in the last eleven years. Moreover, we also prove that this infinite class F 1 is not only with the optimal boomerang uniformity 2 , but also has an interesting property that its differential uniformity is strictly greater than its boomerang uniformity. For another thing, using the multivariate method, including the above infinite class F 1 , we construct seven new infinite classes of 0-APN but not APN power functions.