Optimal attacks on qubit-based Quantum Key Recycling

Abstract

Quantum Key Recycling (QKR) is a quantum cryptographic primitive that allows one to reuse keys in an unconditionally secure way. By removing the need to repeatedly generate new keys, it improves communication efficiency. Škorić and de Vries recently proposed a QKR scheme based on 8-state encoding (four bases). It does not require quantum computers for encryption/decryption but only single-qubit operations. We provide a missing ingredient in the security analysis of this scheme in the case of noisy channels: accurate upper bounds on the required amount of privacy amplification. We determine optimal attacks against the message and against the key, for 8-state encoding as well as 4-state and 6-state conjugate coding. We provide results in terms of min-entropy loss as well as accessible (Shannon) information. We show that the Shannon entropy analysis for 8-state encoding reduces to the analysis of quantum key distribution, whereas 4-state and 6-state suffer from additional leaks that make them less effective. From the optimal attacks we compute the required amount of privacy amplification and hence the achievable communication rate (useful information per qubit) of qubit-based QKR. Overall, 8-state encoding yields the highest communication rates.

Security proof for quantum key recycling with noise

“…, where h is the binary entropy function. Both these results are more favourable than what one would expect based on the min-entropy analysis in [9] and straightforward generalisations of [1] to the noisy case.…”

“…In 2017 Fehr and Salvail [1] introduced a qubit-based QKR scheme (similar to [5]) that does not need a quantum computer, and they were able to prove its security in the regime of extremely low noise.Škorić and de Vries [2] proposed a variant with 8-state encoding, which drastically reduces the need for privacy amplification and tolerates higher noise levels, but the security was not proven. Attacks on the qubit-based QKR schemes of [1,2] were studied in [9], but that did not yield a security proof.…”

“…For 6-state and 4-state (BB84) encoding there is a severe leakage of the qubit payload if Eve intercepts the whole cipherstate. From [2] and [9] it would seem that this leakage necessarily implies low QKR rate. However, in our protocol the leak is masked by the secret key that is used for privacy amplification.…”

“…Attacks on QKR were studied in some detail in [9]. They formulated an EPR version of qubit-based QKR protocol.…”

“…(In the noiseless case we have y =x because of the anti-correlation in the singlet state.) One of the results of [9] is an expression for Eve's mixed ancilla state when v, x, y are fixed,…”