Security Against Eavesdropping in Quantum Cryptography

Quantum cryptography is a method for providing two parties who want to communicate securely with a secret key to be used in established protocols of classical cryptography. For more reviews of this topic see [1–3]. Bennett and Brassard showed that it is possible, at least ideally, to create a secret key, shared by sender and receiver, without both parties sharing any secret beforehand. We refer to this protocol as the BB84 protocol [4]. To achieve this goal, sender and receiver are linked by two channels. The first channel is a public channel. The information distributed on it is available to both parties and to a potential eavesdropper. To demonstrate the principle of quantum cryptography we assume that the signals on this channel can not be changed by third parties. The second channel is a channel with strong quantum features. An eavesdropper can interact with the signal in an effort to extract information about the signals. The signal states are chosen in such a way that there is always, on average, a back reaction onto the signal states. We assume the quantum channel to be noiseless and perfect so that the back reaction of the eavesdropper’s activity manifests itself as an induced error rate in the signal transmission.