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

The two indicators, the sum-of-squares-modulus indicator (SSMI) σ_f,g and the modulus indicator (MI) Δ_f,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 σ_f,g, σ_f (the SSMI of f) and σ_g 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, f₃. Further, we construct a ternary function with low SSMI and MI using perfectly uncorrelated ternary functions and modified ternary bent functions.