On the Nonlinearity of Exponential Welch Costas Functions

We study the nonlinearity of the exponential Welch Costas functions, using the Fourier transform on
Z

_m
. These functions have been proposed for use in nonbinary cryptosystems. High nonlinearity is required to ensure resistance to linear cryptanalysis. We prove some properties of the nonlinearity of these functions, and we suggest a plausible connection of the nonlinearity to the class number of a quadratic field.