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.