Public key cryptosystems on Boolean functions

The objective of this conference paper is to present in Russian a brief review of contents of the recent article by authors (see Prikladnaya Diskrenaya Matematika, 2018, no. 40, pp. 23–33) where a cryptographic system including both public-key encryption and digital signature schemes has been constructed with the help of non-typical for such cryptosystems mathematical means, namely the invertible systems of Boolean functions which are in turn produced from bijective vector Boolean functions by applying the permutation and negation operations to their arguments and coordinates. Besides the cryptosystem definition, the article contains the descriptions of cryptanalysis problems for both encryption and signature schemes in the cryptosystem, their solutions with known plaintext attacks, a general scheme for constructing such attacks on the base of linearization set method for solving a nonlinear system of Boolean equations, specific attacks constructed according to this scheme for all possible types of a private key, and asymptotic estimates for computational complexity of these attacks. All the mentioned results, excluding the specific attacks in plural particular cases, are described in this review.