Average Normalisations of Elliptic Curves
Metadata[+] Show full item record
Ciet, Quisquater, and Sica have recently shown that every elliptic curve E over a finite field Fp is isomorphic to a curve y2 = x3 +ax+b with a and b of size O(p3/4). In this paper, we show that almost all elliptic curves satisfy the stronger bound O(p2/3). The problem is motivated by cryptographic considerations.
William D. Banks and Igor E. Shparlinski (2002). Average normalisations of elliptic curves. Bulletin of the Australian Mathematical Society, 66, pp 353-358.
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License.