On the Security of Quantum Cryptography Against Collective Attacks

We present strong attacks against quantum key distribution schemes which use quantum memories and quantum gates to attack directly the final key. We analyze a specific attack of this type, for which we find the density matrices available to the eavesdropper and the optimal information which can be extracted from them. We prove security against this attack and discuss security against any attack allowed by the rules of quantum mechanics. PACS number(s): 03.65.Bz, 89.70, 89.80 Quantum cryptography [1, 2, 3, 4, 5] uses quantum mechanics to perform new cryptographic tasks — especially information secure key distributions — which are beyond the abilities of classical cryptography. Unfortunately, the security of such a key is still unproven: Sophisticated attacks (called coherent or joint attacks) which are directed against the final key were suggested; The analysis of such attacks is very complicated, and, by the time this work was submitted, security against them was proven only in the non-realistic case of ideal (error-free) channels [6, 7]. The security in the real case, which is crucial for making quantum cryptography practical, is commonly believed but yet unproven. A proof of security must bound the information available to the eavesdropper (traditionally called Eve), on the final key, to be negligible