๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Fast group operations on elliptic curves in Maple

โœ 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.

โœฆ 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.


๐Ÿ“œ SIMILAR VOLUMES


Elliptic operators on Lie groups
โœ A. F. M. Ter Elst; Derek W. Robinson ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Springer Netherlands ๐ŸŒ English โš– 893 KB
On Elliptic Curves with Large Tateโ€“Shafa
โœ Daisuke Atake ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 167 KB

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.

On the variation of Tateโ€“Shafarevich gro
โœ Mihran Papikian ๐Ÿ“‚ Article ๐Ÿ“… 2005 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 368 KB

Let E be an elliptic curve over ] be an irreducible polynomial of odd degree, and let K =F ( โˆš d). Assume (p) remains prime in K. We prove the analogue of the formula of Gross for the special value L(EโŠ— F K, 1). As a consequence, we obtain a formula for the order of the Tate-Shafarevich group I(E/K