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arXiv:1209.0435 · Physical Review A

Unconditionally secure device-independent quantum key distribution with only two devices

Jonathan Barrett, Roger Colbeck, Adrian Kent

Published Dec 26, 2012• 72 citations
arXivHTMLPDF

Abstract

Device-independent quantum key distribution is the task of using uncharacterized quantum devices to establish a shared key between two users. If a protocol is secure, regardless of the device behavior, it can be used to generate a shared key even if the supplier of the devices is malicious. To date, all device-independent quantum key distribution protocols that are known to be secure require separate isolated devices for each entangled pair, which is a significant practical limitation. We introduce a protocol that requires Alice and Bob to have only one device each. Although inefficient and unable to tolerate reasonable levels of noise, our protocol is unconditionally secure against an adversarial supplier limited only by locally enforced signaling constraints.

DOI
10.1103/physreva.86.062326

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Device-independent quantum key distribution is the task of using uncharacterized quantum devices to establish a shared key between two users. If a protocol is secure, regardless of the device behavior, it can be used to generate a shared key even if the supplier of the devices is malicious. To date, all device-independent quantum key distribution protocols that are known to be secure require separate isolated devices for each entangled pair, which is a significant practical limitation. We introduce a protocol that requires Alice and Bob to have only one device each. Although inefficient and unable to tolerate reasonable levels of noise, our protocol is unconditionally secure against an adversarial supplier limited only by locally enforced signaling constraints.
Quantum cryptography promises levels of security that are impossible to replicate in a classical world. Can this security be guaranteed even when the quantum devices on which the protocol relies are untrusted? This central question dates back to the early 1990s when the challenge of achieving device-independent quantum key distribution was first formulated. We answer this challenge by rigorously proving the device-independent security of a slight variant of Ekert's original entanglement-based protocol against the most general (coherent) attacks. The resulting protocol is robust: While assuming only that the devices can be modeled by the laws of quantum mechanics and are spatially isolated from each other and from any adversary's laboratory, it achieves a linear key rate and tolerates a constant noise rate in the devices. In particular, the devices may have quantum memory and share arbitrary quantum correlations with the eavesdropper. The proof of security is based on a new quantitative understanding of the monogamous nature of quantum correlations in the context of a multiparty protocol.
Remote distribution of secret keys is a challenging task in quantum cryptography. A significant step in this direction is the measurement-device independence quantum key distribution (MDI-QKD). For two remote (or independent) parties Alice and Bob who initially no share secret information, the MDI-QKD enables them to share a secret key by the measurement of an untrusted relay. Unfortunately, the MDI-QKD yields the assumption that the devices of both Alice and Bob have to be trusted. Here, we show that QKD between two independent parties can also be realized even if the device of either Alice or Bob is untrusted. We tackle the problem by resorting to the recently developed one-sided device-independent QKD protocol. We derive conditions on the extracted secret key to be unconditionally secure against arbitary attacks in the limit of asymptotic keys. In the presence of Gaussian states and measurements, we theoretically demonstrate our scheme is feasible, which could be an attractive candidate for long distance secret communication.
Abstract In device-independent quantum key distribution (DIQKD), an adversary prepares a device consisting of two components, distributed to Alice and Bob, who use the device to generate a secure key. The security of existing DIQKD schemes holds under the assumption that the two components of the device cannot communicate with one another during the protocol execution. This is called the no-communication assumption in DIQKD. Here, we show how to replace this assumption, which can be hard to enforce in practice, by a standard computational assumption from post-quantum cryptography: we give a protocol that produces secure keys even when the components of an adversarial device can exchange arbitrary quantum communication, assuming the device is computationally bounded. Importantly, the computational assumption only needs to hold during the protocol execution—the keys generated at the end of the protocol are information-theoretically secure as in standard DIQKD protocols.
Key distribution plays a fundamental role in cryptography. Currently, the quantum scheme stands as the only known method for achieving unconditionally secure key distribution. This method has been demonstrated over distances of 508 and 1002 kilometers in the measurement-device-independent and twin-field configurations, respectively. However, quantum key distribution faces transmission distance issues and numerous side channel attacks since the basic physical picture requires the use of quantum channels between users. Even when quantum repeater and quantum constellation are used, commercializing quantum cryptography on a large scale remains unattainable due to the considerable expense and significant technical hurdles associated with establishing a global quantum network and facilitating mobile quantum communication. Here, by discovering the provable quantum one-way function, we propose another key distribution scheme with unconditional security, named probability key distribution, that promises users between any two distances to generate a fixed and high secret key rate. There are no quantum channels for exchanging quantum signals between two legitimate users. Non-local entangled states can be generated, identified and measured in the equivalent virtual protocol and can be used to extract secret keys. We anticipate that this discovery presents a paradigm shift in achieving unconditionally secure cryptography, thereby facilitating its widespread application on a global scale.
Quantum key distribution (QKD) is a provably secure way for two distant parties to establish a common secret key, which then can be used in a classical cryptographic scheme. Using quantum entanglement, one can reduce the necessary assumptions that the parties have to make about their devices, giving rise to device-independent QKD (DIQKD). However, in all existing protocols to date the parties need to have an initial (at least partially) random seed as a resource. In this work, we show that this requirement can be dropped. Using recent advances in the fields of randomness amplification and randomness expansion, we demonstrate that it is sufficient for the message the parties want to communicate to be (partially) unknown to the adversaries---an assumption without which any type of cryptography would be pointless to begin with. One party can use her secret message to locally generate a secret sequence of bits, which can then be openly used by herself and the other party in a DIQKD protocol. Hence our work reduces the requirements needed to perform secure DIQKD and establish safe communication.
Quantum cryptography is based on the discovery that the laws of quantum mechanics allow levels of security that are impossible to replicate in a classical world [2, 8, 12]. Can such levels of security be guaranteed even when the quantum devices on which the protocol relies are untrusted? This fundamental question in quantum cryptography dates back to the early nineties when the challenge of achieving device independent quantum key distribution, or DIQKD, was first formulated [9]. We answer this challenge affirmatively by exhibiting a robust protocol for DIQKD and rigorously proving its security. The protocol achieves a linear key rate while tolerating a constant noise rate in the devices. The security proof assumes only that the devices can be modeled by the laws of quantum mechanics and are spatially isolated from each other and any adversary's laboratory. In particular, we emphasize that the devices may have quantum memory. All previous proofs of security relied either on the use of many independent pairs of devices [6, 4, 7], or on the absence of noise [10, 1].