# Anonymous Conference Key Agreement using GHZ states

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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 ${\displaystyle L}$ and ${\displaystyle D}$

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 ${\displaystyle m}$ receivers

1. The sender notifies the ${\displaystyle m}$ receivers by running the Notification protocol
2. The source generates and shares ${\displaystyle L}$ GHZ states
3. The parties run the Anonymous Multipartite Entanglement protocol on the GHZ states
4. For each ${\displaystyle (m+1)}$-partite GHZ state, the parties do the following:
• They ask a source of randomness to broadcast a bit ${\displaystyle b}$ such that Pr${\displaystyle [b=1]={\frac {1}{D}}}$
• 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 ${\displaystyle m}$ 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