On the sum-of-squares-modulus indicator of q-ary functions

Abstract

The two indicators, the sum-of-squares-modulus indicator (SSMI) σf,g and the modulus indicator (MI) Δf,g of two q-ary functions f and g are important to measure the global avalanche characteristics (GAC) between f and g. In this paper, we establish a relationship among σf,g, σf (the SSMI of f) and σg for two q-ary functions f and g. We provide a method to construct a ternary function on (n + 1)-variables by using decomposition functions f1, f2, f3 on n-variables, and provide a link between SSMI of f and f1, f2, f 3. Further, we construct a ternary function with low SSMI and MI using perfectly uncorrelated ternary functions and modified ternary bent functions. © 2013 IEEE.