Z_4-Nonlinearity of a Constructed Quaternary Cryptographic Functions Class

摘要

New results on quaternary (Z_4 = {0,1, 2, 3}-valued) cryptographic functions are presented. We define and characterize completely the Z_4-balancedness and the Z4-nonlinearity according the Hamming metric and the Lee metric. In the particular case of quaternary Bent functions we show that the maximal nonlinearity of these functions is bounded for the Hamming metric and we give the exact value of the maximal nonlinearity of these functions for the Lee metric. A general construction, based on Galois ring is detailed and applied to obtain a class of balanced and high nonlinearity quaternary cryptographic functions. We use Gray map to derive these constructed quaternary functions to obtain balanced boolean functions having high nonlinearity.