We show how to implement cryptographic primitives based on the realistic assumption that quantum storage of qubits is noisy. To illustrate the power of this new model, we show that a protocol for oblivious transfer (OT) is secure for any amount of quantum-storage noise, as long as honest players can perform perfect quantum operations. We then address a more realistic setting, where the honest players also experience noise. We show trade-offs between the amount of storage noise, the amount of noise in the operations performed by the honest players and the security of oblivious transfer with individual-storage attacks. As an example, we show that for the case of depolarizing noise in storage we can obtain secure oblivious transfer as long as the quantum bit-error rate of the channel does not exceed 11% and the noise on the channel is strictly less than the quantum storage noise. Finally, we show that our analysis easily carries over to quantum protocols for secure identification.
(PLEASE NOTE NON-STANDARD DATE AND TIME)