| Title |
Netiesinės algebrinės lygčių sistemos sprendinių skaičiaus analizė / |
| Translation of Title |
Analysis of number of solutions of an algebraic system of non-linear equations. |
| Authors |
Michalkovič, Aleksejus |
| Full Text |
|
| Pages |
49 |
| Keywords [eng] |
matrix power function ; non-linear system of equations ; one-way function ; mathematical modeling |
| Abstract [eng] |
Since the introduction of Diffie-Hellman key agreement protocol in 1976 computer technology has made a giant step forward. Nowadays there is not much time left before quantum computers will be in every home. However it was theoretically proven that discrete logarithm problem which is the basis for Diffie-Hellman protocol could be solved in polynomial time using such computers. Such possibility would make D-H protocol insecure. Thus cryptologists are searching for different ways to improve the security of the protocol by using hard problems. One of the ways to do so is to introduce secure one-way functions (OWF). In this paper a new kind of OWF called the matrix power function will be analyzed. Professor Eligijus Sakalauskas introduced this function in 2007 and later used this function to construct a Diffie-Hellman type key agreement protocol using square matrices. This protocol is not only based on matrix power function but also on commutative matrices which are defined in finite fields or rings. Thus an algebraic non-linear system of equations is formed. The security of this system will be analyzed. It will be shown that we can use matrix power function in cryptography. We will also be analyzing how does the solution of the system depend on system parameters: the order of matrices and a parameter p which defines a finite group Z_p. We will also briefly discuss the usage of this system in real life and the algebraic properties of the suggested OWF. |
| Type |
Master thesis |
| Language |
Lithuanian |
| Publication date |
2010 |
