Jacobi quartic curves revisited

Hisil, Huseyin, Wong, Kenneth Koon-Ho, Carter, Gary, & Dawson, Edward (2009) Jacobi quartic curves revisited. Lecture Notes in Computer Science, LNCS 5594, pp. 452-468.

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This paper provides new results about efficient arithmetic on Jacobi quartic form elliptic curves, y 2 = d x 4 + 2 a x 2 + 1. With recent bandwidth-efficient proposals, the arithmetic on Jacobi quartic curves became solidly faster than that of Weierstrass curves. These proposals use up to 7 coordinates to represent a single point. However, fast scalar multiplication algorithms based on windowing techniques, precompute and store several points which require more space than what it takes with 3 coordinates. Also note that some of these proposals require d = 1 for full speed. Unfortunately, elliptic curves having 2-times-a-prime number of points, cannot be written in Jacobi quartic form if d = 1. Even worse the contemporary formulae may fail to output correct coordinates for some inputs. This paper provides improved speeds using fewer coordinates without causing the above mentioned problems. For instance, our proposed point doubling algorithm takes only 2 multiplications, 5 squarings, and no multiplication with curve constants when d is arbitrary and a = ±1/2.

Impact and interest:

9 citations in Scopus
4 citations in Web of Science®
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ID Code: 27631
Item Type: Journal Article
Refereed: Yes
Keywords: Efficient elliptic curve arithmetic, point multiplication, Jacobi model of elliptic curves
DOI: 10.1007/978-3-642-02620-1_31
ISBN: 9783642026195
ISSN: 0302-9743
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Past > Institutes > Information Security Institute
Past > Schools > School of Engineering Systems
Copyright Owner: Copyright 2009 Springer 2009
Deposited On: 29 Sep 2009 21:36
Last Modified: 18 Jul 2014 01:33

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