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.
This work is intended as an introduction to cryptographic security and a motivation for the widely used Quantum Key Distribution (QKD) security definition. We review the notion of security necessary for a protocol to be usable in a larger cryptographic context, i.e., for it to remain secure when composed with other secure protocols. We then derive the corresponding security criterion for QKD. We provide several examples of QKD composed in sequence and parallel with different cryptographic schemes to illustrate how the error of a composed protocol is the sum of the errors of the individual protocols. We also discuss the operational interpretations of the distance metric used to quantify these errors.
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.