  A big challenge in continuous variable quantum key distribution is to prove
security against arbitrary coherent attacks including realistic assumptions
such as finite-size effects. Recently, such a proof has been presented in
[Phys. Rev. Lett. 109, 100502 (2012)] for a two-mode squeezed state protocol
based on a novel uncertainty relation with quantum memories. But the
transmission distances were fairly limited due to a direct reconciliation
protocol. We prove here security against coherent attacks of a reverse
reconciliation protocol under similar assumptions but allowing distances of
over 16 km for experimentally feasible parameters. We further clarify the
limitations when using the uncertainty relation with quantum memories in
security proofs of continuous variable quantum key distribution.
