Davies-Batista, Dewi, Mr. (2021) Efficient and secure elliptic curves. Bachelor's Thesis, Mathematics.
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Abstract
In this paper, we study various factors that affect the efficiency of elliptic curve cryptosystems for fixed security levels of 128, 192 and 256 bits of security, with a focus on elliptic curves over finite fields GF(p) with p elements, where p is a prime number. Since elliptic curve cryptography involves many algebraic operations over the field GF(p), it is important to choose p for which modular arithmetic is relatively efficient. The most important factor regarding efficiency is the model of the curve. Group operations such as addition, inversion, and doubling are more effective in some models. We introduce the Weierstrass model, the (twisted) Edwards model, the Montgomery model and the Hessian model. We then compare their cryptographic efficiency and security. We mainly focus on the 2016 paper of Bos, Costello, Longa and Naehrig, in which the authors present efficient and secure elliptic curve families for each model. After this analysis, we present explicit examples of elliptic curves suitable for cryptography, in terms of efficiency and security.
| Item Type: | Thesis (Bachelor's Thesis) |
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| Supervisor name: | Djukanovic, M. and Kilicer, P. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 09 Jul 2021 12:06 |
| Last Modified: | 09 Jul 2021 12:06 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/25058 |
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