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Bachelor's Thesis
Author of thesis: Peter Ďuroň
Acad. year: 2025/2026
Supervisor: doc. Ing. Karel Burda, CSc.
Reviewer: doc. Ing. Václav Zeman, Ph.D.
This bachelor thesis examines the experimental analysis of the statistical properties of HMAC-type authentication functions with a focus on their pseudo-randomness. The primary objective involved the design and implementation of a software tool capable of testing selected hash algorithms—MD5, SHA-256, and SHA3-256—within a modified HMAC framework. Five mapping methods for input and output variables were developed to investigate the impact of bit distribution on the resulting uniformity of the outputs. The analysis utilized the bundle method and Pearson’s chi-squared (𝜒2) goodness-of-fit test to monitor the alignment of measured frequencies with the theoretical binomial distribution. The results demonstrate that while SHA-256 exhibits high stability across various configurations, MD5 and SHA3-256 show local statistical anomalies under specific mapping types. Experimentally, the mapping method based on bit expansion and cumulative XOR (M5) proved to be the most robust, effectively eliminating the influence of static padding on the resulting pseudo-randomness. The developed software provides an efficient platform for evaluating authentication functions and identifying potential vulnerabilities in their statistical distribution.
HMAC, pseudo-randomness, hash function, MD5, SHA-256, SHA-3, statistical testing, goodness-of-fit test, mapping, bundle analysis.
Date of defence
16.06.2026
Result of the defence
Defended (thesis was successfully defended)
Grading
B
Process of defence
Student prezentoval výsledky své práce a komise byla seznámena s posudky. Student obhájil bakalářskou práci a odpověděl na otázky členů komise a oponenta.
Language of thesis
Czech
Faculty
Fakulta elektrotechniky a komunikačních technologií
Department
Department of Telecommunications
Study programme
Information Security (BPC-IBE)
Composition of Committee
doc. Ing. Karel Burda, CSc. (předseda) JUDr. Ing. František Kasl, Ph.D. (místopředseda) RNDr. Ing. Pavel Šeda, Ph.D. (člen) Ing. Ľuboš Nagy, Ph.D. (člen) Ing. Vlastimil Člupek, Ph.D. (člen) Ing. Jan Pospíšil, Ph.D. (člen) Ing. Martin Plšek, Ph.D. (člen)
Supervisor’s reportdoc. Ing. Karel Burda, CSc.
Grade proposed by supervisor: B
Reviewer’s reportdoc. Ing. Václav Zeman, Ph.D.
Grade proposed by reviewer: B
Responsibility: Mgr. et Mgr. Hana Odstrčilová