Investigations on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e1110" altimg="si206.svg"><mml:mi>c</mml:mi></mml:math>-boomerang uniformity and perfect nonlinearity

We defined in Ellingsen et al. (2020) a new multiplicative c-differential, and the corresponding c-differential uniformity we characterized known perfect nonlinear functions with respect to this concept, as well inverse function any characteristic. Here, extend, via differential, boomerang introduced at Eurocrypt ’18 by Cid (2018), differential distinguisher of S-boxes block ciphers. investigate it context nonlinearity related functions. first characterize concept Walsh transforms. further describe for even, respectively, odd The methods are combinatorial number theoretical nature.