Pociene, Jurgita. Informatics Master’s Final Thesis. Elliptic Curve Points Calculation Algorithms and their Application. Work leader dr. R. Steuding. Siauliai University. Siauliai, 2006. 35 pages
In the work I analyse calculation algorithms of the points on elliptic curves above a body Fp (the body is above primary numbers’ field) and their application opportunities.
Basic aims, set for the master’s thesis (to analyse elliptic curve points calculation algorithms and to compare them, to review application of elliptic curve points calculation algorithms, to realize Schoof elliptic curve points calculation algorithm and to analyse their effectivization possibilities) were attained. Elliptic curve points calculation algorithms were analysed and compared. System, realizing Schoof algorithm – one of the most important of elliptic curve points calculation algorithms – was created.
Main problems encountered include: standard programming system data types are insufficient to operate with large (~2150) numbers, therefore MIRACL library was employed, enabling use of large numbers in a program to find out whether the number is primary and to perform calculations with polynomials. For result output HTML was used as the form more acceptable for user (to derive polynomial equations).
Also it was concluded that finding order of elliptic curves is important for cryptosystem to select a safe curve. A number of methods were created to calculate order of a curve, including one or the most... [to full text]
| Identifer | oai:union.ndltd.org:LABT_ETD/oai:elaba.lt:LT-eLABa-0001:E.02~2006~D_20060608_201450-20142 |
| Date | 08 June 2006 |
| Creators | Pocienė, Jurgita |
| Contributors | Martinaitytė, Laima, Kulvietis, Genadijus, Steuding, Rasa, Sirius, Vaclovas, Sakalauskas, Leonidas, Turskienė, Sigita, Bartkus, Jonas, Siauliai University |
| Publisher | Lithuanian Academic Libraries Network (LABT), Siauliai University |
| Source Sets | Lithuanian ETD submission system |
| Language | Lithuanian |
| Detected Language | English |
| Type | Master thesis |
| Format | application/pdf |
| Source | http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2006~D_20060608_201450-20142 |
| Rights | Unrestricted |
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