Analysis of the perfection and strong nonlinearity of encryption algorithms

The paper presents the experimental research results for characteristics of iterative block encryption algorithms based on the shift registers from the classes $R(8,32,3), R(15,32,5), R(16,32,5), R(32,32,9)$ and $R(33,32,11)$ where $R(n,32,m)$ is the class of shift registers of length $n$ with $m$ feedbacks over the set $V_{32}$ of $32$-dimensional binary vectors, $n>m\geq1$, $n,m\in\mathbb N$ (the generalized Feistel network). The researched characteristics are the indices of perfection and strong nonlinearity, i.e. the smallest numbers of rounds after which the product of round substitutions becomes perfect or strongly nonlinear respectively. Empirical estimates of these characteristics are presented. With the use of the results, the recommendations for the number of encryption rounds are given.