Some Special Perfect c-Nonlinear Functions on ℤn.

The notion of c-differential uniformity was proposed by Ellingsen <italic>et al.</italic>, which generalizes the classical differential uniformity measuring the resistance against differential cryptanalysis. Since then, the research of functions with low c-differential uniformity over finite fields attracted many researchers’ attention. However, it seems that there is no study of function with low c-differential uniformity over integer rings modulo n. In this paper, we give an extension of the c-differential uniformity concept to rings of integers module some n > 0, and we present several perfect c-nonlinear polynomial functions on the integer ring ℤn for the different integer n. [ABSTRACT FROM AUTHOR]