Dam, M.R. (2015) Discrete logarithm problems in finite fields and their applications in cryptography. Master's Thesis / Essay, Mathematics.
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Abstract
The discrete logarithm problem in finite fields consists of, given two elements a and b in the finite field, solving a^k = b for k. When the size of the finite field is large, solving a discrete logarithm is assumed to be very difficult. The security of several cryptographic systems is based on the fact that this problem cannot be solved in polynomial time. As it is used in cryptographic systems, it has been intensively studied over the last decades. The most efficient algorithms nowadays to solve discrete logarithm problems are the index calculus algorithms. In this thesis, the number field sieve, the function field sieve and a new index calculus algorithm reaching quasi-polynomial complexity are studied.
| Item Type: | Thesis (Master's Thesis / Essay) |
|---|---|
| Degree programme: | Mathematics |
| Thesis type: | Master's Thesis / Essay |
| Language: | English |
| Date Deposited: | 15 Feb 2018 08:03 |
| Last Modified: | 21 Sep 2023 06:51 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/12620 |
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