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arXiv:quant-ph/0512021 · Physical Review Letters

Small Accessible Quantum Information Does Not Imply Security

Robert König, Renato Renner, Andor Bariska, Ueli M. Maurer

Published Apr 3, 2007• 138 citations
arXivHTMLPDF

Abstract

The security of quantum key distribution is typically defined in terms of the mutual information between the distributed key S and the outcome of an optimal measurement applied to the adversary's system. We show that even if this so-called accessible information is small, the key S might not be secure enough to be used in applications such as one-time pad encryption. This flaw is due to a locking property of the accessible information: one additional (physical) bit of information can increase the accessible information by more than one bit.

DOI
10.1103/physrevlett.98.140502

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The security of quantum key distribution is typically defined in terms of the mutual information between the distributed key S and the outcome of an optimal measurement applied to the adversary's system. We show that even if this so-called accessible information is small, the key S might not be secure enough to be used in applications such as one-time pad encryption. This flaw is due to a locking property of the accessible information: one additional (physical) bit of information can increase the accessible information by more than one bit.
Quantum data locking is a protocol that allows for a small secret key to (un)lock an exponentially larger amount of information, hence yielding the strongest violation of the classical one-time pad encryption in the quantum setting. This violation mirrors a large gap existing between two security criteria for quantum cryptography quantified by two entropic quantities: the Holevo information and the accessible information. We show that the latter becomes a sensible security criterion if an upper bound on the coherence time of the eavesdropper's quantum memory is known. Under this condition, we introduce a protocol for secret key generation through a memoryless qudit channel. For channels with enough symmetry, such as the d-dimensional erasure and depolarizing channels, this protocol allows secret key generation at an asymptotic rate as high as the classical capacity minus one bit.
The problem of security of quantum key protocols is examined. In addition to the distribution of classical keys, the problem of encrypting quantum data and the structure of the operators which perform quantum encryption is studied. It is found that unitary bases are central to both encryption of quantum information, as well as the generation of states used in generalized quantum key distribution (which are called mutually unbiased bases). A one-to-one correspondence between certain unitary bases and mutually unbiased bases is found. Finally, a new protocol for making anonymous classical broadcasts is given along with a security proof. An experimental procedure to implement this protocol is also given. In order to prove these new results, some new bounds for accessible information of quantum sources are obtained.
Using quantum key distribution (QKD) protocols, a secret key is created between two distant users (transmitter and receiver) at a particular key rate. Quantum technology can facilitate secure communication for cryptographic applications, combining QKD with one-time-pad (OTP) encryption. In order to ensure the continuous operation of QKD in real-world networks, efforts have been concentrated on optimizing the use of experimental components and effective QKD protocols to improve secret key rates and increase the transmission between multiple users. Generally, in experimental implementations, the secret key rates are limited by single-photon detectors, which are used at the receivers of QKD and create a bottleneck due to their limited detection rates (detectors with low detection efficiency and high detector dead-time). We experimentally show that secret key rates can be increased by combining the time-bin information of two such detectors on the data line of the receiver for the coherent-one-way (COW) QKD protocol with a minimal increase in quantum bit error rate (QBER, the proportion of erroneous bits). Further, we implement a point-to-multipoint COW QKD protocol, introducing an additional receiver module. The three users (one transmitter and two receivers) share the secret key in post-processing, relying on OTP encryption. Typically, the dual-receiver extension can improve the combined secret key rates of the system; however, one has to optimise the experimental parameters to achieve this within security margins. These methods are general and can be applied to any implementation of the COW protocol.
Alice and Bob share a correlated composite quantum system ABABAB. If ABABAB is used as the key for a one-time pad cryptographic system, we show that the maximum amount of information that Alice can send securely to Bob is the quantum mutual information of ABABAB.
Summary form only given. Quantum information theory suggests the possibility of accomplishing tasks that are beyond the capability of classical computer science, such as information-secure cryptographic key distribution. The lack of security proofs for standard (secret- and public-) key distribution schemes, and the insecurity of the most widely used classical schemes (such as RSA and PGP) against "quantum attacks" emphasises the need for information-secure key distribution. We provide a thorough investigation of security issues for practical quantum key distribution, taking into account channel losses, and a realistic detection process.
It is known that the maximum classical mutual information, which can be achieved between measurements on pairs of quantum systems, can drastically underestimate the quantum mutual information between them. In this article, we quantify this distinction between classical and quantum information by demonstrating that after removing a logarithmic-sized quantum system from one half of a pair of perfectly correlated bitstrings, even the most sensitive pair of measurements might yield only outcomes essentially independent of each other. This effect is a form of information locking but the definition we use is strictly stronger than those used previously. Moreover, we find that this property is generic, in the sense that it occurs when removing a random subsystem. As such, the effect might be relevant to statistical mechanics or black hole physics. While previous works had always assumed a uniform message, we assume only a min-entropy bound and also explore the effect of entanglement. We find that classical information is strongly locked almost until it can be completely decoded. Finally, we exhibit a quantum key distribution protocol that is 'secure' in the sense of accessible information but in which leakage of even a logarithmic number of bits compromises the secrecy of all others.