基于量子BCH码的McEliece及Niederreiter公钥密码算法研究  

Research on McEliece and Niederreiter Public-key Cryptosystem Algorithm Based on Quantum BCH Codes

作　　者：韩海清 张焕国[2] 赵波[2] 王后珍[2] HAN Haiqing;ZHANG Huanguo;ZHAO Bo;WANG Houzhen(School of Mathematics and Physics,Hubei Polytechnic Univ.,Huangshi 435003,China;School of Computer,Wuhan Univ.,Wuhan 430072,China)

机构地区：[1]湖北理工学院数理学院,湖北黄石435003 [2]武汉大学计算机学院,湖北武汉430072

出　　处：《工程科学与技术》2018年第5期152-159,共8页Advanced Engineering Sciences

基　　金：国家自然科学基金重点项目资助(2014CB340600);湖北省教育厅重点项目资助(D20174502;B2014041);湖北省科技厅项目资助(2018CFB550)

摘　　要：针对量子计算攻击对传统密码体制的安全威胁,设计出一类抗量子攻击的McEliece公钥密码体制,因为量子计算没有攻击McEliece公钥密码体制的多项式时间算法。给出了3类量子BCH码的生成算法,第1类是一般性量子BCH码生成算法,第2类是特殊的对称量子BCH码生成算法,第3类是特殊的非对称量子BCH码生成算法。以本文生成的非对称量子BCH码为基础,设计出量子McEliece公钥密码体制和量子Niederreiter公钥密码体制,详细给出这两种公钥体制的加密和解密过程。给出的密码体制既保留了抗量子计算优点,又能在量子态下加密和解密,其基本域为任意有限域。分析了这两种体制的计算复杂性理论、数据结构及算法模式,得到了时间复杂性和空间复杂性达到指数级,得到了抵抗Shor算法和Grover算法攻击的结果。最后,利用量子BCH码的结构特征,设计了一种经典Niederreiter体制数字签名,具有抗量子攻击能力。In order to resist the security threat of quantum computing attacks to the traditional cryptosystem,a class of McEliece public-key cryptosystems was designed in this paper,based on the fact that no quantum computing algorithm can attack the McEliece public-key cryptosystem within polynomial time.Three types of algorithms for generating quantum BCH codes were presented.The first one was general quantum BCH code generation algorithm,the second one was special symmetric quantum BCH code generation algorithm,and the third one was special asymmetric quantum BCH code generation algorithm.Based on the asymmetric quantum BCH codes generated in this paper,the quantum McEliece public-key cryptosystem and the quantum Niederreiter public-key cryptosystem were designed,and the encryption and decryption processes of the two public-key systems were given in detail.The proposed cryptosystems not only retained the advantages of the post-quantum computation,but also can encrypt and decrypt in quantum states.The basic field has been extended to the arbitrary finite field.The computational complexity theory,data structure and algorithm model of the two public-key cryptosystems were analyzed.The exponential time and space complexity were obtained,and the results of resisting the attacks of Shor and Grover algorithms were also obtained.Finally,with the structural characteristics of quantum BCH codes,a classical Niederreiter signature system was designed,which has the ability of resisting quantum attacks.

关 键 词：CSS构造 量子BCH码 基于纠错码公钥密码体制 抗量子攻击 数字签名 

分 类 号：TN918.2[电子电信—通信与信息系统]