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.
| Identifer | oai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:329380 |
| Date | January 2013 |
| Creators | Matocha, Vojtěch |
| Contributors | Příhoda, Pavel, Jedlička, Přemysl |
| Source Sets | Czech ETDs |
| Language | Czech |
| Detected Language | English |
| Type | info:eu-repo/semantics/masterThesis |
| Rights | info:eu-repo/semantics/restrictedAccess |
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