Algebraic immunity of symmetric ciphers

Abstract

A key component of modern symmetric ciphers are nonlinear blocks (non-linear substitutions, substitution tables, S-boxes) that perform functions of hiding statistical links of plaintext and ciphertext, mixing and disseminating data, and introducing nonlinearity into the encryption procedure to counter various crypto-analytical and statistical attacks. The effectiveness of a symmetric cipher, its resistance to the majority of known cryptographic attacks and the level of information technology security provided by it directly depend on the performance of nonlinear nodes (balance, nonlinearity, autocorrelation, correlation immunity etc.). In this paper various methods for  calculating algebraic immunity are examined, their interrelation is studied, and the results of comparative studies of the algebraic immunity of nonlinear blocks of the most well-known modern symmetric ciphers are presented.