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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Essential elements lacking in security proofs for quantum key distribution

Horace P. Yuen

Published Oct 29, 2013• 16 citations
Publisher

Abstract

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.

DOI
10.1117/12.2032082

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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.
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.
It has been widely claimed and believed that many protocols in quantum key distribution, especially the single-photon BB84 protocol, have been proved unconditionally secure at least in principle, for both asymptotic and finite protocols with realistic bit lengths. In this paper it is pointed out that the only known quantitative justification for such claims is based on incorrect assertions. The precise security requirements are described in terms of the attacker's sequence and bit error probabilities in estimating the key. The extent to which such requirements can be met from a proper trace distance criterion is established. The results show that the quantitative security levels obtainable in concrete protocols with ideal devices do not rule out drastic breach of security unless privacy amplification is more properly applied.
The security issues facing quantum key distribution (QKD) are explained, herein focusing on those issues that are cryptographic and information theoretic in nature and not those based on physics. The problem of security criteria is addressed. It is demonstrated that an attacker's success probabilities are the fundamental criteria of security that any theoretic security criterion must relate to in order to have operational significance. The errors committed in the prevalent interpretation of the trace distance criterion are analyzed. The security proofs of QKD protocols are discussed and assessed in regard to three main features: their validity, completeness, and adequacy of the achieved numerical security level. Problems are identified in all these features. It appears that the QKD security situation is quite different from the common perception that a QKD-generated key is nearly perfectly secure. Built into our discussion is a simple but complete quantitative description of the information theoretic security of classical key distribution that is also applicable to the quantum situation. In the appendices, we provide a brief outline of the history of some major QKD security proofs, a rather unfavorable comparison of current QKD proven security with that of conventional symmetric key ciphers, and a list of objections and answers concerning some major points of the paper.
It is claimed in the many papers that a trace distance: d guarantees the universal composition security in quantum key distribution (QKD) like BB84 protocol. In this introduction paper, at first, it is explicitly explained what is the main misconception in the claim of the unconditional security for QKD theory. In general terms, the cause of the misunderstanding on the security claim is the Lemma in the paper of Renner. It suggests that the generation of the perfect random key is assured by the probability (1-d), and its failure probability is d. Thus, it concludes that the generated key provides the perfect random key sequence when the protocol is success. So the QKD provides perfect secrecy to the one time pad. This is the reason for the composition claim. However, the quantity of the trace distance (or variational distance) is not the probability for such an event. If d is not small enough, always the generated key sequence is not uniform. Now one needs the reconstruction of the evaluation of the trace distance if one wants to use it. One should first go back to the indistinguishability theory in the computational complexity based, and to clarify the meaning of the value of the variational distance. In addition, the same analysis for the information theoretic case is necessary. The recent serial papers by H.P.Yuen have given the answer on such questions. In this paper, we show more concise description of Yuen's theory, and clarify that the upper bound theories for the trace distance by Tomamichel et al and Hayashi et al are constructed by the wrong reasoning of Renner and it is unsuitable as the security analysis. Finally, we introduce a new macroscopic quantum communication to replace Q-bit QKD.
The security issues facing quantum key distribution (QKD) are explained, herein focusing on those issues that are cryptographic and information theoretic in nature and not those based on physics. The problem of security criteria is addressed. It is demonstrated that an attacker's success probabilities are the fundamental criteria of security that any theoretic security criterion must relate to in order to have operational significance. The errors committed in the prevalent interpretation of the trace distance criterion are analyzed. The security proofs of QKD protocols are discussed and assessed in regard to three main features: their validity, completeness, and adequacy of the achieved numerical security level. Problems are identified in all these features. It appears that the QKD security situation is quite different from the common perception that a QKD-generated key is nearly perfectly secure. Built into our discussion is a simple but complete quantitative description of the information theoretic security of classical key distribution that is also applicable to the quantum situation. In the Appendixes, we provide a brief outline of the history of some major QKD security proofs, a rather unfavorable comparison of current QKD proven security with that of conventional symmetric key ciphers, and a list of objections and answers concerning some major points of this paper.
Quantum Key Distribution (QKD) is revolutionizing cryptography by promising information-theoretic security through the immutable laws of quantum mechanics. Yet, the challenge of transforming these idealized security models into practical, resilient systems remains a pressing issue, especially as quantum computing evolves. In this review, we critically dissect and synthesize the latest advancements in QKD protocols and their security vulnerabilities, with a strong emphasis on rigorous security proofs. We actively categorize contemporary QKD schemes into three key classes: uncertainty principle-based protocols (e.g., BB84), hybrid architectures that enable secure direct communication (eg, three-stage protocol), and continuous-variable frameworks. We further include two modern classes of QKD protocols, namely Twin-field QKD and Device-Independent QKD, both of which were developed to have practical implementations over the last decade. Moreover, we highlight important experimental breakthroughs and innovative mitigation strategies, including the deployment of advanced Quantum Error Correction Codes (QECCs), that significantly enhance channel fidelity and system robustness. By mapping the current landscape, from sophisticated quantum attacks to state-of-the-art error correction methods, this review fills an important gap in the literature. To bring everything together, the relevance of this review concerning quantum augmented networks (QuANets) is also presented. This allows the readers to gain a comprehensive understanding of the security promises of quantum key distribution from theoretical proofs to experimental validations.