DEVELOPMENT OF AUTHENTICATION METHODS BASED ON MODIFIED CODE THEORETICAL SCHEMES

DOI: 10.31673/2409-7292.2025.041216

Abstract

Development of authentication methods is a key element of modern cryptographic systems used to ensure data
transmission security, digital signatures and protection of confidential information. One of the most common approaches is the
use of traditional RSA and ECC algorithms standardized in NIST recommendations[1,2]. These algorithms are characterized
by high cryptographic stability in classical computing environments and flexibility due to support for various mathematical
structures, which makes them in demand in government and commercial information protection systems. The analysis showed
that, despite a number of advantages, RSA and ECC have significant disadvantages. Among them are vulnerability to quantum
attacks, in particular Shor`s algorithm, increased computational costs for large key data and critical dependence on the quality
of random data. The most significant problem is the lack of resistance to quantum computing, which complicates the assessment
of their characteristics and reduces the predictability of work in critical cryptographic applications. To eliminate the identified
limitations, two variants of authentication methods based on modified McEliece and Niederreiter code-theoretic schemes are
proposed. Algebrogeometric codes are included in their structure, which allows us to formally determine the minimum cycle
length of the sequence and ensure its guaranteed period. Additional algorithmic procedures complicate the analysis of the
internal states of the methods, increasing their cryptoresistance. The article presents structural diagrams of the proposed
methods, describes the stages of their functioning and key analytical dependencies that determine the process of forming
authentication data. The developed approaches preserve the cryptographic stability of traditional schemes, while ensuring postquantum security and improved capabilities for managing authentication parameters. The results obtained can be used in the
creation of software and hardware means of information protection and cryptographic protocols that require high reliability and
predictability of authentication systems.
Keywords: authentication methods, McAlice code-theoretic schemes, Niederreitercode-theoretic schemes, information
protection, cybersecurity, threats

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