Development of a Secure Data Transmission System over an Open Communication Channel Based on Concatenated Codes

Student: Shuklin Alexander

Faculty: HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE)

Educational Programme: Infocommunication Technologies and Systems (Bachelor)

Year of Graduation: 2021

The work is a project of the practical implementation of coding based on concatenated codes with a theoretical study of existing literary sources in the field of knowledge of coding theory. The object of development when writing the work is the class of error-correcting codes that control errors, in the form of concatenated codes. The aim of the thesis is to develop a system for secure data transmission over an open channel. The tasks include: mastering the coding algebra, studying the principles of constructing algebraic codes and cryptosystems, the practical implementation of the system under study. The system based on concatenated codes consists of coding and encryption, coding is represented by two sequentially applied coding procedures, of which outer coding is performed by coding with Reed-Solomon codes, and inner convolutional coding, encryption is performed using the McEllias scheme. A mathematical description of the proposed system is given. Also presented is a software implementation according to the given mathematical model using the MatLab software product. A positive result of the thesis is the reduction in the length of the public key and the noise immunity of the system in comparison with the classical implementation of the McEllias cryptosystem based on Goppa codes. Keywords: coding, coding algebra, concatenated codes, McEllias cryptosystem, Reed-Solomon codes, convolutional codes.

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