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Characterization of Collective Gaussian Attacks and Security of Coherent-State Quantum Cryptography

<01>In continuous variable quantum cryptography, the unconditional security of protocols must be proven against the so–called collective Gaussian attacks, where an eavesdropper uses identical and independent Gaussian unitaries for interacting with the transmitted quantum systems. Since these attacks are very general, past security proofs have been restricted to a specific type of them, the entangling cloner attack. In our paper we provide the simplest parametrisation of collective Gaussian attacks and their classification in canonical forms. As a result, security proofs and thresholds of existing and new protocols can now be extended to the most general scenario.