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arXiv:0711.2895 · Physical Review Letters

Cryptography from Noisy Storage

Stephanie Wehner, Christian Schaffner, Barbara M. Terhal

Published Jun 5, 2008• 141 citations
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Abstract

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 bounded-quantum 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.

DOI
10.1103/physrevlett.100.220502

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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 bounded-quantum 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.
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 bounded-quantum 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.
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 bounded-quantum 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 (OT) is secure for any amount of quantum-storage noise, as long as honest players can perform perfect quantum operations. Our model also allows the security of protocols that cope with noise in the operations of the honest players and achieve more advanced tasks such as secure identification.
It was shown that cryptographic primitives can be implemented based on the assumption that quantum storage of qubits is noisy. In this work we analyze a protocol for the universal task of oblivious transfer that can be implemented using quantum-key-distribution (QKD) hardware in the practical setting where honest participants are unable to perform noise-free operations. We derive trade-offs between the amount of storage noise, the amount of noise in the operations performed by the honest participants and the security of oblivious transfer which are greatly improved compared to the results in \cite{prl:noisy}. 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. This is optimal for the protocol considered. Finally, we show that our analysis easily carries over to quantum protocols for secure identification.
We consider the implementation of two-party cryptographic primitives based on the sole assumption that no large-scale reliable quantum storage is available to the cheating party. We construct novel protocols for oblivious transfer and bit commitment, and prove that realistic noise levels provide security even against the most general attack. Such unconditional results were previously only known in the so-called bounded-storage model which is a special case of our setting. Our protocols can be implemented with present-day hardware used for quantum key distribution. In particular, no quantum storage is required for the honest parties.
The noisy-storage model of quantum cryptography allows for information-theoretically secure two-party computation based on the assumption that a cheating user has at most access to an imperfect, noisy quantum memory, whereas the honest users do not need a quantum memory at all. In general, the more noisy the quantum memory of the cheating user, the more secure the implementation of oblivious transfer, which is a primitive that allows universal secure two-party and multiparty computation. For experimental implementations of oblivious transfer, one has to consider that also the devices held by the honest users are lossy and noisy, and error correction needs to be applied to correct these trusted errors. The latter are expected to reduce the security of the protocol, since a cheating user may hide themselves in the trusted noise. Here we leverage entropic uncertainty relations to derive tight bounds on the security of oblivious transfer with a trusted and untrusted noise. In particular, we discuss noisy storage and bounded storage, with independent and correlated noise.
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, non-interactive and can be implemented using today's technology. On the technical side, a new uncertainty relation is established