  The cloning of quantum variables with continuous spectra is investigated. We
define a Gaussian 1-to-2 cloning machine, which copies equally well two
conjugate variables such as position and momentum or the two quadrature
components of a light mode. The resulting cloning fidelity for coherent states,
namely $F=2/3$, is shown to be optimal. An asymmetric version of this Gaussian
cloner is then used to assess the security of a continuous-variable quantum key
distribution scheme that allows two remote parties to share a Gaussian key. The
information versus disturbance tradeoff underlying this continuous quantum
cryptographic scheme is then analyzed for the optimal individual attack.
Methods to convert the resulting Gaussian keys into secret key bits are also
studied. The extension of the Gaussian cloner to optimal $N$-to-$M$ continuous
cloners is then discussed, and it is shown how to implement these cloners for
light modes, using a phase-insensitive optical amplifier and beam splitters.
Finally, a phase-conjugated inputs $(N,N')$-to-$(M,M')$ continuous cloner is
defined, yielding $M$ clones and $M'$ anticlones from $N$ replicas of a
coherent state and $N'$ replicas of its phase-conjugate (with $M'-M=N'-N$).
This novel kind of cloners is shown to outperform the standard $N$-to-$M$
cloners in some situations.
