| Abstract: | The global avalanche characteristics criterion of two Boolean functions was introduced by Zhou et al. On the global avalanche characteristics criterion of two Boolean functions and the higher order nonlinearity, Inform. Sci. 180(2) (2010), pp. 256–265] to measure the cryptographic behaviour in a global characteristic. The two indicators σ f, g and Δ f, g of Boolean functions f and g were presented. In this paper, a new upper bound on σ f, g is derived, and a technique on constructing Boolean functions to attain the lower bound on the sum-of-squares indicator is described by using the disjoint spectra method. Some new upper bounds on Δ f, g and σ f, g are deduced for two special Boolean functions. Two relationships between σ f, g and algebraic immunity of the two Boolean functions are obtained. Finally, some links among different cryptographic indicators are shown. |
