We defined in~\cite{EFRST20} 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~\cite{RS20},
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.~\cite{Cid18}, to evaluate S-boxes of block ciphers,
and investigate it in the context of perfect nonlinearity and related
functions.Comment: 31 pages, 1 figur