Barnum, Crepeau, Gottesman, Tapp, and Smith (quant-ph 0205128) proposed methods for authentication of quantum messages. The first method is an interactive protocol (TQA') based on teleportation. The second method is a noninteractive protocol (QA) in which the sender first encrypts the message using a protocol QEnc and then encodes the quantum ciphertext with an error correcting 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 entire encryption key provided QA accepts the message. We analyze the resulting integrated protocol for quantum authentication and key generation, which we call 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, this implies 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 an m-qubit message, encryption requires 2m bits of key; but PTC can be performed using 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 net consumption, at the expense of one bit of back communication which can happen any time after the conclusion of QA and before reusing the key. UC-security of QA also extends security to settings not obvious from quant-ph 0205128. Our security proof structure is inspired by and similar to that of quant-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 entanglement generating protocol given in quant-ph 0205128, which could be of independent interest.
The security of key recycling in QA was studied independently by M. Horodecki and Oppenheim @cite_23 in 2003. However @cite_23 does not address the security of QA, and it assumes an adversary who does not possess the purification. For that reason, we believe their claim to UC security, even if it holds, requires a nontrivial proof, but none was given.
@cite_23
2547753369 2530225612 1980534149 2071764857
Barnum, Crepeau, Gottesman, Tapp, and Smith (quant-ph 0205128) proposed methods for authentication of quantum messages. The first method is an interactive protocol (TQA') based on teleportation. The second method is a noninteractive protocol (QA) in which the sender first encrypts the message using a protocol QEnc and then encodes the quantum ciphertext with an error correcting 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 entire encryption key provided QA accepts the message. We analyze the resulting integrated protocol for quantum authentication and key generation, which we call 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, this implies 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 an m-qubit message, encryption requires 2m bits of key; but PTC can be performed using 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 net consumption, at the expense of one bit of back communication which can happen any time after the conclusion of QA and before reusing the key. UC-security of QA also extends security to settings not obvious from quant-ph 0205128. Our security proof structure is inspired by and similar to that of quant-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 entanglement generating protocol given in quant-ph 0205128, which could be of independent interest. We show that a family of quantum authentication protocols introduced in [, FOCS 2002] can be used to construct a secure quantum channel and additionally recycle all of the secret key if the message is successfully authenticated, and recycle part of the key if tampering is detected. We give a full security proof that constructs the secure channel given only insecure noisy channels and a shared secret key. We also prove that the number of recycled key bits is optimal for this family of protocols, i.e., there exists an adversarial strategy to obtain all non-recycled bits. Previous works recycled less key and only gave partial security proofs, since they did not consider all possible distinguishers (environments) that may be used to distinguish the real setting from the ideal secure quantum channel and secret key resource. We present a technique for proving the security of quantum-key-distribution (QKD) protocols. It is based on direct information-theoretic arguments and thus also applies if no equivalent entanglement purification scheme can be found. Using this technique, we investigate a general class of QKD protocols with one-way classical post-processing. We show that, in order to analyze the full security of these protocols, it suffices to consider collective attacks. Indeed, we give new lower and upper bounds on the secret-key rate which only involve entropies of two-qubit density operators and which are thus easy to compute. As an illustration of our results, we analyze the Bennett-Brassard 1984, the six-state, and the Bennett 1992 protocols with one-way error correction and privacy amplification. Surprisingly, the performance of these protocols is increased if one of the parties adds noise to the measurement data before the error correction. In particular, this additional noise makes the protocols more robust against noise in the quantum channel. We prove that the 1984 protocol of Bennett and Brassard (BB84) for quantum key distribution is secure. We first give a key distribution protocol based on entanglement purification, which can be proven secure using methods from Lo and Chau's proof of security for a similar protocol. We then show that the security of this protocol implies the security of BB84. The entanglement purification based protocol uses Calderbank-Shor-Steane codes, and properties of these codes are used to remove the use of quantum computation from the Lo-Chau protocol.