We show how to implement cryptographic primitives based on the
realistic assumption that quantum storage of qubits is noisy. We
thereby consider individual-storage attacks; i.e., the dishonest party
attempts to store each incoming qubit separately. Our model is similar
to the model of boundedquantum storage; however, we consider an
explicit noise model inspired by present-day technology. To illustrate
the power of this new model, we show that a protocol for oblivious
transfer is secure for any amount of quantum-storage noise, as long as
honest players can perform perfect quantum operations. Our model also
allows us to show the security of protocols that cope with noise in
the operations of the honest players and achieve more advanced tasks
such as secure identification.