We describe results from an apparatus and protocol designed to implement quantum key distribution, by which two users, who share no secret information initially: (1) exchange a random quantum transmission, consisting of very faint flashes of polarized light; (2) by subsequent public discussion of the sent and received versions of this transmission estimate the extent of eavesdropping that might have taken place on it, and finally (3) if this estimate is small enough, distill from the sent and received versions a smaller body of shared random information, which is certifiably secret in the sense that any third party's expected information on it is an exponentially small fraction of one bit. Because the system depends on the uncertainty principle of quantum physics, instead of the usual mathematical assumptions such as the difficulty of factoring, it remains secure against an adversary with unlimited computing power.

Abstract.Assuming that Alice and Bob use a secret noisy channel (modelled by a binary symmetric channel) to send a key, reconciliation is the process of correcting errom between Alice's and Bob's version of the key. T h i s is done by public discussion, which leaks some information about the secret key to an eavesdropper. We show how to construct prote cob that leak a minimum amount of information. However this construction cannot be implemented efficiently. If Alice and Bob are willing to reveal an arbitrarily small amount of additional information (beyond the minimum) then they can implement polynomial-time protocols. We also present a more efficient protocol, which leaks an amount of information acceptably close to the minimum possible for sufficiently reliable secret channels (those with probability of any symbol being transmitted incorrectly as large bs 15%). This work improves on earlier reconciliation approaches [R, BBR, BBBSS].

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Abstract. We derive a new entropic quantum uncertainty relation involving min-entropy. The relation is tight and can be applied in various quantum-cryptographic settings. Protocols for quantum 1-out-of-2 Oblivious Transfer and quantum Bit Commitment are presented and the uncertainty relation is used to prove the security of these protocols in the boundedquantum-storage model according to new strong security definitions. As another application, we consider the realistic setting of Quantum Key Distribution (QKD) against quantum-memory-bounded eavesdroppers. The uncertainty relation allows to prove the security of QKD protocols in this setting while tolerating considerably higher error rates compared to the standard model with unbounded adversaries. For instance, for the six-state protocol with one-way communication, a bit-flip error rate of up to 17% can be tolerated (compared to 13% in the standard model). Our uncertainty relation also yields a lower bound on the min-entropy key uncertainty against known-plaintext attacks when quantum ciphers are composed. Previously, the key uncertainty of these ciphers was only known with respect to Shannon entropy.

We describe initial results from an apparatus and protocol designed to implement quantum public key distribution, by which two users, who share no secret information initially: 1) exchange a random quantum transmission, consisting of very faint flashes of polarized light; 2) by subsequent public discussion of the sent and received versions of this transmission estimate the extent of eavesdropping that might have taken place on it, and finally 3) if this estimate is small enough, can distill from the sent and received versions a smaller body of shared random information (key), which is certifiably secret in the sense that any third party's expected information on it is an exponentially small fraction of one bit. Because the system depends on the uncertainty principle of quantum physics, instead of usual mathematical assumptions such as the difficulty of factoring, it remains secure against an adversary with unlimited computing power.