Abstract
The purpose of the work is to develop a method for monitoring and restoring the integrity of information in secure multidimensional data storage systems that ensures the stability of the systems under consideration under the destructive influences of an intruder and disturbances in the operating environment. Research method: in the course of the research, the scientific and methodological apparatus of the theory of algebraic systems was used in conjunction with the methods of cryptographic information protection and the mathematical apparatus of coding theory to implement the procedures of crypto-code transformations. Models of reliable data storage systems were studied to justify the feasibility of procedures for ensuring the confirmed integrity of the processed information. Results of the study: a method for formalized representation of information in secure multidimensional data storage systems used in the interests of information and analytical systems, which makes it possible to visually describe the developed structures for monitoring and restoring data integrity under the destructive influences of an intruder and disturbances in the operating environment. A mathematical model of the process of monitoring and restoring data integrity based on crypto-code transformations based on the aggregation of cryptographic methods and methods of error-correcting coding is presented. Combining well-known classical solutions to ensure data integrity will reduce the introduced redundancy, as well as expand the functionality of secure information and analytical systems, which consists in confirming the reliability of restoring the integrity of distorted or lost data without additional costs of their repeated control by cryptographic methods. The proposed model takes into account the structure of multidimensional representation of information in the considered data storage systems of information and analytical systems. Scientific novelty: the developed method of parametric synthesis of crypto-code structures for monitoring and restoring the integrity of information in secure multidimensional data storage systems differs from the known ones by obtaining optimal crypto-code structures due to the rational aggregation of cryptographic and code transformations in the parameter space of the considered data storage systems. Crypto-code structures formed on the basis of building multidimensional hash codes and performing transformations in extended Galois fields provide cryptographic control and restoration of information integrity with the possibility of flexible introduction of redundancy and confirmation with cryptographic reliability of information integrity after the restoration procedure
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