Opportunities to minimize hardware and software costs for implementing boolean functions in stream ciphers

Currently, nonlinear Boolean functions are actively investigated worldwide. However, many questions remain unanswered. The theory of nonlinear Boolean functions that are suitable for use in cryptographically strong algorithms is significantly incomplete. Despite the existence of numerous publications on these themes, many issues related to the interconnection of design characteristics affecting the generator's performance and its cryptographic characteristics still remain unsolved. The possibility of generating a special type of sequence, called de Bruijn sequence, at minimal hardware and software costs to implement nonlinear Boolean functions in stream encryption systems, is the main subject of this work. The paper presents the possible structure boundaries (algebraic degree of a Boolean function, the number of monomials in a function) of iterative de Bruijn sequence bitrate generators for various generated sequence characteristics, such as linear complexity and autocorrelation function. The profile of the linear complexity of the studied sequences is close to the expected value of the linear complexity, as well as for a truly random sequence.