Cryptography in the Bounded-Quantum-Storage Model

SIAM Journal on Computing (Impact Factor: 0.74). 01/2008; 37(6):1865-1890. DOI: 10.1137/060651343
Source: DBLP


We initiate the study of two-party cryptographic primitives with unconditional security, assuming that the adversary's quantum memory is of bounded size. We show that oblivious transfer and bit commitment can be implemented in this model using protocols where honest parties need no quantum memory, whereas an adversarial player needs quantum memory of size at least $n/2$ in order to break the protocol, where $n$ is the number of qubits transmitted. This is in sharp contrast to the classical bounded-memory model, where we can only tolerate adversaries with memory of size quadratic in honest players' memory size. Our protocols are efficient and noninteractive and can be implemented using today's technology. On the technical side, a new entropic uncertainty relation involving min-entropy is established.

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Available from: Ivan Damgård
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    • "However, the assumption of noisy and bounded storage comes in here to give a sufficiently high min-entropy which is crucial for the security proof. For simplicity in further proofs, we also introduce a simpler version, considering only bounded storage, which is a simple consequence of the chain rule and monotonicity of the min-entropy [12] [27]. "
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    • "This approach to defining approximate security has been well established in the context of arXiv:1108.5571v2 [quant-ph] 30 Aug 2011 cryptography, and more recently extended to the case of quantum key distribution [13] and other quantum cryptographic primitives secure in the bounded and the noisy storage models [14] [15]. The security parameter of our proposed UBQC protocol using states generated by the remote blind single qubit preparation protocol is then shown to exponentially approach zero with N (the number of coherent states), without making any assumption on the adversary's capabilities. "
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    • "Such a test could, for example, be used by manufacturers to certify the quality of a source creating BB84-states [3] and to proof to a skeptical audience that their devices fulfill the desired specifications. Sources of BB84-states are widely used in quantum cryptography, including quantum key distribution and bit commitment or oblivious transfer secure in the bounded/noisy storage model [12] [27]. Moreover, recent security proofs for quantum key distribution [5] [51] [52] are based on uncertainty relations of the form (2). The overlap of the source enters there as the crucial parameter determining the secrecy of the resulting key — in particular, there is no need to do tomography of the produced states. "
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