On the Security of Quantum Cryptography Against Collective Attacks

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Abstract
We present strong attacks against quantum key distribution schemes which use quantum memories and quantum gates to attack {\em 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.

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