Quantum cryptography is not provably secure

The idea, not the reality, is straightforward. Think of it like quantum mechanic’s uncertainty principle. In laymen’s terms, at a subatomic level, you can know where an electron is, but not when; or when it is but not where. The energy involved in finding the electron disturbs it; so you can never know both simultaneously. If this principle can be applied to cryptographic keys, it means that any attempt to eavesdrop will create a discernible anomaly that can be used to break the communication. Combined with a one-time-pad, the theory is that such quantum key distribution is provably secure.

Although there have been doubts about this provability for some years, the received opinion has remained: quantum key distribution is unconditionally secure. However, in a talk titled “Incompleteness and Limit of Quantum Key Distribution Theory” due to be delivered next week at the SPIE conference on Quantum Communication and Quantum Imaging in San Diego, researchers from Japan’s Tamagawa University will debunk this idea. 

The provability of quantum key distribution is based on the trace distance, which is a quantum version of the evaluation of a mathematical cipher. The theory states that it can provide a perfect random key sequence. Although H.P. Yuen at Northwestern University has proven that the trace distance quantity does not give the probability of such an event, since if it is not small enough, the generated key sequence is never perfectly random, this criticism has never been generally accepted.

What the new research does is prove that Yuen is correct. The bottom line to be demonstrated next week is that the fundamental claim that quantum key distribution provides unconditional security is a false premise: there is at present no theoretical proof of the unconditional security for any quantum key distribution.

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