利用多基数系统的高效椭圆曲线多标量乘算法

doi:10.19678/j.issn.1000-3428.0057438

计算机工程 ›› 2021, Vol. 47 ›› Issue (2): 182-187. doi: 10.19678/j.issn.1000-3428.0057438

利用多基数系统的高效椭圆曲线多标量乘算法

尤文珠, 葛海波

西安邮电大学电子工程学院, 西安 710121

收稿日期:2020-02-20 修回日期:2020-03-23 出版日期:2021-02-15 发布日期:2020-03-27
作者简介:尤文珠(1995-),女,硕士研究生,主研方向为物联网安全;葛海波,教授。
基金资助:
陕西省自然科学基金（2011JM8038）；陕西省重点产业创新链（群）项目（S2019-YF-ZDCXL-ZDLGY-0098）。

Efficient Algorithm for Multi-Scalar Multiplication of Elliptic Curves Using Multi-Base Number System

YOU Wenzhu, GE Haibo

School of Electronic Engineering, Xi'an University of Posts and Telecommunications, Xi'an 710121, China

Received:2020-02-20 Revised:2020-03-23 Online:2021-02-15 Published:2020-03-27

摘要/Abstract

摘要： 针对椭圆曲线密码体制中标量乘与多标量乘运算耗时过长的问题，设计以2、3、7为基元的多基整数表示方法，并结合多基数系统（MBNS）及滑动窗口算法，提出基于MBNS滑动窗口（Sliding MBNS）和交错MBNS滑动窗口（I-MBNS）的多标量乘快速算法，分析并比较两种多标量乘快速算法在二元域和素域及不同窗口宽度下的平均运算量。实验结果表明，与Shamir和交错非邻接形式算法相比，Sliding MBNS和I-MBNS算法在标量长度为160 bit的二元域上的平均运算量分别减少了10.00%、1.69%和13.00%、4.97%，具有更低的运算复杂度和更高的标量乘算法效率。

关键词: 多标量乘, 椭圆曲线密码, 多基数系统, 公钥密码体制, 滑动窗口算法

Abstract: To address the time-consuming scalar multiplication and multi-scalar multiplication in Elliptic Curve Cryptography(ECC) system,this paper designs a multi-base integer representation method based on 2,3 and 7.On this basis,it combines Multi-Base Number System(MBNS) and sliding window algorithm to proposes two fast multi-scalar multiplication algorithms based on MBNS sliding window and interleaved MBNS sliding window,called Sliding MBNS and I-MBNS.The average computation amounts of two fast multi-scalar multiplication algorithms in the binary domain,prime domain and different window widths are analyzed and compared.Experimental results show that compared with the Shamir and interleaved Non-Adjacent Form(NAF) algorithm,Sliding MBNS and I-MBNS reduce the average computation amount by 10.0%,1.69% and 13.00%,4.97% respectively on a binary field with a scalar length of 160 bit.Their computational complexity is reduced,and the efficiency of the scalar multiplication algorithm is improved.

Key words: multi-scalar multiplication, Elliptic Curve Cryptography(ECC), Multi-Base Number System(MBNS), public key cryptosystem, sliding window algorithm

中图分类号:

TP309

尤文珠, 葛海波. 利用多基数系统的高效椭圆曲线多标量乘算法[J]. 计算机工程, 2021, 47(2): 182-187.

YOU Wenzhu, GE Haibo. Efficient Algorithm for Multi-Scalar Multiplication of Elliptic Curves Using Multi-Base Number System[J]. Computer Engineering, 2021, 47(2): 182-187.

http://www.ecice06.com/CN/Y2021/V47/I2/182

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