Pronalaženje balansiranih maksimalno nelinearnih Booleovih funkcija

undergraduate thesis

• Title (english): Searching for balanced Boolean functions with maximal nonlinearity
• Author: Magdalena Mucić
• Mentor: Marko Čupić (mentor)
• Committee member: Marko Čupić (predsjednik povjerenstva)
• Committee member: Vjeko Kužina (član povjerenstva)
• Committee member: Eugen Vušak (član povjerenstva)
• Granter: University of Zagreb; Faculty of Electrical Engineering and Computing; Zagreb
• Defense date and country: 2021-07-07, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Computing

Abstract

Booleove funkcije jedan su od najvažnijih elemenata mnogih kriptografskih algoritama te su razlog zašto su mnogi od njih vrlo efektivni. Posebna svojstva Booleovih funkcija koja su vrlo bitna za kriptografske algoritme su nelinearnost, balansiranost i korelacijska otpornost. Pomoću tih svojstva kriptografski algoritmi postaju sigurniji.
U okviru ovog rada definirane su Booleove funkcije, opisani načini zapisivanja Booleovih funkcija te su opisana njihova svojstva s povećanom pažnjom posvećenom maksimalnoj nelinearnosti i balansiranosti. Uz to, implementiran je genetski algoritam za pronalaženje maksimalno nelinearnih balansiranih Booleovih funkcije, eksperimentalno je vrednovan te su navedeni najbolji rezultati.

Abstract (english)

Boolean functions are one of the most important elements of many cryptographic algorithms and are the reason why many of them are so efficient. Special properties of Boolean functions that are very important for cryptographic algorithms are nonlinearity, balance and correlation resistance. With these properties, cryptographic algorithms become more secure.
This paper defines Boolean functions, describes the ways of defining Boolean functions and describes their properties with increased attention paid to maximum nonlinearity and balance. In addition, a genetic algorithm for finding maximally nonlinear balanced Boolean functions was implemented, experimentally evaluated and the best results were listed.

• Keywords: Booleove funkcije; nelinearnost; balansiranost; genetski algoritam
• Keywords (english): Boolean functions; nonlinearity; balanced; genetic algorithm
• Language: croatian
• URN:NBN: urn:nbn:hr:168:664452
• 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: 2023-01-14 21:16:28