  Users of quantum networks can securely communicate via so-called (quantum)
conference key agreement --making their identities publicly known. In certain
circumstances, however, communicating users demand anonymity. Here, we
introduce a security framework for anonymous conference key agreement with
different levels of anonymity, which is inspired by the epsilon-security of
quantum key distribution. We present efficient and noise-tolerant protocols
exploiting multipartite Greenberger-Horne-Zeilinger (GHZ) states and prove
their security in the finite-key regime. We analyze the performance of our
protocols in noisy and lossy quantum networks and compare with protocols that
only use bipartite entanglement to achieve the same functionalities. Our
simulations show that GHZ-based protocols can outperform protocols based on
bipartite entanglement and that the advantage increases for protocols with
stronger anonymity requirements. Our results strongly advocate the use of
multipartite entanglement for cryptographic tasks involving several users.
