A key exchange method based on Boolean functions as subsets of columns

Abstract

The representation of Boolean functions as subsets of columns and one of its possible applications is discussed in this paper. Depending on the area of application, different Boolean function representations are used. Boolean functions as subsets of columns were investigated by the author together with other colleagues and published in many scientific works, which allow to apply this kind of representation in different domains. Based on the properties of the subsets of columns of Boolean functions, an algorithm of encryption key exchange between two or more entities is proposed. The algorithm consists of a long-lived secret key which consist of a family of n Boolean functions. The session key kses is defined by a subset of column of the partial derivative of one of the Boolean functions, randomly chosen from the secret key. The parameters that uniquely determine the secret key are generated randomly by one of the parties and may be sent nonencrypted to all other who are involved in the communication session. The main advantage of the algorithm is that it doesn’t use public key cryptography, which is much more computationally demanding than calculation of the particular subset of column. The main challenge of the algorithm is choosing the correct type of functions that have as diverse subsets of columns as possible. The parameters of the table of partial derivatives of the Boolean functions also are very important and they need to best suit our purpose. These two particularities need further investigations. CZU: 330.4:517.987.3; JEL: C61, C63; DOI: https://doi.org/10.53486/cike2022.39