Elliptic curve cryptosystems were proposed in 1985 by Victor Miller and by Neal Koblitz independently. Since elliptic curve discrete logarithm problem is harder to solve than discrete logarithm problem in finite fields. If is believed that the key length of elliptic curve cryptosystems can be shorter then that of RSA with the same security strength.
The most important work of using elliptic curve cryptosystem is constructing a group from a proper elliptic curve. The major work of constructing an elliptic curve is counting points on elliptic curves over finite fields. In 1985, Schoof published a deterministic polynomial time algorithm for computing the number of points on the elliptic curves over finite fields. We consult IEEE P1363 to implement pseudo random elliptic curve.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0824105-115839 |
| Date | 24 August 2005 |
| Creators | Jen, Li-hsiang |
| Contributors | D. J. Guan, Chun-Hung Richard Lin, Chun-I Fan |
| Publisher | NSYSU |
| Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
| Language | Cholon |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0824105-115839 |
| Rights | unrestricted, Copyright information available at source archive |
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