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The use of information technologies in the development of cryptographic and algebraic algorithms


Author: Maliutina Nadejda
Degree:doctor of physics and mathematics
Speciality: 01.05.04 - Mathematical modelling, mathematical methods, software
Year:2023
Scientific adviser: Andrei Corlat
doctor, associate professor (docent)
Institution: Moldova State University

Status

The thesis was presented on the 21 April, 2023 at the meeting of the Scientific Council and now it is under consideration of the National Council.

Abstract

Adobe PDF document – 1.07 Mb / in romanian
Adobe PDF document – 1.16 Mb / in english
Adobe PDF document – 1.24 Mb / in russian

Thesis

CZU 519.21:004.421(043.3)

Adobe PDF document 3.81 Mb / in russian
217 pages

Keywords

Markovski algorithm, quasigroup, left and right quasigroup, translation, plaintext, ciphertext, attack, key, encryption, decryption

Summary

Thesis structure: the thesis consists of Introduction, four main chapters, general conclusions and recommendations, bibliography of 201 sources, and 3 annexes. The thesis contains 145 pages of the main text, one figure, and 71 tables. The obtained results were published in 21 scientific works.

The purpose of the thesis: construction of new modifications and improvement of already developed cryptographic algorithms and their cryptanalysis.

The objectives of the work: 1. Development of an effective cryptographic algorithm based on the Markovski algorithm using -ary groupoids; 2. Writing programs that perform the work of the constructed algorithms; 3. Carrying out attacks on all built ciphers; 4. Comparative analysis of the attacks carried out; 5. Finding texts of the minimum length for all investigated types of attacks.

The scientific novelty and originality: the main results of the work are new and original. They are a continuation of previous research in this area. Algorithms were developed and generalized that allowed us improving the work of the classical Markovski algorithm, the attacks on the constructed ciphers were studied, and the degree of resistance of these ciphers was shown.

The important scientific problem being solved in the research:

it consists in the development of new generalizations of the classical algorithm, which contribute to an increase in the resistance of the constructed cipher to known types of attacks.

The theoretical significance of the thesis: is determined by obtaining new algorithms and ciphers built using non-associative structures such as -ary groupoids. New generalizations of coding algorithms using left and right quasigroups, -ary groupoids invertible in one fixed place are developed.

The applicative value of the thesis: it lies in the use of the obtained results in coding theory and cryptanalysis.

The implementation of the scientific results: the results obtained can be used in scientific research related to data coding, study of the efficiency of information presentation, and data cryptanalysis. They can also be used in the design of an elective course for university students related to the study of cryptology on abstract algebraic structures.