广西师范大学学报（自然科学版） ›› 2023, Vol. 41 ›› Issue (4): 1-11.doi: 10.16088/j.issn.1001-6600.2022122001

• 综述 •    下一篇

几类纠错码及其相关McEliece密码体制

李志豪1, 吴严生1*, 张钰芃2   

  1. 1.南京邮电大学计算机学院/软件学院/网络空间安全学院, 江苏南京 210023;
    2.南京航空航天大学计算机科学与技术学院/人工智能学院/软件学院, 江苏南京 210016
  • 收稿日期:2022-12-20 修回日期:2023-03-06 出版日期:2023-07-25 发布日期:2023-09-06
  • 通讯作者: 吴严生(1989—),男,安徽安庆人,南京邮电大学副教授,博士。E-mail:yanshengwu@njupt.edu.cn
  • 基金资助:
    国家自然科学基金青年基金(12101326);江苏省自然科学基金青年基金(BK20210575);江苏省高等学校基础科学(自然科学)面上项目(21KJB110005);南京市留学人员科技创新项目择优资助、南京邮电大学华礼人才计划、综合业务网理论及关键技术国家重点实验室开放课题(ISN23-22)

Several Kinds of Error-Correcting Codes and Related McEliece Cryptosystem

LI Zhihao1, WU Yansheng1*, ZHANG Yupeng2   

  1. 1. School of Computer Science, Nanjing University of Posts and Telecommunications, Nanjing Jiangsu 210023, China;
    2. Colloge of Computer Science and Technology/Colloge of ArtificialIntelligence/Colloge of Software, Nanjing University of Aeronautics and Astronautics, Nanjing Jiangsu 210016, China
  • Received:2022-12-20 Revised:2023-03-06 Online:2023-07-25 Published:2023-09-06

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摘要： 随着量子计算机的迅速发展,抗量子攻击密码算法俨然成为密码学的研究热点。基于纠错码的McEliece公钥加密体制由Robert McEliece于1978年提出,是一种非对称抗量子攻击加密算法。本文首先介绍几种常见的纠错码——Reed-Solomon码、Goppa码、Twisted Reed-Solomon码的定义与基本性质,系统分析线性码的纠错译码算法;其次,详细阐述基于纠错码的McEliece公钥加密体制的加解密过程,并从NP-Hard问题对该加密体制进行安全性分析;最后,在前人研究成果的基础上,结合最近研究热点,提出几点思考和一些公开问题,为未来的研究提供参考。

关键词: 纠错码, Goppa码, Reed-Solomon码, Twisted Reed-Solomon码, McEliece加密体制, 纠错译码算法

Abstract: With the rapid development of quantum computers, cryptographic algorithms against quantum attacks have become a research hotspot in cryptography. McEliece encryption system based on error-correcting codes, proposed by Robert McEliece in 1978, is an asymmetric encryption algorithm against quantum attacks. In this paper, firstly, the definitions and basic properties of several common error-correcting codes, such as Reed-Solomon codes, Goppa codes, and Twisted Reed-Solomon codes are introduced. Secondly, the encryption and decryption process of McEliece public-key encryption system based on error-correcting codes is described in detail, and the security of the encryption system is analyzed from the perspective of NP-Hard problems. Finally, on the basis of previous research results, combined with recent research hotspots, several considerations and open problems are proposed to point out the direction for future research.

Key words: error-correcting codes, Goppa codes, Reed-Solomon codes, Twisted Reed-Solomon codes, McEliece encryption system, error-correcting decoding algorithm

中图分类号:  TN918.3

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