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 f
₁
, f
₂
, f
₃
on n-variables, and provide a link between SSMI of f and f
₁
, f
₂
, f
₃
. Further, we construct a ternary function with low SSMI and MI using perfectly uncorrelated ternary functions and modified ternary bent functions.