基于伪四维投射坐标的多基链标量乘法

徐明; 史量

doi:10.11959/j.issn.1000-436x.2018078

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基于伪四维投射坐标的多基链标量乘法

学术论文 | 更新时间：2024-06-05

- 基于伪四维投射坐标的多基链标量乘法
- Pseudo 4D projective coordinate-based multi-base scalar multiplication
- 通信学报 2018年39卷第5期页码：74-84
- 作者机构：
  
  1. 上海海事大学信息工程学院，上海 201306
  2. 同济大学电子与信息工程学院，上海 201804
- 作者简介：
  
  [ "徐明（1977-），男，安徽马鞍山人，博士，上海海事大学副教授，主要研究方向为无线通信网络、网络空间安全等。" ]
  [ "史量（1992-），男，重庆人，上海海事大学硕士生，主要研究方向为椭圆曲线密码学、网络空间安全等。" ]
- 基金信息：
  
  国家自然科学基金资助项目(61202370);中国博士后科学基金资助项目(2014M561512)
- DOI：10.11959/j.issn.1000-436x.2018078
  中图分类号： TP393
- 网络首发：2018-05，
  
  纸质出版：2018-05-25
- 稿件说明：
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徐明, 史量. 基于伪四维投射坐标的多基链标量乘法[J]. 通信学报, 2018,39(5):74-84.

Ming XU, Liang SHI. Pseudo 4D projective coordinate-based multi-base scalar multiplication[J]. Journal on Communications, 2018, 39(5): 74-84.
徐明, 史量. 基于伪四维投射坐标的多基链标量乘法[J]. 通信学报, 2018,39(5):74-84. DOI： 10.11959/j.issn.1000-436x.2018078.

Ming XU, Liang SHI. Pseudo 4D projective coordinate-based multi-base scalar multiplication[J]. Journal on Communications, 2018, 39(5): 74-84. DOI： 10.11959/j.issn.1000-436x.2018078.

摘要

针对椭圆曲线密码系统的标量乘运算开销较大和易受能量分析攻击的问题，提出基于伪四维投射坐标的快速群运算和基于伪四维投射坐标的多基链标量乘法，对椭圆曲线密码系统的群运算层和标量乘运算层进行优化，旨在提高椭圆曲线密码系统的整体性能并抵御常见的能量分析攻击。实验表明，与现有算法相比，所提算法离散群运算的倍点运算开销降低 5.71%，三倍点运算开销降低 3.17%，五倍点运算开销降低 8.74%。此外，在密钥长度为160位的情况下，所提算法连续群运算的三倍点运算开销降低36.32%，五倍点运算开销降低17.42%，系统整体开销降低8.70%。能量波形分析表明，所提算法可以有效抵御SPA攻击和DPA攻击。

Abstract

In order to address the problem of elliptic curve cryptosystem (ECC) for the expensive cost in scalar multiplication and the vulnerability to the power analysis attacks

a pseudo 4D projective coordinate-based multi-base scalar multiplication was proposed to optimize group operation layer and scalar multiplication operation layer

which aimed at increasing the performance of ECC and resisting common power analysis attacks.Experimental results show that compared with the state-of-the-art algorithms

the proposed algorithm decreases 5.71% of point doubling cost

3.17% of point tripling cost

and 8.74% of point quintupling cost under discrete group operations.When the key length is 160 bit

the proposed algorithm decreases 36.32% of point tripling cost

17.42% of point quintupling cost

and 8.70% of the system cost under continuous group operations.The analyzing of power consumption wave shows that the proposed algorithm can resist SPA and DPA attack.

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Keywords

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