  Cryptographic protocols are the backbone of our information society. This
includes two-party protocols which offer protection against distrustful
players. Such protocols can be built from a basic primitive called oblivious
transfer. We present and experimentally demonstrate here the first quantum
protocol for oblivious transfer for optical continuous-variable systems, and
prove its security in the noisy-storage model. This model allows to establish
security by sending more quantum signals than an attacker can reliably store
during the protocol. The security proof is based on new uncertainty relations
which we derive for continuous-variable systems, that differ from the ones used
in quantum key distribution. We experimentally demonstrate the proposed
oblivious transfer protocol for various channel losses by using entangled
two-mode squeezed states measured with balanced homodyne detection. Our work
enables the implementation of arbitrary two-party quantum cryptographic
protocols with continuous-variable communication systems.
