cc-differential uniformity, (almost) perfect cc-nonlinearity, and equivalences

01/23/2023

∙

by   Nhan-Phu Chung, et al.

∙

0

∙

share

In this article, we introduce new notions cc-differential uniformity, cc-differential spectrum, PccN functions and APccN functions, and investigate their properties. We also introduce c-CCZ equivalence, c-EA equivalence, and c1-equivalence. We show that c-differential uniformity is invariant under c1-equivalence, and cc-differential uniformity and cc-differential spectrum are preserved under c-CCZ equivalence. We characterize cc-differential uniformity of vectorial Boolean functions in terms of the Walsh transformation. We investigate cc-differential uniformity of power functions F(x)=x^d. We also illustrate examples to prove that c-CCZ equivalence is strictly more general than c-EA equivalence.