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Title: Fast point quadrupling on elliptic curves
Authors: Le, D.-P. 
Nguyen, B.P.
Keywords: Affine coordinates
Elliptic curve cryptography
Fast arithmetic
Issue Date: 2012
Citation: Le, D.-P.,Nguyen, B.P. (2012). Fast point quadrupling on elliptic curves. ACM International Conference Proceeding Series : 218-222. ScholarBank@NUS Repository.
Abstract: Ciet et al. (2006) proposed an elegant method for trading inversions for multiplications when computing [2]P +Q from two given points P and Q on elliptic curves of Weierstrass form. Motivated by their work, this paper proposes a fast algorithm for computing [4]P with only one inversion in affine coordinates. Our algorithm that requires 1I + 8S + 8M, is faster than two repeated doublings whenever the cost of one field inversion is more expensive than the cost of four field multiplications plus four field squarings (i.e. I > 4M + 4S). It saves one field multiplication and one field squaring in comparison with the Sakai-Sakurai method (2001). Even better, for special curves that allow \a = 0" (or \b = 0") speedup, we obtain [4]P in affine coordinates using just 1I + 5S + 9M (or 1I + 5S + 6M, respectively). Copyright © 2012 ACM.
Source Title: ACM International Conference Proceeding Series
ISBN: 9781450312325
DOI: 10.1145/2350716.2350750
Appears in Collections:Staff Publications

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