Correlation immunity of three-valued logic functions

The current stage in the development of cryptography is characterized by attention of researchers to the methods of many-valued logic. Of particular importance are the methods of three-valued logic, which are used in quantum cryptography, as well as in three-valued cryptographic algorithms with an increased level of cryptographic strength, implemented on binary computers. This circumstance leads to the need for further improvement of methods for constructing of high-quality cryptographic primitives. This paper is devoted to the generalization of definition of the correlation immunity of three-valued logic functions in the context of the properties of matrices of correlation coefficients of S-boxes built on their basis. The paper proposes methods for the synthesis of complete classes of 3-functions of length N = 9, the output of which does not depend on the input variable x (1) or x (2), as well as the full set of correlation immune 3-functions. The relationship between the introduced criterion of the correlation immunity of 3-functions and the criterion for the absence of a correlation interconnection between the output and input vectors of S-boxes of length N = 9 is also established.