Postupci konstrukcije i optimizacije adicijskih lanaca

master's thesis

• Title (english): Methods for construction and optimization of addition chains
• Author: Josip Užarević
• Mentor: Domagoj Jakobović (mentor)
• Committee member: Domagoj Jakobović (predsjednik povjerenstva)
• Committee member: Marin Golub (član povjerenstva)
• Committee member: Marko Čupić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Electrical Engineering and Computing; Zagreb
• Defense date and country: 2018-02-15, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Computing

Abstract

Uvod rada sadrži opći pregled sadržaja rada te povezuje odnose između pojedinih poglavlja. Sljedeće poglavlje razmatra problem potenciranja velikih brojeva te ga povezuje s pojmom adicijskog lanca. Uz to, opisuje se problematika traženja kratkih adicijskih lanaca te se predlažu dva nasuprotna načela rješavanja problema: deterministički i stohastički. Treće poglavlje opisuje opće načelo rada genetskog algoritma te specifičnosti vezane za adicijske lance, dok se četvrto poglavlje bavi determinitičkim metodama, postojećim te novorazvijenim u okviru rada. Peto poglavlje povezuje ova dva pristupa, a u šestom poglavlju su opisane priprema mjerenja, dobiveni rezultati te analiza rješenja. Naposljetku, u Zaključku su iznesena sva važna zapažanja izvedena tokom izrade programskog rješenja te analize rezultata.

Abstract (english)

The introduction is a general overview of the thesis and interconnects individual chapters. The next chapter discusses the problem of exponentiation of large numbers and links it to the concept of the addition chain. Additionally, the problem of searching of short additional chains is described and two contrasting problem-solving principles are proposed: deterministic and stochastic. Chapter 3 describes the general principle of the genetic algorithm and the specifics associated with the addition chains, while the fourth chapter deals with deterministic methods, existing and newly developed within the thesis. The fifth chapter links these two approaches and in the sixth chapter describes the preparation of measurements, the obtained results as well as the analysis of results. Finally, all the important observations made during the design of the software solution and the results analysis are presented in the Conclusion.

• Keywords: adicijski lanac; optimizacija; eksponenciranje; genetski algoritam; deterministička metoda; binarna metoda; metoda prozora
• Keywords (english): addition chain; optimization; exponentiation; genetic algorithm; deterministic method; binary method; window method
• Language: croatian
• URN:NBN: urn:nbn:hr:168:616439
• Study programme: Title: Computing; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra inženjer/inženjerka računarstva (magistar/magistra inženjer/inženjerka računarstva)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Closed access
• Created on: 2019-03-14 01:48:02