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arXiv:1411.2310

Security Issues Associated With Error Correction And Privacy Amplification In Quantum Key Distribution

Horace P. Yuen

Published Nov 10, 2014• 1 citation
arXivHTMLPDF

Abstract

Privacy amplification is a necessary step in all quantum key distribution protocols, and error correction is needed in each except when signals of many photons are used in the key communication in quantum noise approach. No security analysis of error correcting code information leak to the attacker has ever been provided, while an ad hoc formula is currently employed to account for such leak in the key generation rate. It is also commonly believed that privacy amplification allows the users to at least establish a short key of arbitrarily close to perfect security. In this paper we show how the lack of rigorous error correction analysis makes the otherwise valid privacy amplification results invalid, and that there exists a limit on how close to perfect a generated key can be obtained from privacy amplification. In addition, there is a necessary tradeoff between key rate and security, and the best theoretical values from current theories would not generate enough near-uniform key bits to cover the message authentication key cost in disturbance-information tradeoff protocols of the BB84 variety.

DOI
10.48550/arxiv.1411.2310

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Privacy amplification is a necessary step in all quantum key distribution protocols, and error correction is needed in each except when signals of many photons are used in the key communication in quantum noise approach. No security analysis of error correcting code information leak to the attacker has ever been provided, while an ad hoc formula is currently employed to account for such leak in the key generation rate. It is also commonly believed that privacy amplification allows the users to at least establish a short key of arbitrarily close to perfect security. In this paper we show how the lack of rigorous error correction analysis makes the otherwise valid privacy amplification results invalid, and that there exists a limit on how close to perfect a generated key can be obtained from privacy amplification. In addition, there is a necessary tradeoff between key rate and security, and the best theoretical values from current theories would not generate enough near-uniform key bits to cover the message authentication key cost in disturbance-information tradeoff protocols of the BB84 variety.
We study the practical effectiveness of privacy amplification for classical key distribution schemes. We find that in contrast to quantum key distribution schemes, the high fidelity of the raw key generated in classical systems allow the users to always sift a secure shorter key if they have an upper bound on the eavesdropper probability to correctly guess the exchanged key bits. The number of privacy amplification iterations needed to achieve information leak of 10−8 in existing classical communicators is 2 or 3 resulting in a corresponding slowdown 4 to 8. We analyze the inherent tradeoff between the number of iterations and the security of the raw key. This property which is unique to classical key distribution systems render them highly useful for practical, especially for noisy channels where sufficiently low quantum bit error ratios are difficult to achieve.
It is pointed out that treatments of the error correcting code in current quantum key distribution protocols of the BB84 type are not correct under joint attack, and the general interpretation of the trace distance security criterion is also incorrect. With correct interpretation of the criterion as well as a correct treatment of the error correcting code and privacy amplification code, it is shown that even for an ideal system under just collective attack, the maximum tolerable quantum bit error rate is about 1.5% and a net key cannot actually be generated with practical error correcting codes even at such low rates, contrary to claims in the literature.
All the currently available unconditional security proofs on quantum key distribution, in particular for the BB84 protocol and its variants including continuous-variable ones, are invalid or incomplete at many points. In this paper we discuss some of the main known problems, particularly those on operational security guarantee and error correction. Most basic are the points that there is no security parameter in such protocols and it is not the case the generated key is perfect with probability ≥1−ε\geq 1-ε≥1−ε under the trace distance criterion d≤εd\leqεd≤ε, which is widely claimed in the technical and popular literature. The many serious security consequences of this error about the QKD generated key would be explained, including practical ramification on achievable security levels. It will be shown how the error correction problem alone may already defy rigorous quantitative analysis. Various other problems would be touched upon. It is pointed out that rigorous security guarantee of much more efficient quantum cryptosystems may be obtained by abandoning the disturbance-information tradeoff principle and utilizing instead the known KCQ (keyed communication in quantum noise) principle in conjunction with a new DBM (decoy bits method) principle that will be detailed elsewhere.
We study the practical effectiveness of privacy amplification for classical key distribution schemes. We find that in contrast to quantum key distribution schemes, the high fidelity of the raw key generated in classical systems allow the users to always sift a secure shorter key if they have an upper bound on the eavesdropper probability to correctly guess the exchanged key bits. The number of privacy amplification iterations needed to achieve information leak of 10 −8 in existing classical communicators is 2 or 3 resulting in a corresponding slowdown 4 to 8. We analyze the inherent tradeoff between the number of iterations and the security of the raw key. This property which is unique to classical key distribution systems render them highly useful for practical, especially for noisy channels where sufficiently low quantum bit error ratios are difficult to achieve.
All the currently available unconditional security proofs on quantum key distribution, in particular for the BB84 protocol and its variants including continuous-variable ones, are invalid or incomplete at many points. In this paper we discuss some of the main known problems, particularly those on operational security guarantee and error correction. Most basic are the points that there is no security parameter in such protocols and it is not the case the generated key is perfect with probability ≥ 1 - ϵ under the trace distance criterion d ≤ ϵ, which is widely claimed in the technical and popular literature. The many serious security consequences of this error about the QKD generated key would be explained, including practical ramification on achievable security levels. It will be shown how the error correction problem alone may already defy rigorous quantitative analysis. Various other problems would be touched upon. It is pointed out that rigorous security guarantee of much more efficient quantum cryptosystems may be obtained by abandoning the disturbance-information tradeoff principle and utilizing instead the known KCQ (keyed communication in quantum noise) principle in conjunction with a new DBM (decoy bits method) principle that will be detailed elsewhere.
Quantum key distribution (QKD) is a method that enables secure communication between two parties by applying the ideas of quantum physics. By minimizing information leakage that can happen during the key generation process, privacy amplification is a technique used to improve the security of QKD. The technique involves processing the raw key obtained from QKD through a randomization procedure to remove any residual information that may have been leaked during the quantum transmission. While privacy amplification can significantly improve the security of QKD, the effectiveness of the technique is limited by the quality of the initial raw key. The BB84 QKD protocol has been improved with the proposed En-BB84 protocol, which includes built-in authentication and integrity checks. The En-BB84 protocol ensures secure distribution of secret keys and protects against tampering by attackers. Key distillation and error correction techniques are employed to extract a shorter, more secure shared secret key and correct errors introduced during qubit transmission. The protocol utilizes a four-state QKD approach, expanding on the traditional two-state scheme of BB84. A simulation of the En-BB84 protocol is demonstrated using a quantum circuit implemented with Qiskit in Python. The circuit employs various gates and operations, including Hadamard, CX, controlled swap, and RZ gates, to achieve encoding and error correction. Furthermore, we have designed a better protocol with improved error rates by incorporating improvisations on the BB84 protocol. Experimental results indicate the successful integration of the B92 error correction scheme into the modified BB84 protocol, enhancing the security and performance of QKD systems.