THE METHOD OF CONSTRUCTING A NETHERWRITER CRYPTOSYSTEM BASED ON M-CODES

DOI: 10.31673/2409-7292.2025.031083

Abstract

The article proposes a method for increasing the cryptoresistance of the Niederreiter cryptosystem by using M-codes –
algebrogeometric codes built on elliptic curves. The relevance of developing a mathematical apparatus for designing secure
information networks in the context of growing cyberthreats is substantiated. The purpose of the study is to develop approaches
to the system design of cryptosystems based on structural specifications. The Niederreiter crypto-code construction is
considered, the stability of which is based on the NP-complete problem of decoding a random linear code. The use of
algebrogeometric codes over GF(q) based on elliptic curves (genus g=1) is proposed, which provides improved combinatorial and asymptotic properties of codes. The mathematical apparatus for constructing a code verification matrix using geometric
parameters of curves is presented. It is shown that such an approach allows to increase the number of corrected errors and
increase noise immunity. An equilibrium coding algorithm for forming an error vector is also described. The proposed method
allows to determine the minimum number of processing modules, distribute functions between them and set performance
specifications, which significantly reduces the development time of protection systems. The results have practical significance
for creating survivable information networks, especially in conditions of intensive cyberattacks, in particular during wartime.
Keywords: information protection, cybersecurity, crypto-code system, coding, codegram, crypto-resistance.

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