New Instances of Quadratic APN Functions

09/15/2020

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by   Christof Beierle, et al.

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By applying a recursive tree search, we find many new instances of quadratic APN functions up to CCZ-equivalence. In particular, we present 12,923 new quadratic APN instances in dimension eight and five new quadratic APN instances in dimension ten. The vast majority of those functions have been found by utilizing linear self-equivalences. Among our 8-bit APN functions, there are three extended Walsh spectra that were not known to be valid extended Walsh spectra of quadratic 8-bit APN functions before and, surprisingly, there exist at least four CCZ-inequivalent 8-bit APN functions with linearity 2^7, i.e. the highest possible non-trivial linearity.