Implementing 4-Dimensional GLV Method on GLS Elliptic Curves with j-Invariant 0

Abstract. The Gallant-Lambert-Vanstone (GLV) method is a very efcient technique for accelerating point multiplication on elliptic curves with eciently computable endomorphisms. Galbraith, Lin and Scott (J. Cryptol. 24(3), 446-469 (2011)) showed that point multiplication exploiting the 2-dimensional GLV method on a large class of curves over Fp2 was faster than the standard method on general elliptic curves over Fp, and left as an open problem to study the case of 4-dimensional GLV on special curves (e.g., j(E) = 0) over Fp2 . We study the above problem in this paper. We show how to get the 4-dimensional GLV decomposition with proper decomposed coecients, and thus reduce the number of doublings for point multiplication on these curves to only a quarter. The resulting implementation shows that the 4-dimensional GLV method on a GLS curve runs in about 0.78 the time of the 2-dimensional GLV method on the same curve and in between 0.78-0.87 the time of the 2dimensional GLV method using t...

• Type: Journal
• Year: 2011
• Where: IACR
• Authors: Zhi Hu, Patrick Longa, Maozhi Xu
• Keywords: Elliptic Curves, Glv, IACR 2011, Special Curves