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Information security and encryption methods based on sets of multi-ary relations


Author: Zgureanu Aureliu
Degree:doctor of physics and mathematics
Speciality: 01.01.09 - Mathematical cybernetics and operation research
Year:2011
Scientific adviser: Sergiu Cataranciuc
doctor, associate professor (docent), Moldova State University
Scientific consultant: Mihai Bulat
doctor, associate professor (docent), Moldova State University
Institution: Moldova State University

Status

The thesis was presented on the 18 November, 2011
Approved by NCAA on the 22 December, 2011

Abstract

Adobe PDF document0.47 Mb / in romanian

Keywords

encryption system, multidimensional matrix, prime number, Boolean function, q-valent function, partial derivative, sets of multi-ary relations

Summary

The thesis contains the introduction, three chapters, conclusions and recommendations, the bibliography (126 titles) and 2 annexes. It consists of 160 pages, from which 121 pages of the main part, including 62 figures and 24 tables. Obtained results are published in 13 scientific papers. Keywords: encryption system, multidimensional matrix, prime number, Boolean function, q-valent function, partial derivative, sets of multi-ary relations.

The area of study refers to the research and elaboration of new information encryption algorithms. Theoretical basis of these algorithms include large prime numbers, multidimensional matrixes, polynomial equations with undetermined coefficients, Boolean and q-valent functions. The aim of this work consists in following: elaboration of a deterministic algorithm for generating of large prime numbers, researching of multidimensional matrices for use their in cryptography, study of Boolean functions and their implementation in elaboration of encryption algorithms with reduced resources, description of the theoretical aspects of the proposed algorithms, software development and presentation of evaluative and comparative results.

The scientific novelty and originality of obtained results consist in presentation of new methods of data protection using encryption. In this thesis are presented four new methods of encryption. For one of these methods is developed a deterministic algorithm for generate large prime numbers, which allows us to place it among methods of encryption with high security. An important feature of the presented methods in the thesis is to apply multidimensional matrices (meaning direct generalization of the usual two-dimensional matrices) in the development of three of these algorithms. Another feature is the application of Boolean functions and functions of q-valent logic. These functions are defined by subsets of the column to perform some simple operations on them, one of the basic operations is calculation of partial derivatives of these functions. Important scientific problem solved. In this thesis are proposed new effective methods of encryption, that exceed current methods by a number of parameters (time of encryption, volume memory, security algorithm etc). Is developed the theoretical basis for these methods based on new properties of the Boolean functions, functions of q-valent logic and of multidimensional matrices.

The theoretical signification consists in: in the development of the methods of encryption, exposed in the thesis were obtained new theoretical results related to the study of multi-ary relations theory, properties of multidimensional matrices and Boolean functions. The results related to the implementation of the functions of q-valued logic represents interest. Obtained encryption methods ensure a high degree of security and reliability of the system of information encryption.

The practical value of the work: for every proposed method has been developed a program. Elaborated software is simple, efficient and does not require considerable computing resources.