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Pokročilé metody hledání diskrétního logaritmu / Advanced techniques for calculations of discrete logarithm

Let G be a finite cyclic group. Solving the equation g^x = y for a given generator g and y is called the discrete logarithm problem. This problem is at the core of many modern cryptographic transformations. In this paper we provide a survey of algorithms to attack this problem, including the function field sieve, the fastest known algorithm applicable to the multiplicative group of a finite field. We also discuss the index calculus algorithm and some techniques improving its performance: the Coppersmith's algorithm and the polynomial sieving. The most important contribution of this paper is a C-language implementation of the function field sieve and its application to real inputs.

Identiferoai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:329380
Date January 2013
CreatorsMatocha, Vojtěch
ContributorsPříhoda, Pavel, Jedlička, Přemysl
Source SetsCzech ETDs
LanguageCzech
Detected LanguageEnglish
Typeinfo:eu-repo/semantics/masterThesis
Rightsinfo:eu-repo/semantics/restrictedAccess

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