We present a construction for hash-based one-time group signature schemes, and develop a traceable post-quantum multi-time group signature upon it. A group signature scheme allows group members to anonymously sign a message on behalf of the entire group. The signatures are unforgeable, and the scheme enables authorized openers to trace the signature back to the original signer when needed. Our construction utilizes three nested layers to build the group signature scheme. The first layer performs the key-management task; it deploys a transversal design to assign keys to the group members and the openers, establishing anonymity and providing the construction with traceability. The second layer utilizes sets of hash values, hash pools, to build the group public verification key and to connect group members together. The final layer uses a post-quantum hash-based signature scheme, that adds unforgeability to our construction. We extend our scheme to multi-time signatures using Merkle trees and show that this process maintains the scalability property of Merkle-based signatures, while it supports the group members signing any number of messages.

我们提出了一种基于哈希的一次性组签名方案的构造，并在其上开发了可追溯的量子后多次组签名。组签名方案允许组成员代表整个组匿名签名邮件。签名是不可伪造的，该方案使授权的开启者可以在需要时将签名追溯到原始签名者。我们的构造利用三个嵌套层来构建组签名方案。第一层执行密钥管理任务；第二层执行密钥管理任务。它部署了一个横向设计，以将密钥分配给组成员和开启者，建立匿名性并为构造提供可追溯性。第二层利用哈希值集，哈希池，以建立群组公开验证密钥并将群组成员连接在一起。最后一层使用基于量子后哈希的签名方案，这为我们的构造增加了不可伪造性。我们将方案扩展为使用Merkle树的多次签名，并表明此过程保持了基于Merkle签名的可伸缩性，同时它支持对任意数量的消息进行签名的组成员。