Generatori pseudo-nasumičnih brojeva

undergraduate thesis

• Title (english): Pseudorandom number generators
• Author: Blanka Matijević
• Mentor: Ivan Dunđer (mentor)
• Committee member: Sanja Seljan (predsjednik povjerenstva)
• Committee member: Ivan Dunđer (član povjerenstva)
• Committee member: Vjera Lopina (član povjerenstva)
• Granter: University of Zagreb; Faculty of Humanities and Social Sciences; (Department of information and Communication sciences); Zagreb
• Defense date and country: 2023-09-14, Croatia
• Scientific / art field, discipline and subdiscipline: SOCIAL SCIENCES; Information and Communication Sciences

Abstract

U radu su opisane metode kojima se može generirati niz pseudo-slučajnih brojeva. Pojašnjeni generatori uključuju metodu sredine kvadrata, LCG, LFG, Mersenne Twister te ANSI X9.17 generator. Prikazana je i programska implementacija LCG i LGF generatora. Rezultati LCG programa testirani su vizualnim testovima. Korišteno je više setova parametara od kojih su neki uzeti od uvriježenih generatora, a neki su proizvoljno odabrani. Jedan set proizvoljno odabranih parametara se pokazao lošim, a drugi je dao zadovoljavajuće rezultate. Opisani su i neki kriptografski sigurni generatori (Blum Blum Shub, CryptMT te RSA generator). Pojašnjeni su problemi generatora pseudo-slučajnih brojeva u kontekstu kriptografske sigurnosti. Rad pruža povijesni pregled slučajnih brojeva i njihovih generatora. Opisano je što čini niz brojeva slučajnim i koje su razlike između istinski slučajnih i pseudo-slučajnih brojeva. Za obje skupine brojeva pojašnjena su njihova ograničenja i prednosti. Isto je napravljeno i za generatore istinskih te pseudo-slučajnih brojeva. Nadalje, prikazane su i razne primjene generatora pseudo-nasumičnih brojeva te su dani konkretni primjeri tih primjena.

Abstract (english)

This thesis describes methods that can be used to generate a sequence of pseudo-random numbers. Generators that are explained include middle square method, LCG, LFG, Mersenne Twister and ANSI X9.17 generator. The program implementation of the LCG and LGF generator is also shown. The results of the LCG program were tested with visual tests. Several sets of parameters were used, some of which were taken from established generators, and some of which were arbitrarily selected. One set of arbitrarily chosen parameters turned out to be bad, and the other gave satisfactory results. Some cryptographically secure generators (Blum Blum Shub, CryptMT and RSA generator) are also described. The problems of pseudo-random number generators in the context of cryptographic security are clarified. The thesis provides a historical overview of random numbers and their generators. It describes what makes a sequence of numbers random and what the differences are between truly random and pseudorandom numbers. For both groups of numbers, their limitations and advantages are explained. The same was done for true and pseudorandom number generators. Furthermore, various applications of pseudo-random number generators are presented and the thesis provides specific examples of these applications.

• Keywords: pseudo-slučajni brojevi; PRNG; LCG; LFG; kriptografska sigurnost
• Keywords (english): pseudorandom numbers; PRNG; LCG; LFG; cryptographic security
• Language: croatian
• URN:NBN: urn:nbn:hr:131:983195
• Study programme: Title: Information Sciences; Study programme type: university; Study level: undergraduate; Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) informacijskih znanosti (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) informacijskih znanosti)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2023-09-15 20:22:01