Average normalisations of elliptic curves

Abstract

Ciet, Quisquater, and Sica have recently shown that every elliptic curve E over a finite field 𝔽 p is isomorphic to a curve y 2 = x 3 + ax + b with a and b of size O ( p ¾ ). In this paper, we show that almost all elliptic curves satisfy the stronger bound O ( p ⅔ ). The problem is motivated by cryptographic considerations.

Locations

• Bulletin of the Australian Mathematical Society - View - PDF
• MOspace Institutional Repository (University of Missouri) - View - PDF