  We investigate the asymptotic security of one-way continuous variable quantum
key distribution against Gaussian two-mode coherent attacks. The one-way
protocol is implemented by arranging the channel uses in two-mode blocks. By
applying symmetric random permutations over these blocks, the security analysis
is in fact reduced to study two-mode coherent attacks and, in particular,
Gaussian ones, due to the extremality of Gaussian states. We explicitly show
that the use of two-mode Gaussian correlations by an eavesdropper leads to
asymptotic secret key rates which are strictly larger than the rate obtained
under standard single-mode Gaussian attacks.
