Abstract
Building upon the observation that the newly defined Ellingsen, et al. (2020) concept of c-differential uniformity is not invariant under EA or CCZ-equivalence Hasan et al. (2021), we showed in Stănică and Geary (2021) that adding some appropriate linearized monomials increases the c-differential uniformity of the inverse function, significantly, for some c. We continue that investigation here. First, by analyzing the involved equations, we find bounds for the uniformity of the Gold function perturbed by a single monomial, exhibiting the discrepancy we previously observed on the inverse function. Secondly, to treat the general case of perturbations via any linearized polynomial, we use characters in the finite field to express all entries in the c-Differential Distribution Table (DDT) of an (n, n)-function on the finite field \({\mathbb {F}}_{p^{n}}\), and further, we use that method to find explicit expressions for all entries of the c-DDT of the perturbed Gold function (via an arbitrary linearized polynomial).
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This article belongs to the Topical Collection: Boolean Functions and Their Applications V
Guest Editors: Lilya Budaghyan, Claude Carlet, Tor Helleseth and Kaisa Nyberg
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Stănică, P., Riera, C. & Tkachenko, A. Characters, Weil sums and c-differential uniformity with an application to the perturbed Gold function. Cryptogr. Commun. 13, 891–907 (2021). https://doi.org/10.1007/s12095-021-00485-z
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DOI: https://doi.org/10.1007/s12095-021-00485-z
Keywords
- Boolean and p-ary functions
- c-differentials
- Differential uniformity
- Perfect and almost perfect c-nonlinearity
- Perturbations