Heuristic methods of gradient search of cryptographic Boolean functions that satisfy the required properties of balance, nonlinearity, autocorrelation, and other stability indicators are considered. The proposed method of gradient descent is investigated, in particular, estimates of nonlinearity and correlation immunity of the synthesized Boolean functions are given. A method for evaluating the computational efficiency of gradient search methods is proposed, based on the construction of sample (empirical) distribution functions, which characterize the probability of the formation of Boolean functions with persistence indicators not lower than those required. As an indicator of computational efficiency, we propose the average number of attempts that need to be performed using the heuristic method to form a cryptographic Boolean function with the required properties. It is shown that the proposed gradient descent method allows the formation of cryptographic functions with the required durability indicators in fewer steps. The results of investigations of the cryptographic properties of the formed Boolean functions in comparison with the best known assessments are given.

Linear block noise-proof codes constructed according to algebraic curves (algebraic geometric codes) are considered, their design properties are evaluated, algorithms of construction and decoding are studied. The energy efficiency of the transmission of discrete messages by M-ary orthogonal signals in the application of algebraic geometric codes is studied; the achievable energy gain from the use of noise-immune coding is estimated. It is shown that in discrete channels without memory it is possible to obtain a significant energy gain, which increases with the transition to long algebraic geometric codes constructed by curves with a large number of points with respect to the genus of the curve. It is established that the computational complexity of implementing algebraic geometric codes is comparable to other known noise-resistant codes, for example, the Reed-Solomon codes and others. Thus, high energy efficiency in combination with acceptable computational complexity of implementation confirm the prospects of algebraic geometric codes using in modern telecommunication systems and networks to improve the noise immunity of data transmission channels.

A new direction of technical steganography related to the concealment of information in the process of layer-by-layer creation (cultivation) of a solid-state object using various 3D-printing technologies is investigated. Information data are converted into a digital 3D-model of elementary physical objects that are placed inside this 3D-model of the container product. After printing, a solid object physically contains the hidden information that cannot be deleted or distorted without damaging the container product. In addition, the applied methods do not reduce the operational, aesthetic and any other properties of the finished product. The proposed complex is invariant to the method of layer-by-layer growing, that is, it can be equipped with any peripheral devices of 3D-printing of various manufacturers with any materials and principles of layer-by-layer creation.

The code-based schemes, which were submitted to the contest of post-quantum crypto algorithms NIST PQC, are studied in this work. The general characteristics of the algorithms are explored and basic properties and parameters are estimated. A comparative analysis of the electronic digital signature schemes, public-key cryptosystems and key encapsulation schemes are carried out according to the criteria of speed and length of the main cryptographic parameters.