Article:Lupo, Cosmo orcid.org/0000-0002-5227-4009, Ottaviani, Carlo orcid.org/0000-0002-0032-3999, Papanastasiou, Panagiotis et al. (1 more We present a rigorous security analysis of continuous-variable measurement-device-independent quantum key distribution (CV MDI QKD) in a finite-size scenario. The security proof is obtained in two steps: by first assessing the security against collective Gaussian attacks, and then extending to the most general class of coherent attacks via the Gaussian de Finetti reduction. Our result combines recent state-of-the-art security proofs for CV QKD with findings about min-entropy calculus and parameter estimation. In doing so, we improve the finite-size estimate of the secret key rate. Our conclusions confirm that CV MDI protocols allow for high rates on the metropolitan scale, and may achieve a nonzero secret key rate against the most general class of coherent attacks after 10 7 -10 9 quantum signal transmissions, depending on loss and noise, and on the required level of security.