关键词: 数字签名, 椭圆曲线, 无可信中心的门限群签名方案

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