基于多变量公钥密码体制的门限环签名方案  

Threshold Ring Signature Scheme Based on Multivariate Public Key Cryptosystems

作　　者：郭秋玲 向宏[1,2] 蔡斌[1,2] 桑军[1,2] 向涛[2,3] GUO Qiu-Ling1, XIANG Hong1,2, CAI Bin1,2, SANG Jun1,2, XIANG Tao2,3(1. School of Software Engineering, Chongqing University, Chongqing 400044, China;2. Key Laboratory of Dependable Service Computing in Cyber Physical Society, Ministry of Education Chongqing University, Chongqing 400044, China; 3. College of Computer Science, Chongqing University, Chongqing 400044, Chin)

机构地区：[1]重庆大学软件学院,重庆400044 [2]重庆大学信息物理社会可信服务计算教育部重点实验室,重庆400044 [3]重庆大学计算机学院,重庆400044

出　　处：《密码学报》2018年第2期140-150,共11页Journal of Cryptologic Research

基　　金：国家自然科学基金(61472054);中央高校基本科研业务费(106112014CDJZR095501);国家重点研发计划(2017YFB0802000)~~

摘　　要：多变量公钥密码是后量子密码的主要候选者之一.目前,大多数多变量公钥密码的加密方案都存在安全性问题,但有很多安全且高效的签名方案.不过,人们对具有特殊性质的多变量公钥密码签名方案的研究并不多,比如门限环签名、盲签名、群签名等.2011年,Shangping Wang等人首次提出了基于多变量公钥密码体制的环签名方案,该方案具有较高的效率.门限环签名确保了一个群体中至少有t个成员参与了签名,又不泄露签名者的身份.本文结合Shangping Wang等人提出的环签名方案的特点,提出一个基于多变量公钥密码体制的门限环签名方案.该方案利用公平划分思想,对一个环进行重复划分,每次划分成t个互斥的子环,形成一个(n,t)-完全划分系统.签名时,先计算各个子环的签名,再将这些签名连接起来,形成一个类环机制.本文所提出的方案是一个关于多变量双极系统的门限环签名方案,该方案可以抵抗量子计算机的攻击.经过分析,新方案满足门限环签名的正确性、匿名性要求.同时,在已知的关于多变量公钥密码的攻击下,新方案具备不可伪造性.Multivariate public-key cryptosystems（MPKCs） are the main candidates of post-quantum cryptosystems. At present, most of multivariate encryption schemes have security problems, while there are many secure and efficient signature schemes. However, less researches are conducted on multivariate signature schemes such as threshold ring signature, blind signature, group signature, and so on. The ring signature scheme based on multivariate public key cryptosystems first proposed by Shangping Wang et al. in 2011 has high efficiency. Threshold ring signature scheme ensures at least t members of a group to sign a message without revealing the identity of the signers. In this study, by combining the characteristics of ring signature scheme proposed by Shangping Wang et al., we propose a threshold ring signature scheme based on MPKCs. The scheme uses the idea of fair partition to split a ring into t disjoint sub-rings repeatedly and form an（n, t）-complete partitioning system. When signing, it needs to compute the signature of each sub-rings, then concatenate the signatures to form a ring-like mechanism. Our scheme is a threshold ring signature scheme for multivariate bipolar systems,which can resist the attacks of quantum computers. Analysis shows that, it satisfies the completeness and anonymity of threshold ring signatures. Furthermore, the new scheme is proven to achieve the unforgeability under known attacks against MPKCs.

关 键 词：多变量公钥密码 门限环签名 量子计算机 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]