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Barnum, Crepeau, Gottesman, Tapp, and Smith (quant-ph/0205128) proposedmethods for authentication of quantum messages. The first method is aninteractive protocol (TQA') based on teleportation. The second method is anoninteractive protocol (QA) in which the sender first encrypts the messageusing a protocol QEnc and then encodes the quantum ciphertext with an errorcorrecting code chosen secretly from a set (a purity test code (PTC)).Encryption was shown to be necessary for authentication.  We augment the protocol QA with an extra step which recycles the entireencryption key provided QA accepts the message. We analyze the resultingintegrated protocol for quantum authentication and key generation, which wecall QA+KG. Our main result is a proof that QA+KG is universal composably (UC)secure in the Ben-Or-Mayers model (quant-ph/0409062). More specifically, thisimplies the UC-security of (a) QA, (b) recycling of the encryption key in QA,and (c) key-recycling of the encryption scheme QEnc by appending PTC. For anm-qubit message, encryption requires 2m bits of key; but PTC can be performedusing only O(log m) + O(log e) bits of key for probability of failure e. Thus,we reduce the key required for both QA and QEnc, from linear to logarithmic netconsumption, at the expense of one bit of back communication which can happenany time after the conclusion of QA and before reusing the key. UC-security ofQA also extends security to settings not obvious from quant-ph/0205128.  Our security proof structure is inspired by and similar to that ofquant-ph/0205128, reducing the security of QA to that of TQA'. In the process,we define UC-secure entanglement, and prove the UC-security of the entanglementgenerating protocol given in quant-ph/0205128, which could be of independentinterest.

The Universal Composable Security of Quantum Message Authentication with Key Recyling