Ciet, Quisquater, and Sica have recently shown that every elliptic curve E over a finite field double-struck F signp 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.
|Number of pages||6|
|Journal||Bulletin of the Australian Mathematical Society|
|Publication status||Published - Dec 2002|