On APN Functions with Boomerang Uniformity One over $\mathbb F_{3^n}$: Differential and Boomerang Spectra and CCZ-Inequivalence
Cryptographic construction yields infinite APN function families with boomerang uniformity one over odd-characteristic fields, proving CCZ-inequivalence to power functions.
For q=3^n with odd n>1, every sign-switch of a perfect nonlinear Dembowski-Ostrom polynomial is proven APN with boomerang uniformity one or two, attaining uniformity one for (q-3)/2 parameters. This gives the first general construction of infinite APN families achieving boomerang uniformity one over odd-characteristic finite fields. The authors determine common differential and complete boomerang spectra, ruling out CCZ equivalence with power and Ness-Helleseth binomials, and exhibit three pairwise CCZ-inequivalent PN functions for infinitely many n, with the smallest degree n=45.