Security of the Bennett 1992 quantum-key distribution protocol against individual attack over a realistic channel

Abstract

The security of two-state quantum key distribution against individual attack is estimated when the channel has losses and noises. We assume that Alice and Bob use two nonorthogonal single-photon polarization states. To make our analysis simple, we propose a modified B92 protocol in which Alice and Bob make use of inconclusive results and Bob performs a kind of symmetrization of received states. Using this protocol, Alice and Bob can estimate Eve's information gain as a function of a few parameters which reflect the imperfections of devices or Eve's disturbance. In some parameter regions, Eve's maximum information gain shows counter-intuitive behavior, namely, it decreases as the amount of disturbances increases. For a small noise rate Eve can extract perfect information in the case where the angle between Alice's two states is small or large, while she cannot extract perfect information for intermediate angles. We also estimate the secret key gain which is the net growth of the secret key per one pulse. We show the region where the modified B92 protocol over a realistic channel is secure against individual attack.

High-speed free-space quantum key distribution system for urban daylight applications

“…In our case we have considered the worst case scenario where Eve performs two types of attacks on the channel simultaneously: the unambiguous state discrimination (USD) attack [22] and the photon number splitting (PNS) attack [23,24]. It is known that the B92 protocol is vulnerable to the USD with a lossless channel attack, whereby Eve can gain 100% of the key if the loss of the channel is ≥71% [25]. If the loss of the transmission channel is lower, Alice and Bob can distill a secret key, albeit at the cost of discarding the information gained by Eve through privacy amplification.…”

Security of differential-phase-shift quantum key distribution against individual attacks

“…The security of BB84 against individual attacks has been investigated in several works [11,12,13]. The security of the B92 protocol against individual attacks has also been proven [14]. The restriction to individual attacks is often considered a realistic assumption because the capability to perform joint attacks is well beyond the domain of modern technology.…”

Practical Limitation for Continuous-Variable Quantum Cryptography using Coherent States

“…The estimation of G for continuous schemes, if possible, is important as a comparison with discrete schemes. At least, the framework [14,15] can be adapted to hybrid schemes.For these discrete schemes, the experimental imperfections are mostly determined by observed bit error rate and dark count rate of single photon detectors [11,12,13]. In continuous-variable schemes, the experimental imperfections appear as the change of quadrature distributions.…”

“…For these discrete schemes, the experimental imperfections are mostly determined by observed bit error rate and dark count rate of single photon detectors [11,12,13]. In continuous-variable schemes, the experimental imperfections appear as the change of quadrature distributions.…”

“…The question is how high G can be for a given loss or transmission distance in realistic conditions. The estimations are given for BB84 protocol [11], entangled photon protocol [12], and B92 protocol [13]. The estimation of G for continuous schemes, if possible, is important as a comparison with discrete schemes.…”