几类纠错码及其相关McEliece密码体制  

Several Kinds of Error-Correcting Codes and Related McEliece Cryptosystem

作　　者：李志豪 吴严生 张钰芃 LI Zhihao;WU Yansheng;ZHANG Yupeng(School of Computer Science,Nanjing University of Posts and Telecommunications,Nanjing Jiangsu 210023,China;Colloge of Computer Science and Technology/Colloge of ArtificialIntelligence/Colloge of Software,Nanjing University of Aeronautics and Astronautics,Nanjing Jiangsu 210016,China)

机构地区：[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

出　　处：《广西师范大学学报（自然科学版）》2023年第4期1-11,共11页Journal of Guangxi Normal University:Natural Science Edition

基　　金：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)。

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RobertMcEliece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、TwistedReed-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。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.

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 

分 类 号：TN918.3[电子电信—通信与信息系统]