Average Normalisations of Elliptic Curves
Abstract
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.
Part of
Citation
William D. Banks and Igor E. Shparlinski (2002). Average normalisations of elliptic curves. Bulletin of the Australian Mathematical Society, 66, pp 353-358.
Rights
OpenAccess.
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