Based on the properties of the class of residues in the article, a mathematical model of the process of tabular implementation of modular multiplication was synthesized, for both positive and negative numerical ranges of information processing by means of integer information processing. This model is recommended for practical application in the development of methods and algorithms for rapid processing of cryptographic information. Finding ways to simplify the structure of the table operating device integer information processing has led to the need to improve the mathematical model, methods and algorithms for modular operations, which increase the efficiency of the use of table arithmetic in the class of residues. A feature of the implementation of this model is the possibility of reducing the number of equipment operating device integer information by reducing the (50-70)% of logical elements "And" in the nodes of the table permanent storage device, directly implement the operation of modular multiplication by arbitrary mi module residual class. This is possible by using the symmetry properties of the aibi (mod mi) implementation table of the modular multiplication operation.