The c-differential behavior of the inverse function under the EA-equivalence

05/30/2020

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by   Pantelimon Stanica, et al.

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While the classical differential uniformity (c=1) is invariant under the CCZ-equivalence, the newly defined <cit.> concept of c-differential uniformity, in general is not invariant under EA or CCZ-equivalence, as was observed in <cit.>. In this paper, we find an intriguing behavior of the inverse function, namely, that adding some appropriate linearized monomials increases the c-differential uniformity significantly, for some c. For example, adding the linearized monomial x^p^d, where d is the largest nontrivial divisor of n, increases the mentioned c-differential uniformity from 2 or 3 (for c≠ 0) to ≥ p^d+2, which in the case of AES' inverse function on _2^8 is a significant value of 18.