We show the security of multi-user key establishment on a single line of quantum communication. More precisely, we consider a quantum communication architecture where the qubit generation and measurement happen at the two ends of the line, whilst intermediate parties are limited to single-qubit unitary transforms. This network topology has been previously introduced to implement quantum-assisted secret-sharing protocols for classical data, as well as the key establishment, and secure computing. This architecture has numerous advantages. The intermediate nodes are only using simplified hardware, which makes them easier to implement. Moreover, key establishment between arbitrary pairs of parties in the network does not require key routing through intermediate nodes. This is in contrast with quantum key distribution (QKD) networks for which non-adjacent nodes need intermediate ones to route keys, thereby revealing these keys to intermediate parties and consuming previously established ones to secure the routing process. Our main result is to show the security of key establishment on quantum line networks. We show the security using the framework of abstract cryptography. This immediately makes the security composable, showing that the keys can be used for encryption or other tasks.

翻译：我们证明了在单线量子通信上进行多用户密钥建立的安全性。更具体地说，我们考虑一种量子通信架构，其中量子比特的产生和测量在线的两端进行，而中间方仅限于执行单量子比特酉变换。这种网络拓扑此前已被引入用于实现经典数据的量子辅助秘密共享协议，以及密钥建立和安全计算。该架构具有诸多优势：中间节点仅使用简化硬件，使其更易于实现；此外，网络中任意方之间的密钥建立无需通过中间节点进行密钥路由。这与量子密钥分发（QKD）网络形成对比——在QKD网络中，非相邻节点需要中间节点来路由密钥，从而将密钥暴露给中间方，并消耗先前建立的密钥来保护路由过程。我们的主要结果是证明了量子线路网络上密钥建立的安全性。我们使用抽象密码学框架证明该安全性，这立即赋予了安全性的可组合性，表明这些密钥可用于加密或其他任务。