Abstract: Based on [(t,n)] threshold secret sharing, this paper proposes a simple asynchronous [(t,m,n)] group authentication scheme to verify whether all participants belong to a pre-defined group at once. In the scheme, each user uses a single share as the token. Each participant constructs a component to bind the token with all [m] participants and recovers the secret with all components to check whether all participants are legal. Moreover, the scheme does not depend on any public key system. Analyses show the proposed scheme can resist up to [t-1] insiders conspiring and outsiders with no more than [m-1] components. Compared with Harn’s group authentication scheme, the proposed scheme is simpler, more efficient and flexible.

Key words: group authentication, [(t,n)] threshold secret sharing, component

摘要： 基于[(t,n)]门限秘密共享方案，提出了一种简单异步[(t,m,n)]组认证方案，用以一次性验证所有参与者是否属于同一组。在该方案中，每个组成员只需拥有一个share作为认证令牌。在组认证过程中，每个参与者通过计算分量（Component）将自己的令牌与所有参与者绑定，并利用分量重构秘密从而一次性验证所有参与者是否全部为合法的组成员。该方案不依赖于任何数学难题，并可有效抵御至多[t-1]个内部攻击者的合谋攻击以及已知[m-1]个分量的外部攻击者的攻击。与Harn的组认证方案相比，该方案更加高效和灵活。

关键词: 组认证, [(t, n)]门限秘密共享, 分量