Abstract of the diploma thesis: This dissertation includes three fields of mathematical science, which are needed to understand random bit generators' randomness testing. These are: cryptography, probability theory and mathematical statistics. In the beginning, this paper describes how to generate pseudorandom bit sequence with good statistical properties (LFSR generator) and how to use it in cryptography. Next, it presents the basic knowledge of probability theory and statistics, which is needed to understand not only the results, but also properties of statistical tests, which are described in the fourth chapter. These pseudorandom bit generators' tests verify basic statistical properties, which an output sequence generator should have, as well as establish the possibility of seed reconstruction from this pseuderandom sequence.
Keywords: cryptography, security, cryptoanalysis, attacks,
stream cyphers, pseudorandom, random bit sequence,
LFSR, Diehard, Crypt-X,
probabylity theory, mathematical statistics, statistical test,
nonparametric tests, chi square test, Kolmogorovs' test.
Math. subj. class (2000): 60F05, 6204, 62G10, 68P25, 94A24, 94A55,
94A60
Povzetek diplomskega dela: Delo vključuje tri področja matematične znanosti, ki so potrebna za razumevanje preverjanja naključnosti generatorjev naključnih zaporedij bitov. To so: kriptografija, verjetnostni račun in statistika. Delo najprej opiše, kako lahko zgeneriramo psevdonaključno zaporedje bitov z lepimi statističnimi lastnostmi (LFSR generator) in na kakšen način ga potem lahko uporabimo v kriptografiji. Nato predstavi osnovno znanje verjetnostnega računa in statistike, ki je potrebno za razumevanje ne le rezultatov, ampak tudi lastnosti posameznih statističnih testov, ki so opisani v četrtem poglavju. To so testi psevdonaključnih generatorjev bitov, ki poleg osnovnih statističnih lastnosti, ki naj bi jih imelo izhodno zaporedje generatorja, preverjajo tudi, ali je iz tega psevdonaključnega zaporedja možna rekonstrukcija semena.