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We consider the continuous-variable protocol of Pirandola et al. [NaturePhotonics 9, 397-402 (2015), see also arXiv.1312.4104] where the secret-key isestablished by the measurement of an untrusted relay. In this network protocol,two authorized parties are connected to an untrusted relay by insecure quantumlinks. Secret correlations are generated by a continuous-variable Belldetection performed on incoming coherent states. In the present work we providea detailed study of the symmetric configuration, where the relay is midwaybetween the parties. We analyze symmetric eavesdropping strategies against thequantum links explicitly showing that, at fixed transmissivity and thermalnoise, two-mode coherent attacks are optimal, manifestly outperforming one-modecollective attacks based on independent entangling cloners. Such an advantageis shown both in terms of security threshold and secret-key rate.

Continuous-variable quantum cryptography with an untrusted relay: Detailed security analysis of the symmetric configuration