Abstract: The paper proposes a group key agreement scheme based on [(t,n)] secret sharing. The scheme needs not to secure the communication channel between users in the group in advance by symmetric polynomials. Each user constructs a Component with the share to evaluate and verify the group key. Moreover, the scheme enables a new user to negotiate a new group key with original group users by secret sharing without online Trusted Third Party（TTP）, and thus allows the new user to join the existing group. It has the low computational cost in multicast and multi-hop communication due to the use of group key in communication encryption. Compared with traditional group key agreement scheme, the scheme is able to resist the coalition of up to [t-1] internal attackers without online TTP, eliminates the dependence of pre-existing secure channels between users, and allows a new user to join the group dynamically. Thus, the proposed scheme is more secure and flexible.

Key words: dynamically join, symmetric polynomials, Trusted Third Party（TTP）, group key agreement, secret sharing

摘要： 基于[(t,n)]门限秘密共享的思想，提出一种组密钥协商方案，该方案应用对称多项式可以不需要提前保证组内用户间通信信道的安全。每个用户根据share计算自己的分量（Component），通过秘密恢复机制实现组密钥协商和验证。在线可信第三方的情况下，新用户通过秘密共享机制与原有组用户协商新的组密钥，实现新用户的动态加入。使用组密钥加密通信信息，可以降低多播、组播及多跳通信时的计算开销。与传统的组密钥协商方案相比，该方案可以抵御[t-1]个内部攻击者，无需在线可信第三方，无需用户间预先存在安全信道，并且支持新用户的动态加入。因此，方案更加安全灵活。

关键词: 动态加入, 对称多项式, 可信第三方, 组密钥协商, 秘密共享