Dependence of the Algebraic Nonlinearity of 4-Functions of Two Variables from the Cryptographic Properties of Their Component Boolean Functions

Abstract

Further development and improvement of the efficiency of ciphers largely depend on the success of solving the problem of synthesizing cryptographic primitives that correspond to the quality criteria both when they are represented by Boolean functions and manyvalued logic functions. Among these most significant cryptographic quality criteria are algebraic nonlinearity, distance nonlinearity, error propagation criterion, and correlation immunity criterion. To solve the problem of synthesizing high-quality cryptographic structures, it is important to research the relationship between the level of cryptographic quality of the resulting functions of many-valued logic and their component Boolean functions. In this paper, we represent the results of the research on the algebraic nonlinearity of 4-functions of two variables when they are constructed based on two Boolean functions with given cryptographic quality parameters. The results obtained can be considered as a theoretical basis for improving existing and developing new methods for synthesizing cryptographic primitives, which are characterized by the high cryptographic quality of both component Boolean functions and component many-valued logic functions.