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Chapter 2

CODE-BASED PUBLIC-KEY CRYPTOSYSTEMS BASED ON ALGEBRAIC CODING:

THE CURRENT STATE, THE EXISTING CONTRADICTIONS AND PROSPECTS OF
PRACTICAL USE FOR THE POST-QUANTUM PERIOD

Alexandr A. Kuznetsov

Department of Information Systems and Technologies Security, V.N. Karazin Kharkiv National

University, Svobody sq., 4, Kharkov, 61022, Ukraine;
kuznetsov@karazin.ua

Sergii V. Kavun

Department of Information Technologies, Kharkiv Educational and Research Institute of the
University of Banking, Peremogy av. 55, Kharkiv, 61174, Ukraine;

kavserg@gmail.com

Vyacheslav V. Kalashnikov

Department of Systems & Industrial Engineering, ITESM, Campus Monterrey,

Av. Eugenio Garza Sada 2501 Sur, Monterrey, N.L., 64849, Mexico;
kalash@itesm.mx

Nataliya I. Kalashnykova

Department of Physics and Mathematics (FICA), Universidad Autónoma de Nuevo León (UANL),
Avenida Universidad S/N, San Nicolás de los Garza, Monterrey, N.L., 66450, Mexico;

nkalash@einstein.fcfm.uanl.mx

Abstract

Code-Based Public-Key Cryptosystems based on algebraic coding were been considered in this chapter. In addition, the
current state, the existing contradictions and prospects of practical use for the post-quantum period were been studied.
The authors have proposed new scheme of crypto-transformation that significantly exceeds the relative speed of
information transmission. An advantage of the proposed scheme compared with the well known the McEliece and
Niederreiter schemes has shown.

Keywords: public-key cryptosystems, post-quantum cryptography, code-based cryptography, methods and algorithms for
the information coding theory, combinatorial optimization and problems

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