Anonymous Conference Key Agreement using GHZ states

This example protocol achieves the functionality of quantum conference key agreement anonymously. This protocol allows multiple parties in a quantum network to establish a shared secret key anonymously.

Outline

• First, the sender notifies each receiver in the network anonymously
• The entanglement source generates and distributes sufficient GHZ states to all nodes in the network
• The GHZ states are distilled to establish multipartite entanglement shared only by the participating parties (the sender and receivers)
• Each GHZ state is randomly chosen to be used for either Verification or Key Generation. For Key Generation rounds, a single bit of the key is established using one GHZ state by measuring in the Z-basis
• If the sender is content with the Verification results, they can anonymously validate the protocol and conclude that the key has been established successfully.

Protocol Description

Protocol 1: Anonymous Verifiable Conference Key Agreement

Input: Parameters $L$ and $D$

Requirements: A source of n-party GHZ states; private randomness sources; a randomness source that is not associated with any party; a classical broadcasting channel; pairwise private communication channels

Goal: Anonymoous generation of key between sender and $m$ receivers

1. The sender notifies the $m$ receivers by running the Notification protocol
2. The source generates and shares $L$ GHZ states
3. The parties run the Anonymous Multipartite Entanglement protocol on the GHZ states
4. For each $(m+1)$-partite GHZ state, the parties do the following:
   • They ask a source of randomness to broadcast a bit $b$ such that Pr$[b=1]={\frac {1}{D}}$
   • Verification round: If b = 0, the sender runs Verification as verifier on the state corresponding to that round, while only considering the announcements of the $m$ receivers. The remaining parties announce random values.
   • KeyGen round: If b = 1, the sender and receivers measure in the Z-basis.
5. If the sender is content with the checks of the Verification protocol, they can anonymously validate the protocol