Abstract

The weighted ambiguity and deficiency are two new security measures for a mapping between two finite Abelian groups of the same size. In this talk, we obtain the optimum lower bounds of these measures for permutations of an Abelian group. We then find a proper relation between the non-linearity and ambiguity of functions. We also show that the M?bius function in the multiplicative group of $\mathbb{F}_q$ is closer to being optimal in ambiguity than the inverse function in the additive group of $\mathbb{F}_q$ which is used in AES. In addition, we provide an explicit formula in terms of the ranks of matrices on the ambiguity and deficiency of a Dembowski-Ostrom (DO) polynomial and using this technique, we find exact values for known cases of DO permutations with few terms.