RSA algoritam

undergraduate thesis

• Title (english): RSA Algorithm
• Author: Andrea Perica
• Mentor: Andrea Aglić Aljinović (mentor)
• Committee member: Andrea Aglić Aljinović (predsjednik povjerenstva)
• Committee member: Josipa Pina Milišić (član povjerenstva)
• Committee member: Krešimir Pripužić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Electrical Engineering and Computing; Zagreb
• Defense date and country: 2017-07-10, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Computing
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Electrical Engineering

Abstract

Kriptografija je grana primijenjene matematike koja se bavi sigurnošću prijenosa poruka komunikacijskim kanalom.
RSA je asimetrični algoritam s javnim ključem i danas je jedan od najpoznatijih kriptografskih algoritama. Zbog asimetričnosti, osjetno je sporiji i stoga se ne koristi za kriptiranje većih sadržaja. Primjenjuje se kod razmjene zajedničkog tajnog ključa kojim se onda kriptira veći sadržaj.
Funkcije kriptiranja i dekriptiranja e_K i d_K su jednosmjerne te pripadaju modularnoj aritmetici.
Sigurnost ovog kriptosustava temelji se na složenosti faktorizacije velikih brojeva i jednosmjernosti funkcija e_K i d_K. Ključno je na pravilan način odabrati parametre koji čine tajni i javni ključ. Neoprezan korisnik može puno olakšati napadaču probijanje sustava ako ne prati preporuke za odabir parametara.
Kriptoanaliza je grana primijenjene matematike koja se bavi otkrivanjem šifri i postupcima „probijanja“ zaštićenih podataka. Postoji mnogo poznatih vrsta napada na RSA kriptosustav. Svaki od njih se u konačnici oslanja na takav splet okolnosti u kojem je korisnik odabrao lošu kombinaciju parametara. RSA još uvijek nije probijen te ga zasad možemo smatrati sigurnim, iako za to ne postoji matematički dokaz.

Abstract (english)

Cryptography is a branch of applied mathematics whose main focus represents safeness of messages sent through the communication channel.
RSA is an asymmetric public key algorithm and it is one of the most famous cryptographic algorithms nowadays. Due to the asymmetry, it is considerably slower and therefore not used for encryption of larger contents. It is applied in the secret key exchange, which is then used to encrypt larger content.
Encryption and decryption functions, e_K and d_K, are one-way functions that are based on modular arithmethics.
Safeness of this cryptosystem is based on complexity of large number factorization and on the fact that e_K and d_K are one-way functions. The key is to properly choose the parameters that form the secret and public key. An unwary user can make the cracking much easier for the attacker if he does not follow the recommendations when choosing parameters.
Cryptoanalysis is a branch of applied mathematics that deals with the detection of ciphers and methods of cracking encrypted data. There are many common methods for attacking the RSA cryptosystem, but in the end, all of them rely on a combination of circumstances in which the user has chosen a poor set of parameters. RSA still hasn’t been cracked, and for now, it can be considered safe, even though there is no mathematical proof of that.

• Keywords: RSA algoritam; kriptosustav; kriptografija; simetrična kriptografija; asimetrična kriptografija javnog ključa; tajni i javni ključ; prosti broj; Eulerova funkcija; modularna aritmetika; kriptoanaliza
• Keywords (english): RSA algorithm; cryptosystem; cryptography; symmetric cryptography; asymmetric public key cryptography; secret and public key; prime number; Euler’s function; modular arithmethics; cryptoanalysis
• Language: croatian
• URN:NBN: urn:nbn:hr:168:991913
• Study programme: Title: Computing; Study programme type: university; Study level: undergraduate; Academic / professional title: sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva (sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Closed access
• Created on: 2019-03-13 23:49:08