We analyze the fundamental security significance of the quantitative criteria on the final generated key
K in quantum key generation including the quantum criterion
d, the attacker's mutual information on
K, and the statistical distance between her distribution on
K and the uniform distribution. For operational significance a criterion has to produce a guarantee on the attacker's probability of correctly estimating some portions of
K from her measurement, in particular her maximum probability of identifying the whole
K. We distinguish between the raw security of
K when the attacker just gets at
K before it is used in a cryptographic context and its composition security when the attacker may gain further information during its actual use to help get at
K. We compare both of these securities of
K to those obtainable from conventional key expansion with a symmetric key cipher. It is pointed out that a common belief in the superior security of a quantum generated
K is based on an incorrect interpretation of
d which cannot be true, and the security significance of
d is uncertain. Generally, the quantum key distribution key
K has no composition security guarantee and its raw security guarantee from concrete protocols is worse than that of conventional ciphers. Furthermore, for both raw and composition security there is an exponential catch-up problem that would make it difficult to quantitatively improve the security of
K in a realistic protocol. Some possible ways to deal with the situation are suggested.
Cryptographic security of quantum key distribution is currently based on a trace distance criterion. The widespread misinterpretation of the criterion as failure probability and also its actual scope have been discussed previously. Recently its distinguishability advantage interpretation is re-emphasized as an operational guarantee, and the failure probability misinterpretation is maintained with a further failure probability per bit interpretation. In this paper we explain the basic perpetuating error as a confusion on the correspondence between mathematics and reality. We note that the assignment of equal a priori probability of 1/2 to the real and ideal situations for distinguishability advantage would not lead to operational guarantee. We explain why operational guarantee in terms of Eve's probabilities of getting various key bits is necessary for security, and why the failure probability interpretation misrepresents the security situation. The scope and limits of the trace distance guarantee are summarized. It is shown that there would have been no security problem to begin with if the failure probability per bit interpretation validity.
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.
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 repeatedly and persistently claimed in the literature that a specific trace criterion
d would guarantee universal composition security in quantum cryptography. Currently that is the sole basis of unconditional security claim in quantum key distribution. In this paper, it is shown that just security against known-plaintext attacks when the generated key is used in direct encryption is not provided by
d. The problem is directly connected with several general problems in the existing unconditional security proofs in quantum key distribution. A number of issues will be clarified concerning the nature of true security, privacy amplification, key generation rate and the mathematical approach needed for their determination in concrete protocols.
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.