  We present the first protocol for oblivious transfer that can be implemented
with an optical continuous-variable system, and prove its security in the
noisy-storage model. This model allows security to be achieved by sending more
quantum signals than an attacker can reliably store at one specific point
during the protocol. Concretely, we determine how many signals need to be sent
in order to achieve security by establishing a trade-off between quantum
uncertainty generated in the protocol and the classical capacity of the memory
channel. As our main technical tool, we study and derive new uncertainty
relations for continuous-variable systems. Finally, we provide explicit
security parameters for realistic memory models.
