Jacobi quartic curves revisited
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.
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|Item Type:||Journal Article|
|Keywords:||Efficient elliptic curve arithmetic, point multiplication, Jacobi model of elliptic curves|
|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:||30 Sep 2009 07:36|
|Last Modified:||29 Feb 2012 23:55|
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