Nonlinear functions of complication for symmetric stream ciphers

Currently, the nonlinear Boolean functions are being investigated very actively around the world. However, many open questions remain in this area. The theory of nonlinear Boolean functions suitable for use in robust cryptographic algorithms is largely incomplete. Despite the presence of numerous publications on these topics, many issues related to the interrelation of design characteristics affecting the performance of the generator and its cryptographic characteristics are still open. The generation of a special type of sequences, called de Brain sequences, with minimal hardware and software costs, the rationale for their use as non-linear functions of the complexity of stream encryption systems, is the main theme of this work. The paper presents estimates of cryptographic indicators of nonlinear complexity functions of iterative bit sequence generators with various characteristics of the generated sequence, such as linear complexity and autocorrelation.