Continuous-variable quantum cryptography is secure against non-Gaussian attacks

A general study of arbitrary finite-size coherent attacks against continuous-variable quantum cryptographic schemes is presented. It is shown that, if the size of the blocks that can be coherently attacked by an eavesdropper is fixed and much smaller than the key size, then the optimal attack for a given signal-to-noise ratio in the transmission line is an individual Gaussian attack. Consequently, non-Gaussian coherent attacks do not need to be considered in the security analysis of such quantum cryptosystems.