Abstract: Adopting Shamir threshold secret sharing technique, a new （t, n） threshold group signature scheme without trusted party based on an improved elliptic curve digital signature algorithm and jointing secret sharing technique is proposed. This scheme includes four major parts：initial phase of the system（for the determination of system parameters）, phase of key generation（for the generation of each group member’s public key and private key, and the group public key）, phase of partial signature generation and verification, phase of the group signature generation and verification. In this new scheme all members decide group public key and each group member’s private key with no trusted party required. Thus, each group member only knows the group public key without knowing any information about other member’s private key, in order to effectively avoid divulging secret information. There is no secret information leakage during the total signature process. This new scheme has following advantages: it softens the precondition for threshold signature scheme and extends the extent of application of it; this scheme is easier in key management, significantly reduces the communication cost and computation cost, improves the system’s efficiency and provides better adaptability. The thesis analyzes some commonly used attacks in detail to verify its security, including the effectual forgery attack, collusion attack etc. The analysis shows that the proposed new scheme is secure and effective. So this scheme makes good sense both in theory and practice.

Key words: digital signature, Elliptic Curve Cryptosystem（ECC）, threshold group signature scheme without trusted party

摘要： 在一种改进的椭圆曲线数字签名算法的基础上，采用Shamir门限秘密共享方案和联合秘密共享技术设计了一种新的基于身份证书机制的无可信中心的（t，n）门限群签名方案，该方案由以下四个步骤组成：系统初始化阶段（确定系统参数）、密钥生成阶段（群公钥及分存秘密的生成）、部分签名的生成和验证阶段、群签名的生成和验证阶段。在这个新方案中由全体成员来共同决定群公钥和成员的私钥，无需可信中心的参与。这样每个成员只了解群公钥，没有掌握与其他成员的私钥有关的任何信息，从而有效地避免了成员私人密钥的泄漏，并且在整个方案的执行过程中都没有任何系统秘密信息的泄露。新方案具有以下优点：弱化了应用门限签名方案的前提条件，扩大了其应用范围；密钥管理简单，显著地减少了通信量和计算量，提高了系统效率，具有更好的适应性。详细分析了对该方案各种可能的攻击方式，包括在门限签名方案中常见的、非常有效的伪造攻击、合谋攻击等。分析表明所提出的方案是安全有效的。因此，该方案具有较强理论意义和较好的实际应用价值。

关键词: 数字签名, 椭圆曲线, 无可信中心的门限群签名方案