Triprojective almost perfect nonlinear permutations and functions
It advances the theory of APN functions in finite fields, offering new constructions for specific dimensions, but the results are incremental within the domain of cryptography and coding theory.
The paper constructs a large family of APN permutations for odd dimensions divisible by three and APN functions for even dimensions, providing new highly nonlinear functions with a triprojective structure.
We give a large family of almost perfect nonlinear (APN) permutations of finite vector spaces of every odd dimension divisible by three. We also give APN functions that are not bijective on even dimensions and related highly nonlinear functions. The functions we provide admit a so-called triprojective structure induced by the general linear group $\mathrm{GL}(3,2^m)$.