more elusive (see [@WPG11] for a recent review). This is mainly due to the fact that the infinite dimensional Hilbert space required to describe these protocols makes the analysis quite challenging.

Among all CVQKD schemes, the protocol GG02 is certainly the easiest one to analyze [@GG02]. In this protocol, Alice sends $n$ coherent states $|\alpha_k\rangle = |x_{2k} + i x_{2k+1}\rangle$ to Bob who measures the states he receives either with a homodyne detection (thus randomly choosing one quadrature to measure for each state) or a heterodyne detection (in which case, Bob measures both quadratures at the same time). Alice’s modulation is Gaussian, meaning that $x_k$ is a centered normal random variable with a given variance. In the case of a heterodyne detection for instance [@WLB04], Bob obtains a classical vector ${\bf y} = [y_1,\cdots, y_{2n}]$ which is correlated to Alice’s vector ${\bf x}= [x_1,\cdots, x_{2n}]$. In this paper, we use bold font to refer to vectors. Then, using parameter estimation, reconciliation and privacy amplification, they can extract a secret key. For this specific protocol, Gaussian attacks (where the action of the eavesdropper can be modeled by a Gaussian quantum channel between Alice and Bob) are known to be optimal among 