基于半直积的密钥交换协议的群论密码分析  

Group-based cryptanalysis of a key exchange protocol based on semidirect products

作　　者：杨军[1] 李庆[1] 

机构地区：[1]西南民族大学计算机科学与技术学院,四川成都610041

出　　处：《西南民族大学学报（自然科学版）》2017年第2期157-160,共4页Journal of Southwest Minzu University(Natural Science Edition)

基　　金：国家自然科学基金青年科学基金项目(11401493);中央高校基本科研业务费专项资金项目(2014NYB04)

摘　　要：群论密码学被认为是抗量子计算机攻击的一种现代密码候选解决方案,而因特网上的密钥交换协议是保障通信安全的基元之一.不同于所有Diffie-Hellman类协议的工作原理,2016年Habeeb等人基于两群的半直积而安全性基于比目前"离散对数难题"更强的计算群论假设,提出了一个带宽高效的密钥交换协议.严格证明其代数系统成群,并构建该群到经典定义的半直积群之间的一个同构.结果表明,其半直积系统并非真正创新的代数系统,从而其被动安全性在未来具有一定的脆弱性.Group-based cryptography is viewed as a modern cryptographic candidate solution to blocking quantum computer at- tacks, and the key exchange protocol on the Internet are one of the primitives to ensure the security of communication. Unlike all the operating principles of the existing Diffie-Hellman-like protocols, in 2016 Habeeb et al proposed a bandwidth-efficient key exchange protocol based on the semidirect product of two groups whose security is based on a stronger computational group-theo- retic assumption than the current assumptions of hardness of discrete logarithm problems. In this paper, the algebraic system of their protocol is strictly proven to be a group, and an isomorphism from this group onto a classically defined semidirect product group is constructed. The result shows that their semidirect product system is not a really innovative algebraic system, and there- fore its passive security will bear certain vulnerability in the future.

关 键 词：公钥密码学 群论密码学 密钥交换协议 半直积 自同构群 同构 伪创新 

分 类 号：TN918.4[电子电信—通信与信息系统]