@SAA07]. This is, however, far from being sufficient for two reasons: first, Gaussian attacks are not believed to be optimal against this protocol; second, one can never prove in practice that a given quantum channel is indeed Gaussian. The problem is that the only tool currently available to establish the security of a CV protocol against collective attacks, namely Gaussian optimality [@WGC06] does not seem to help much for protocols with postselection (see, however, a recent approach along those lines in Ref. [@WSR11]).

In this paper, we introduce a new proof technique based on a symmetrization procedure that allows us to make some progress concerning the security analysis of CVQKD with postselection. In particular, we will show how this symmetrization allows us, under some verifiable conditions, to consider that the quantum channel is indeed Gaussian, even though the physical channel may actually be non-Gaussian. This then means that checking the security against Gaussian attacks (which can be done with present tools) is indeed sufficient to get full security against collective attacks, and in fact against arbitrary attacks in the asymptotic limit thanks to de Finetti theorem [@RC09].

A symmetrized protocol
======================

The usual technique to prove the security of a 