Investigations on c-Boomerang Uniformity and Perfect Nonlinearity
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We defined in <cit.> a new multiplicative c-differential, and the corresponding c-differential uniformity and we characterized the known perfect nonlinear functions with respect to this new concept, as well as the inverse in any characteristic. The work was continued in <cit.>, investigating the c-differential uniformity for some further APN functions. Here, we extend the concept to the boomerang uniformity, introduced at Eurocrypt '18 by Cid et al. <cit.>, to evaluate S-boxes of block ciphers, and investigate it in the context of perfect nonlinearity and related functions.
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