Discrete Lyapunov Exponent and Resistance to Differential Cryptanalysis

In a recent paper, Jakimoski and Subbalakshmi provided a nice connection between the so-called discrete Lyapunov exponent of a permutation F defined on a finite lattice and its maximal differential probability, a parameter that measures the complexity of a differential cryptanalysis attack on the substitution defined by F. In this brief, we take a second look at their result to find some practical shortcomings. We also discuss more general aspects.