Application of heuristic methods to search for Boolean functions with good cryptographic characteristics

{Currently, one of the most promising and developing methods of cipher analysis is linear and algebraic cryptanalysis. To ensure resistance to this type of attack, it is necessary to use Boolean functions with high nonlinearity and algebraic immunity when constructing components of block and stream ciphers. We propose a combined approach to the search for Boolean functions with nonlinearity and algebraic immunity based on heuristic methods, in particular, a genetic algorithm and a hill climbing algorithm. Computational experiments have been carried out for Boolean functions in $n\leq 8$ variables, which demonstrated the effectiveness of the proposed approach, as well as a comparative analysis of the results obtained by random search. On the basis of the obtained Boolean functions, vector Boolean functions are constructed and among them the number of functions with the component algebraic immunity and nonlinearity is calculated. }