Improvement of modern data exchange applications increases the complexity of cybersecurity. This leads to most applicable low-cost cryptographic algorithms becoming ineffective in the near future. On the other hand, CET encryption offers a great opportunity for development of the low-cost cryptography. The following article analyzes previously published results of CET-operations modeling, which serves as the foundation of CET encryption. The CET operations mentioned above use elementary functions as their basis. The results of our analysis allow to conclude that elementary functions of data-controlled operations have not been researched in the past. The primary goal of this article is to research these elementary functions of data-controlled operations and develop a method suitable for synthesis of a group of elementary functions of data-controlled operations. This can assist in automating the process of creating CET operations with defined attributes. This article proves that known discrete models of elementary functions of data-controlled operations do not represent their content and usage specifications during creation of CET operations. We suggest using discrete and algebraic presentation for modeling elementary functions data. The results of our analysis of the synthesized models of elementary functions of data-controlled operations allow us to develop a proper method of their synthesis. This method is adapted for usage in the automated systems of CET-operations modeling. We also provide examples of models of CET operations created based on elementary functions of data-controlled operations. The aforementioned method for synthesis of a group of elementary functions of data-controlled operations allows expanding possibilities for generating these elementary functions within the automated system used for research and creation of CET operations. Presented scientific results can be used for experimental modeling of CET operations, while the implementation algorithms of such operations will be defined by the operations themselves, as well as transformed data. Utilization of these operations allows modification of cryptographic algorithms controlled by encrypted data.

The object of the study is the processes of building groups of symmetric double-operand operations of cryptographic coding of information. The subject of the study are features of the implementation of a generalized method of synthesis groups of symmetric two-operand operations of cryptographic coding information for "lightweight cryptography". The purpose of this work is to investigate the process of building and implementing a method of synthesis of groups of symmetric multibit double-operand operations of information cryptographic coding to provide automation for finding ways to increase the variability, and stability of lightweight cryptoalgorithms. The following tasks are solved in the article: to determine the mathematical group of single-operand operations, on the basis of which the realization of the method of synthesis of groups of symmetric double-operand operations of cryptographic coding will be presented; to offer the search technology of symmetric double-operand operations; to evaluate power of synthesized groups of operations, and their influence on variability and stability of " lightweight cryptography" algorithms. The following results were obtained: the technology for determining symmetric double-operand operations, which will be the basis for the synthesis of a group of symmetric double-operand operations, was proposed. A method for synthesizing groups of symmetric double-operand cryptographic information coding operations for block encryption systems was proposed and implemented. On the example of module-two addition with correction and the use of three-digit single-operand operations, the practical implementation of this method was shown. Based on the synthesized operations and the given quantitative characteristics of the set of single-operand operations, the power of synthesized groups of operations and their influence on the variability and stability of "lightweight cryptography" algorithms were evaluated. Conclusions: the proposed and implemented method of synthesis of groups of symmetric double-operand operations of cryptographic coding information allows to provide the possibility of increasing the variability of lightweight crypto-algorithms. Synthesis of symmetric cryptographic coding operations belonging to different mathematical groups provides increase of algorithm's crypto stability. Application of synthesized cryptographic coding operations leads to significant increase of variability of cryptoalgorithms and their complexity.

The main results of research and synthesis of a group of two-operand two-bit symmetric operations of righthanded addition by module four by using a group of two-bit single-operand cryptocurrency operations are presented in the article. Synthesis of a group of operations on the basis of operation of right-handed addition by module four has not previously been investigated. It is established that the constructed group of operations of cryptographic transformations differs from cryptocurrency groups built on the basis of addition by module two and classic left-handed addition by module four. The use of a new synthesized group allows to improve the quality of streaming encryption by increasing the variability of cryptographic transformations. It is revealed that up to twenty-four substitution tables will be used due to symmetrical synthesized operations in streaming encryption systems

The subject matter of the article is the scientific and methodological apparatus for constructing and implementing information-driven SET-operations. The goal of the work is to construct a model for the synthesis of symmetric two-operand SET-operations that allow permutation of operands and to determine the restrictions on their use in the development of low-resource stream ciphers. The following tasks are solved in the article: a model for the synthesis of symmetric two-operand SET-operations that allow permutation of operands is developed; restrictions on the use of this model are determined, which guarantee the construction of symmetric two-operand SET-operations that allow permutation of operands; it is shown that a pseudo-random change in the operating modes of the cryptographic system significantly complicates the processes of cryptanalysis of ciphergrams; modeling of SET-operations based on duplication of single-operand two-bit SET operations is carried out; the technology for constructing two-operand SET-operations based on duplication is applied to obtain a set of two-operand SET-operations. Methods of discrete mathematics, Set-theory and situational management have been introduced. Achieved results. Synthesized on the basis of this model of SET-operations allow changing the operating mode of stream cryptographic systems from symmetric to asymmetric when permuting operands in the operation. At present, the forefront of modern world experience in cryptographic science is a low-resource cryptographic system. Low-resource cryptography allows ensuring sufficiently stable cryptosystem performance with significant limitations on computational, mass-dimensional, cost and energy resources of the object of interest. One of the most relevant areas of further development of low-resource cryptography is considered to be cryptographic coding. In the process of cryptographic coding, cryptographic coding operations are implemented. The selection of operations is carried out under the control of a pseudo-random sequence, which is implemented by a cryptographic algorithm. Conclusions. A model for the synthesis of symmetric two-operand SET-operations that allow permutation of operands has been developed. Restrictions on the use of this model have been determined, which guarantee the construction of symmetric two-operand SET-operations that allow permutation of operands. The achieved results can be useful for the construction of low-resource stream encryption systems. Pseudo-random change of the operating modes of the cryptographic system significantly complicates the processes of cryptanalysis of ciphertexts.