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Security of Quantum Key Distribution

Hoi-Kwong Lo, H. F. Chau

Published Mar 3, 1998• 6 citations
OpenAlex

Abstract

We construct a new quantum key distribution scheme and prove its security against the most general type of attacks and the most general type of noises allowed by quantum physics. The novel technique we use is reduction from a quantum scheme to a classical scheme. We first show that, rather surprisingly, the proof of security of our quantum key distribution in the error-free case can be reduced to that of a classical verification scheme. In other words, the quantum verification procedure employed by us has a classical interpretation. By proving the security of the classical scheme, the security of our quantum key distribution scheme in the error-free case follows immediately. The security against the most general types of noises (channel noises, storage errors and computational errors) is then proven by using fault-tolerant quantum computation.

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We construct a new quantum key distribution scheme and prove its security against the most general type of attacks and the most general type of noises allowed by quantum physics. The novel technique we use is reduction from a quantum scheme to a classical scheme. We first show that, rather surprisingly, the proof of security of our quantum key distribution in the error-free case can be reduced to that of a classical verification scheme. In other words, the quantum verification procedure employed by us has a classical interpretation. By proving the security of the classical scheme, the security of our quantum key distribution scheme in the error-free case follows immediately. The security against the most general types of noises (channel noises, storage errors and computational errors) is then proven by using fault-tolerant quantum computation.
Quantum cryptography has long been claimed to be useful for achieving many tasks that are impossible from the perspective of conventional cryptography. Arguably, the most important problem in quantum cryptography has been a rigorous proof of the security of quantum key distribution, the most well-known application. This notoriously hard problem has eluded researchers for the last fifteen years and has become even more important after the recent surprising demonstration of the insecurity of many other quantum cryptographic schemes including quantum bit commitment. Here, we solve this long standing problem by showing that, given quantum computers, quantum key distribution over an arbitrarily long distance of a realistic noisy channel can be made unconditionally secure. The novel technique we use is reduction from a quantum scheme to a classical scheme. The security in realistic noisy environments is then proven by using the recent theory of fault-tolerant quantum computation.
Quantum cryptography has long been claimed to be useful for achieving many tasks that are impossible from the perspective of conventional cryptography. Arguably, the most important problem in quantum cryptography has been a rigorous proof of the security of quantum key distribution, the most well-known application. This notoriously hard problem has eluded researchers for years and has become even more important after the recent surprising demonstration of the insecurity of many other quantum cryptographic schemes including quantum bit commitment. Here, we solve this long standing problem by showing that, given quantum computers, quantum key distribution over an arbitrarily long distance of a realistic noisy channel can be made unconditionally secure. The novel technique we use is reduction from a quantum scheme to a classical scheme. The security in realistic noisy environments is then proven by using the recent theory of fault-tolerant quantum computation.
Quantum key distribution is the best known application of quantum cryptography. Previously proposed proofs of security of quantum key distribution contain various technical subtleties. Here, a conceptually simpler proof of security of quantum key distribution is presented. The new insight is the invariance of the error rate of a teleportation channel: we show that the error rate of a teleportation channel is independent of the signals being transmitted. This is because the non-trivial error patterns are permuted under teleportation. This new insight is combined with the recently proposed quantum-to-classical reduction theorem. Our result shows that assuming that Alice and Bob have fault-tolerant quantum computers, quantum key distribution can be made unconditionally secure over arbitrarily long distances even against the most general type of eavesdropping attacks and in the presence of all types of noises.
Quantum key distribution is widely thought to offer unconditional security in communication between two users. Unfortunately, a widely accepted proof of its security in the presence of source, device, and channel noises has been missing. This long-standing problem is solved here by showing that, given fault-tolerant quantum computers, quantum key distribution over an arbitrarily long distance of a realistic noisy channel can be made unconditionally secure. The proof is reduced from a noisy quantum scheme to a noiseless quantum scheme and then from a noiseless quantum scheme to a noiseless classical scheme, which can then be tackled by classical probability theory.
We present a technique for proving the security of quantum-key-distribution (QKD) protocols. It is based on direct information-theoretic arguments and thus also applies if no equivalent entanglement purification scheme can be found. Using this technique, we investigate a general class of QKD protocols with one-way classical post-processing. We show that, in order to analyze the full security of these protocols, it suffices to consider collective attacks. Indeed, we give new lower and upper bounds on the secret-key rate which only involve entropies of two-qubit density operators and which are thus easy to compute. As an illustration of our results, we analyze the Bennett-Brassard 1984, the six-state, and the Bennett 1992 protocols with one-way error correction and privacy amplification. Surprisingly, the performance of these protocols is increased if one of the parties adds noise to the measurement data before the error correction. In particular, this additional noise makes the protocols more robust against noise in the quantum channel.