Fast group operations on elliptic curves in Maple
โ Scribed by S.Y. Yan; G. James
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 516 KB
- Volume
- 37
- Category
- Article
- ISSN
- 0898-1221
No coin nor oath required. For personal study only.
โฆ Synopsis
In this paper, a fast and systematic method for group operations on elliptic curves is developed, and its implementation in Maple discussed. Some applications of the fast method in computer security, as well as some future work on parallel group operations are also discussed.
๐ SIMILAR VOLUMES
Generalizing results of Lemmermeyer, we show that the 2-ranks of the Tate Shafarevich groups of quadratic twists of certain elliptic curves with a rational point of order 2 can be arbitrarily large. We use only quadratic residue symbols in a quadratic field to obtain our results.
Let E be an elliptic curve over ] be an irreducible polynomial of odd degree, and let K =F ( โ d). Assume (p) remains prime in K. We prove the analogue of the formula of Gross for the special value L(Eโ F K, 1). As a consequence, we obtain a formula for the order of the Tate-Shafarevich group I(E/K