ScholarWorks@성균관대학교

초록

In this paper, we investigate the differential and boomerang properties of a class of binomial (Formula presented) over the finite field (Formula presented), where (Formula presented), and (Formula presented) is the quadratic character in (Formula presented). We show that Fr,±1 is locally-PN with boomerang uniformity 0 when pn ≡ 3 (mod 8). To the best of our knowledge, it is the second known non-PN function class with boomerang uniformity 0, and the first such example over odd characteristic fields with p > 3. Moreover, we show that Fr,±1 is locally-APN with boomerang uniformity at most 2 when pn ≡ 7 (mod 8). We also provide complete classifications of the differential and boomerang spectra of Fr,±1. Furthermore, we thoroughly investigate the differential uniformity of Fr,u for (Formula presented).

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