Low c-differential and c-boomerang uniformity of the swapped inverse function

09/19/2020

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by   Pantelimon Stanica, et al.

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Modifying the binary inverse function in a variety of ways, like swapping two output points has been known to produce a 4-differential uniform permutation function. Recently, in <cit.> it was shown that this swapped version of the inverse function has boomerang uniformity exactly 10, if n≡ 0 6, 8, if n≡ 3 6, and 6, if n≢0 3. Based upon the c-differential notion we defined in <cit.> and c-boomerang uniformity from <cit.>, in this paper we characterize the c-differential and c-boomerang uniformity for the (0,1)-swapped inverse function in characteristic 2: we show that for all c≠ 1, the c-differential uniformity is upper bounded by 4 and the c-boomerang uniformity by 5 with both bounds being attained for n≥ 4.