Average normalisations of elliptic curves

William D. Banks; Igor E. Shparlinski

Average normalisations of elliptic curves

William D. Banks^*, Igor E. Shparlinski

^*Corresponding author for this work

School of Computing

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

Ciet, Quisquater, and Sica have recently shown that every elliptic curve E over a finite field double-struck F sign_p is isomorphic to a curve y² = x³ + ax + b with a and b of size O(p^3/4). In this paper, we show that almost all elliptic curves satisfy the stronger bound O(p^2/3). The problem is motivated by cryptographic considerations.

Original language	English
Pages (from-to)	353-358
Number of pages	6
Journal	Bulletin of the Australian Mathematical Society
Volume	66
Issue number	3
Publication status	Published - Dec 2002

Cite this

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abstract = "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.",

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AU - Banks, William D.

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AB - 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.

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JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

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Average normalisations of elliptic curves

Abstract

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