Faster Scalar Multiplication on the x-Line: Three-Dimensional GLV Method with Three-Dimensional Differential Addition Chains

  • Hairong YiEmail author
  • Guiwen Luo
  • Dongdai Lin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11445)


On the quadratic twist of a GLV curve, we explore faster scalar multiplication on its x-coordinate system utilizing three-dimensional GLV method. We construct and implement two kinds of three-dimensional differential addition chains, one of which is uniform and the other is non-uniform but runs faster. Implementations show that at about 254-bit security level, the triple scalar multiplication using our second differential addition chains runs about \(26\%\) faster than the straightforward computing using Montgomery ladder, and about \(6\%\) faster that the double scalar multiplication using DJB chains.


Scalar multiplication GLV methods Differential Addition Chains DJB chains 



We would like to thank Yuqing Zhu for his kind advice and selfless help on the first version of this work. And we would like to thank the anonymous reviewers for their detailed comments and suggestions. This work is supported by National Natural Science Foundation of China (Grant No. 61872359).


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Authors and Affiliations

  1. 1.State Key Laboratory of Information Security, Institute of Information EngineeringChinese Academy of SciencesBeijingChina
  2. 2.School of Cyber SecurityUniversity of Chinese Academy of SciencesBeijingChina

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