The information that is leaked to an eavesdropper during the error reconciliation phase of quantum key distribution (QKD) protocols limits the maximum bit error rate (BER) of a system. In a standard QKD protocol, parity bits are transmitted over an authenticated noiseless channel, to which Eve has access. This Letter presents the concept of using a covert classical communication channel to transmit the parity bits between Alice and Bob without Eve gaining information of the transmitted parity bits. This allows for higher secure key generation rates and operation of a QKD system in which the BER exceeds the limit of the standard protocol. This concept is then applied to a practical free-space optical system that contains multiple parallel channels, where channel loss, crosstalk, atmospheric turbulence effects, and noise are considered.
The information that is leaked to an eavesdropper during the error reconciliation phase of quantum key distribution (QKD) protocols limits the maximum bit error rate (BER) of a system. In a standard QKD protocol, parity bits are transmitted over an authenticated noiseless channel, to which Eve has access. This Letter presents the concept of using a covert classical communication channel to transmit the parity bits between Alice and Bob without Eve gaining information of the transmitted parity bits. This allows for higher secure key generation rates and operation of a QKD system in which the BER exceeds the limit of the standard protocol. This concept is then applied to a practical free-space optical system that contains multiple parallel channels, where channel loss, crosstalk, atmospheric turbulence effects, and noise are considered.
The rate at which a secure key can be generated in a quantum key distribution (QKD) protocol is limited by the channel loss and the quantum bit-error rate (QBER). Increases to the QBER can stem from detector noise, channel noise, or the presence of an eavesdropper, Eve. Eve is capable of obtaining information of the unsecure key by performing an attack on the quantum channel or by listening to all discussion performed via a noiseless public channel. Conventionally a QKD protocol will perform the information reconciliation over the authenticated public channel, revealing the parity bits used to correct for any quantum bit errors. In this invited paper, the possibility of limiting the information revealed to Eve during the information reconciliation is considered. Using a covert communication channel for the transmission of the parity bits, secure key rates are possible at much higher QBERs. This is demonstrated through the simulation of a polarization based QKD system implementing the BB84 protocol, showing significant improvement of the SKRs over the conventional QKD protocols.
When using quantum key distribution (QKD), one of the trade-offs for security is that the generation rate of a secret key is typically very low. Recent works have shown that using a weak coherent source allows for higher secret key generation rates compared to an entangled photon source, when a channel with low loss is considered. In most cases, the system that is being studied is over a fiber-optic communication channel. Here a theoretical QKD system using the BB92 protocol and entangled photons over a free-space maritime channel with multiple spatial modes is presented. The entangled photons are generated from a spontaneous parametric down conversion (SPDC) source of type II. To employ multiple spatial modes, the transmit apparatus will contain multiple SPDC sources, all driven by the pump lasers assumed to have the same intensity. The receive apparatuses will contain avalanche photo diodes (APD), modeled based on the NuCrypt CPDS-1000 detector, and located at the focal point of the receive aperture lens. The transmitter is assumed to be located at Alice and Bob will be located 30 km away, implying no channel crosstalk will be introduced in the measurements at Alice’s side due to turbulence. To help mitigate the effects of atmospheric turbulence, adaptive optics will be considered at the transmitter and the receiver. An eavesdropper, Eve, is located 15 km from Alice and has no control over the devices at Alice or Bob. Eve is performing the intercept resend attack and listening to the communication over the public channel. Additionally, it is assumed that Eve can correct any aberrations caused by the atmospheric turbulence to determine which source the photon was transmitted from. One, four and nine spatial modes are considered with and without applying adaptive optics and compared to one another.
Quantum Key Distribution (QKD) is a communication method which exchanges secret keys using cryptographic protocols involving elements from quantum science. Continuous Variable (CV) QKD is a method to implement key exchange using sampling of Gaussian signals. Reconciliation in CV-QKD is fundamentally realized via coding of the Alice or Bob binary labels of the Gaussian samples using either one-way or interactive communications between the parties, Alice and Bob, over a public authenticated channel. We assume that the communication is performed through an Optical Wireless (OW) or Free Space Optics (FSO) channel. In that case the received signal suffers from stochastic fading due to pointing jitter or atmospheric turbulence. As a result of the channel fading and noise Alice and Bob Gaussian samples will not match. Information Reconciliation (IR) is the phase of the CV-QKD protocol that makes sure that Alice and Bob agree on a common and identical labeling of their samples, i.e. agree on a common stream of bits that we denote as “reconciled key.” The information reconciliation in CV-QKD could be done by one-way or two-way channel coding to correct the actual labels so that they do match. To do so Bob generates a sequence of parity bits using a systematic code. These bits are sent to Alice over an authenticated public channel. Alice then uses her own sequence of labels she obtains after quantization with the redundancy provided by Bob to recover Bob’s binary sequence. In this work we analyze the problem of information reconciliation for continuous variable quantum key distribution over a free space optics channel.
