Technology of Information Security
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App. Res. of Comp. Printed Article
Vol. 37, 2020 No. 9
2776-2780

Research on fast scalar multiplication algorithm for Edwards curve

Ming Jiaojiao1
Gao Xianwei1,2
Dong Xiuze2
Li Jiangfeng1
1. School of Communication Engineering, Xidian University, Xi'an 710071, China
2. Dept. of Electronic, Beijing Electronics Science & Technology Institute, Beijing 100070, China
DOI: 10.19734/j.issn.1001-3695.2019.03.0151

Abstract

Scalar multiplication is the most core operation in the elliptic curve cryptography algorithm, and its operation speed affects the efficiency of the entire cryptosystem. Firstly, this paper introduced the basic concept of Edwards curve in detail. Secondly, in order to improve the operation of scalar multiplication, this paper studied the elliptic curve scalar multiplication algorithm, and introduced an algorithm CDA(continues doubling algorithm) which could be used to calculate 2mP of continuous doubling points. In order to improve the computational efficiency of CDA, it proposed expressing the scalar k as the 4-NNAF form to reduce the length of k and combined with CDA to calculate scalar multiplication could effectively reduce the amount of computation. Finally, according to the analysis of the computational complexity of the algorithm and the concrete examples, the computational efficiency is improved by more than 13% after reducing the length of scalar k. In order to further speed up the operation, this paper proposed to use a parallel structure for multiplication and modular inverse operations in CDA to reduce the number of operations of scalar multiplication. The calculation result shows that the parallel computing efficiency is improved by more than 36%.

Foundation Support

国家自然科学基金资助项目(61701008)
中央高校基本科研业务费(328201801)

Publish Information

DOI: 10.19734/j.issn.1001-3695.2019.03.0151
Publish at: Application Research of Computers Printed Article, Vol. 37, 2020 No. 9
Section: Technology of Information Security
Pages: 2776-2780
Serial Number: 1001-3695(2020)09-043-2776-05

Publish History

[2020-09-05] Printed Article

Cite This Article

明娇娇, 高献伟, 董秀则, 等. Edwards曲线快速标量乘算法研究 [J]. 计算机应用研究, 2020, 37 (9): 2776-2780. (Ming Jiaojiao, Gao Xianwei, Dong Xiuze, et al. Research on fast scalar multiplication algorithm for Edwards curve [J]. Application Research of Computers, 2020, 37 (9): 2776-2780. )

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  • Application Research of Computers Monthly Journal
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Application Research of Computers, founded in 1984, is an academic journal of computing technology sponsored by Sichuan Institute of Computer Sciences under the Science and Technology Department of Sichuan Province.

Aiming at the urgently needed cutting-edge technology in this discipline, Application Research of Computers reflects the mainstream technology, hot technology and the latest development trend of computer application research at home and abroad in a timely manner. The main contents of the journal include high-level academic papers in this discipline, the latest scientific research results and major application results. The contents of the columns involve new theories of computer discipline, basic computer theory, algorithm theory research, algorithm design and analysis, blockchain technology, system software and software engineering technology, pattern recognition and artificial intelligence, architecture, advanced computing, parallel processing, database technology, computer network and communication technology, information security technology, computer image graphics and its latest hot application technology.

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