The authors show how to implement cryptographic primitives based on the realistic assumption that quantum storage of qubits is noisy. They thereby consider individual-storage attacks, i.e. the dishonest party attempts to store each incoming qubit separately. Their model is similar to the model of bounded-quantum storage; however, they consider an explicit noise model inspired by present-day technology. To illustrate the power of this new model, they 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.