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.
Highlights
1.1 Quantum Key RecyclingQuantum communication differs significantly from classical communication
If Bob detects no disturbance on the quantum channel, it may be safe to reuse the encryption key, in stark contrast to, e.g. one-time pad (OTP) encryption on a classical channel
Škoricand de Vries [6] showed that it is advantageous to switch from 4-state conjugate coding to 8-state encoding and that 8-state encoding is equivalent to applying the quantum one-time pad (QOTP) [7,8,9]
Summary
If Bob detects no disturbance on the quantum channel, it may be safe to reuse the encryption key, in stark contrast to, e.g. one-time pad (OTP) encryption on a classical channel. Fehr and Salvail [5] used BB84 states and introduced a new proof technique Their scheme is provably secure when there is very little channel noise. Škoricand de Vries [6] showed that it is advantageous to switch from 4-state conjugate coding to 8-state encoding and that 8-state encoding is equivalent to applying the quantum one-time pad (QOTP) [7,8,9] Their scheme is designed to work at similar noise levels as QKD. One QKD instance followed by repeated QKR runs is more communication efficient
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