2023/12/03 by Mohit Pal, Pal, Mohit, Pantelimon Stănică +1 · 1 citation
Computer Science · Engineering · Medicine · #11T06 #12E20 #94A60 #Berberine and alkaloids research #Coding theory and cryptography #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Number Theory (math.NT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2312.01434
openalex publication_date 2023/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper makes the first bridge between the classical differential/boomerang uniformity and the newly introduced c-differential uniformity. We show that the boomerang uniformity of an odd APN function is given by the maximum of the entries (except for the first row/column) of the function's (-1)-Difference Distribution Table. In fact, the boomerang uniformity of an odd permutation APN function equals its (-1)-differential uniformity. We next apply this result to easily compute the boomerang uniformity of several odd APN functions. In the second part we give two classes of differentially low-uniform functions obtained by modifying the inverse function. The first class of permutations (CCZ-inequivalent to the inverse) over a finite field \mathbbFpn (p, an odd prime) is obtained from the composition of the inverse function with an order-3 cycle permutation, with differential uniformity 3 if p=3 and n is odd; 5 if p=13 and n is even; and 4 otherwise. The second class is a family of binomials and we show that their differential uniformity equals~4. We next complete the open case of p=3 in the investigation started by G" olo\u glu and McGuire (2014), for p≥ 5, and continued by Kölsch (2021), for p=2, n≥ 5, on the characterization of L1(Xpn-2)+L2(X) (with linearized L1,L2) being a permutation polynomial. Finally, we extend to odd characteristic a result of Charpin and Kyureghyan (2010) providing an upper bound for the differential uniformity of the function and its switched version via a trace function.