## Cryptology ePrint Archive: Report 2013/617

Some results concerning global avalanche characteristics of two $q$-ary functions

Brajesh Kumar Singh

Abstract: The global avalanche characteristics criteria was first introduced by Zhou et al. (Inform. Sci. 180(2) (2010) 256-265). This article is concerned with some new bounds on global avalanche characteristics of two $q$-ary functions. Based on the above result we obtain a bound on $\sigma_{f}$ of $f \in \cB_{n, q}$ in terms of $\sigma_{f_{\ell}}'$s of the restricted functions on $\BBZ_{n-1}^q$, and construct a class of $q$-ary bent functions from $1$-plateaued functions having dijoint Walsh spectra.

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