Optimality of Gaussian Attacks in Continuous Variable Quantum   Cryptography
  We analyze the asymptotic security of the family of Gaussian modulated Quantum Key Distribution protocols for Continuous Variables systems. We prove that the Gaussian unitary attack is optimal for all the considered bounds on the key rate when the first and second momenta of the canonical variables involved are known by the honest parties. 
Miguel Navascues, Frederic Grosshans, and Antonio Acin