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Investigation of the corrective ability of modular codes used in AES systems
Authors
	Provornov I.A.
Date of publication
	2022
DOI
	10.31114/2078-7707-2022-4-136-141
Abstract
	It is known that at present, high requirements are placed on the reliability of cryptographic systems (including SPN systems). As a rule, the fulfillment of these requirements is achieved through the implementation of methods that significantly increase circuit costs, which is their undoubted disadvantage. A promising direction for solving this problem is the introduction of corrective modular codes of the polynomial system of residue classes in SPN systems. The article analyzes the functioning of SPN-systems, defines their main components and procedures. The task of increasing the reliability of the SPN cryptosystem can be reduced to increasing the reliability of the execution of the SubBytes and MixColumns procedures. It is proposed to introduce the assumption that errors occur when performing mathematical operations of addition and multiplication. Then there remains the need to modernize the SubBytes and MixColumns procedures. The article discusses in detail the mathematical apparatus that makes it possible to implement error correction, including the reasons for replacing the polynomial used in the standard AES algorithm with alternative ones. The article describes the results of using modular polynomial codes in the SubBytes and MixColumns procedures of SPN systems, describes the principles of forming the tables used, investigates the effectiveness of the corrective ability of such codes, and evaluates the gain relative to the classical version of the construction of cryptosystems. When conducting research, the probability of failure-free operation is used as an indicator of reliability. It is proved that the use of corrective codes in a polynomial system of residue classes increases the overall reliability of the system. As a promising area of research, the development of circuit solutions for constructing a block for detecting and correcting errors in SPN cryptosystems is determined.
Keywords
	SPN-cryptosystems, reliability, modular arithmetic, Galois fields.
Library reference
	Provornov I.A. Investigation of the corrective ability of modular codes used in AES systems // Problems of Perspective Micro- and Nanoelectronic Systems Development - 2022. Issue 4. P. 136-141. doi:10.31114/2078-7707-2022-4-136-141
URL of paper
	http://www.mes-conference.ru/data/year2022/pdf/D061.pdf