Hybrid approach to the search for Boolean functions with high algebraic immunity based on heuristics

Currently, one of the most promising and developing methods for analyzing ciphers is algebraic cryptanalysis. In order to provide resilience to such type of attack, it is necessary to use Boolean functions with high algebraic immunity in constructing components of block and stream ciphers. The paper proposes a combined approach to the search for Boolean functions with high algebraic immunity based on heuristic methods, in particular, the genetic algorithm and the Hill Climbing algorithm. Computational experiments for Boolean functions in $n\leq8$ variables demonstrate the effectiveness of the proposed approach.