Security of coherent state quantum cryptography in the presence of Gaussian noise

We investigate the security against collective attacks of a continuous variable quantum key distribution scheme in the asymptotic key limit for a realistic setting. The quantum channel connecting the two honest parties is assumed to be lossy and imposes Gaussian noise on the observed quadrature distributions. Secret key rates are given for direct and reverse reconciliation schemes including postselection in the collective attack scenario. The effect of a non-ideal error correction and two-way communication in the classical post-processing step is also taken into account.