This paper proposes a novel quantum key distribution (QKD) set-up designed to enhance the security of a free-space optical (FSO) quantum communication system. By incorporating channel ordering information, the proposed QPSK-QKD (P-QPSK-QKD) system leverages the inherent randomness of FSO channels, providing dual protection against eavesdroppers (Eve). The first layer of security is achieved through the QPSK-QKD mechanism, while the second arises from the randomness of the FSO channels. To ensure a comprehensive investigation, the performance of P-QPSK-QKD and the existing QPSK-QKD (E-QPSK-QKD) system is analyzed using a Málaga distributed atmospheric turbulence channel model incorporating pointing errors. Novel closed-form expressions are derived for different performance metrics, including probability of sifted keys, quantum bit error rate, probability of Eve (Peve), and ergodic secret key rate (ESKR), under both perfect and imperfect feedback conditions. Intensive examination indicates that, unlike E-QPSK-QKD, wherePeveshows a water-falling trend with increasing signal-to-noise ratios (SNR) under dual thresholds, P-QPSK-QKD achieves a saturatedPeve, enhancing security. Moreover, under the single threshold,Peveof P-QPSK-QKD is twice that of E-QPSK-QKD. Additionally, due to channel randomness, the mutual information between Alice and Eve remains zero (for both single and dual thresholds), even at infinite SNR for P-QPSK-QKD, providing consistently higher ESKR than E-QPSK-QKD system under both perfect and imperfect feedback conditions.
The security of prepare-and-measure satellite-based quantum key distribution (QKD), under restricted eavesdropping scenarios, is addressed.We particularly consider cases where the eavesdropper, Eve, has limited access to the transmitted signal by Alice and/or Bob's receiver station.This restriction is modeled by lossy channels between relevant parties, where the transmissivity of such channels can, in principle, be bounded by monitoring techniques.An artifact of such lossy channels is the possibility of having bypass channels, those that are not accessible to Eve but that may not necessarily be characterized by the users either.This creates interesting unexplored scenarios for analyzing QKD security.In this paper, we obtain generic bounds on the key rate in the presence of bypass channels and apply them to continuousvariable QKD protocols with Gaussian encoding with direct and reverse reconciliation.We find regimes of operation in which the above restrictions on Eve can considerably improve system performance.We also develop customized bounds for several protocols in the BB84 family and show that, in certain regimes, even the simple protocol of BB84 with weak coherent pulses is able to offer positive key rates at high channel losses, which would otherwise be impossible under an unrestricted Eve.In this case, the limitation on Eve would allow Alice to send signals with larger intensities than the optimal value under an ideal Eve, which effectively reduces the effective channel loss.In all these cases, the part of the transmitted signal that does not reach Eve can play a nontrivial role in specifying the achievable key rate.Our work opens up new security frameworks for spaceborne quantum communications systems.
This paper studies a multiple-input multiple-output (MIMO) free-space optical (FSO) communication system employing continuous-variable quantum key distribution (CV-QKD), with the goal to support secret key transmission between two legitimate users, Alice and Bob. All involved wireless channels are subjected to atmospheric turbulence leading to beam spreading, pointing error, and turbulence-induced fading, which along with the presence of hybrid quantum noise negatively impact secret key exchange. Furthermore, the legitimate MIMO FSO system faces the threat of compromise from an eavesdropper, Eve, employing a collective Gaussian attack to intercept the secret key exchange. Novel one- and two-way protocols for enhancing the security of the transmitted keys are proposed. To this end, the transmissivity of the FSO channels is mathematically formulated and bounds on the mutual information between the transmitted and received coherent states are obtained, which are then used for deriving novel expressions for the secret key rates (SKRs) for both one- and two-way protocols. The presented numerical results corroborate the proposed analytical secrecy framework, quantifying the SKR gains obtained by employing MIMO and the two-way protocol for FSO CV-QKD systems.