Algoritem RSA

diplomsko delo

Niki Veček (Author), Uroš Milutinović (Mentor)

Abstract

Komuniciranje je velik del našega vsakdana, s tem pa se pokaže tudi potreba po varnem komuniciranju. Ljudje vsakodnevno uporabljamo bankomate, trgovske kartice popustov, pošiljamo elektronsko pošto, plačujemo račune preko spletnega bančništva, preverjamo in urejamo osebne podatke preko spletnih strani državnih uprav in podobno, pri tem pa se ne sprašujemo, kam in kako pošiljamo naše osebne podatke. Vsak tak sistem temelji na svojem kriptosistmu, ki omogoča varno komunikacijo, ne da bi njegovi uporabniki morali za karkoli skrbeti. Eden najbolj zanesljivih je RSA kriptosistem, ki je podrobneje predstavljen v diplomskem delu. Teorija števil, ki stoji za RSA kriptosistemom, obravnava področja praštevil, deljivosti in kongruenc, ki jih predstavimo v uvodu diplomskega dela. Sledijo drugi matematični pojmi, ki so tesno povezani z RSA: testi praštevilskosti, generiranje velikih praštevil, faktorizacija števil in diskretni logaritmi. Za konec so predstavljeni nekateri bolj znani napadi na RSA kriptosistem, v okviru katerih preverimo, kdaj je RSA ranljiv in kaj so njegove šibke točke.

Keywords

diplomska dela;matematika;algoritem RSA;kriptografija;šifriranje;dešifriranje;diskretni logaritem;

Data

Language:	Slovenian
Year of publishing:	2012
Source:	Maribor
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[N. Veček]
UDC:	51(043.2)
COBISS:	19346952
Views:	2103
Downloads:	207
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	RSA Algorithm
Secondary abstract:	Communication is a big part of our everyday lives, and we can clearly see the need for secure communication. We daily use ATMs, discount cards and e-mails, we pay bills via online banking systems, and manage personal information through the national administration websites, but we don't ask ourselves where and how we send our personal data. Each above mentioned system is based on its own cryptosystem that allows secure communication, and users don't have to worry about anything. One of the most reliable cryptosystems is RSA cryptosystem which is described in the following thesis. Number theory behind the RSA cryptosystem discuses the areas of prime numbers, divisibility and congruences, and it's presented in the introduction of the thesis. Other mathematical concepts follow which are closely related to the RSA: primality tests, generation of large prime numbers, factorization and discrete logarithms. In conclusion we present some of the more famous attacks on the RSA cryptosystem, under which we see when is the RSA most vulnerable and what are its weaknesses.
Secondary keywords:	RSA algorithm;cryptography;encryption;decryption;prime numbers;factorization;congruence;discrete logarithm;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	78 f.
Keywords (UDC):	mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID:	992006