Combining and filtering functions based on the nonlinear feedback shift registers

Strong cryptography of stream ciphers is determined, among other things, by the ability of a generated pseudorandom sequence to resist analytical attacks. One of the main components of the pseudorandom stream cipher sequence generating algorithm are Boolean functions for combining and filtering. The paper considers the possibility of applying nonlinear-feedback shift registers that generate a maximum length sequence as a combining or filtering function. This work examines the main indicators of cryptographic strength of such functions, as: balance, the prohibitions presence, correlation immunity and nonlinearity. The study analyzes and demonstrates correlation experimental immunity and nonlinearity values for all nonlinear feedback shift registers, that generate a maximum length sequence, for register sizes up to 6 cells inclusively, and registers sizes up to 9 cells inclusively with algebraic degree of the polynomial under 2. The possibility of optimizing the process of selecting the Boolean functions according to the criteria of maximum correlation immunity and nonlinearity with various algebraic degree and minimization of the number of monomials in the polynomial are studied.