Security and communication distance improvement in decoy states based quantum key distribution using pseudo-random bases choice for photon polarization measurement
Abstract This paper proposes a new quantum key distribution(QKD) protocol, namely the pseudo-random bases entangled photon based QKD (PRB-EPQKD) protocol. The latest mainly focuses on three properties, including the security of the protocol, the secure key size and the maximum communication distance between legitimate communication users (Alice and Bob). To achieve this, we first consider a spontaneous-parametric-down (SPDC) photon source located in a low-earth-orbit (LEO) type satellite capable of producing and distributing entangled photons pairs to Alice and Bob. Secondly, we assume that Alice's and Bob's photons state measurement bases are identically generated via a pseudo-random number generator (PRNG), namely the quantum logistic map (QLM). Finally, we also assume that in addition to their photons states, Alice and Bob intentionally share a set of decoy states at each pulse with randomly selected intensity, and with the goal to detect the presence of the eavesdropper (Eve). Under these considerations, the secure key rate upper bound is evaluated applying the Gottesman-Lo-Lutkenhaus-Preskill's (GLLP) formula, for two different implementations, namely the non-decoy states and the infinite active decoy states based QKD. It is observed a significant improvement in the secure key size and the communication distance as well, compared to existing protocols, since we realize that under daylight, downlinks satellite conditions, a kindly selected light source, and good crystal's properties, the maximum communication distance can reach up to 70000 km. In addition, using the combined type-I and type-II SPDC photons source as our entangled photons pairs generator, significantly improved the photon mean number and render our protocol more robust against photon number division attack and against attenuation-induced atmospheric propagation. Furthermore, the protocol is more secure as compared to existing ones, given that any eavesdropper must crack simultaneously the chaotic system used as PRNG and the QKD system, before getting any useful information as regards to the measurement bases used by Alice and Bob, and thus the secure key.
Abstract This paper proposes a new quantum key distribution(QKD) protocol, namely the pseudo-random bases entangled photon based QKD (PRB-EPQKD) protocol. The latest mainly focuses on three properties, including the security of the protocol, the secure key size and the maximum communication distance between legitimate communication users (Alice and Bob). To achieve this, we first consider a spontaneous-parametric-down (SPDC) photon source located in a low-earth-orbit (LEO) type satellite capable of producing and distributing entangled photons pairs to Alice and Bob. Secondly, we assume that Alice's and Bob's photons state measurement bases are identically generated via a pseudo-random number generator (PRNG), namely the quantum logistic map (QLM). Finally, we also assume that in addition to their photons states, Alice and Bob intentionally share a set of decoy states at each pulse with randomly selected intensity, and with the goal to detect the presence of the eavesdropper (Eve). Under these considerations, the secure key rate upper bound is evaluated applying the Gottesman-Lo-Lutkenhaus-Preskill's (GLLP) formula, for two different implementations, namely the non-decoy states and the infinite active decoy states based QKD. It is observed a significant improvement in the secure key size and the communication distance as well, compared to existing protocols, since we realize that under daylight, downlinks satellite conditions, a kindly selected light source, and good crystal's properties, the maximum communication distance can reach up to 70000 km. In addition, using the combined type-I and type-II SPDC photons source as our entangled photons pairs generator, significantly improved the photon mean number and render our protocol more robust against photon number division attack and against attenuation-induced atmospheric propagation. Furthermore, the protocol is more secure as compared to existing ones, given that any eavesdropper must crack simultaneously the chaotic system used as PRNG and the QKD system, before getting any useful information as regards to the measurement bases used by Alice and Bob, and thus the secure key.
Abstract Ideal quantum key distribution (QKD) protocols require perfect single photon sources, detectors, and lossless channels. However, the present technology cannot ensure all of the requirements. Among the variants of practical QKD schemes, decoy state QKD in its present form approaches nearly the theoretical security. In any decoy state method, a compromise is made between the security of the key distribution and the rate of key generation by optimizing the two major protocol parameters: the number of decoy states and their relative intensities, and the length of the data string as well. Use of more number of decoy states and higher range of intensities though improve security, their optimization becomes too complex. Therefore, from practical consideration, some restrictions are to be imposed on the choice of decoy states and their intensities. In addition, the treatment of correlations among the laser pulses in security analysis is not fully understood. Normally, lack of correlations or randomness among the signal states is considered to gain security, but, in a different approach, described in the proposed protocol, additional correlation is introduced to improve key generation rate without compromising security. To do that, a one-way function is shared among the legitimate users to provide a semi-random choice of bases depending on the outcome of the receiver’s detector. The initial communication is made through a set of bits with predefined bases and intensity distribution. Then, with the help of the positive outcome of the receiver’s detector, the basis set as well as the length of the bit string for subsequent communications are computed. This results in correlation among the bases and the relative intensities of the signal states and provides a self-checking mechanism to identify eavesdropping. The security analysis of the protocol provides a low error rate and a relatively high key generation rate.
Abstract: The quantum key distribution (QKD) technique establishes secret keys shared between two communicating parties. Theoretically, unconditional security provided by QKD is guaranteed by the fundamental laws of quantum physics. in the real life, it is still possible to obtain unconditionally secure QKD, even with (phase randomized) attenuated laser pulses, as theoretically demonstrated by Gottesman-Lo-L¨utkenhaus-Preskill (GLLP). However, one must pay a steep price by placing severe limits on the distance and the key generation rate. These problems were solved using the decoy state method introduced by Hwang. In this paper, we have proposed a method to estimate parameters of the decoy state method based on two decoy state protocol for both BB84 and SARG04. The vacuum and weak decoy state protocol has been introduced as a special case of two decoy states protocol. This method has given different lower bound of the fraction of single-photon counts (y1), the fraction of two-photon counts (y2), the upper bound QBER of single-photon pulses (e1), the upper bound QBER of two-photon pulses (e2) and the lower bound of key generation rate for both BB84 and SARG04. The fiber based QKD systems also have been simulated using the proposed method for BB84 and SARG04. The numerical simulation has shown that the fiber based QKD systems using the proposed method for BB84 are able to achieve both a higher secret key rate and greater secure distance than that of SARG04. Key words: Quantum cryptography Quantum key distribution Decoy state protocol and optical communications
Problem statement: Quantum key distribution provides unconditional security guaranteed by the fundamental laws of quantum physics. Unfortunately, for real-life experimental set-ups, which mainly based on faint laser pulses, the occasional production of multi-photons and channel loss make it possible for sophisticated eavesdroppers to launch various subtle eavesdropping attacks including the Photon Number Splitting (PNS) attack. The decoy state protocols recently proposed to beat PNS attack and to improve dramatically distance and secure key generation rate of Quantum Key Distribution (QKD). Approach: Objective of this study was experimental implementation of weak decoy + vacuum states QKD for increasing the performance of QKD system. To show conceptually how simple it was to apply the weak decoy + vacuum state idea to a commercial QKD system, we chosen ID-3000 commercial quantum key distribution system manufactured by id quantique. To implement the weak decoy + vacuum state protocol, we had to add some new optical and electronics components to id quantique and to attenuate each signal to the intensity of either signal state or weak decoy or vacuum state randomly. Results: In our implementation, the attenuation will be done by placing a VOA (variable optical attenuator) in Alice’s side. Specifically, our QKD system required the polarizations of 2 pulses from the same signal to be orthogonal. Therefore the VOA must be polarization independent so as to attenuate the two pulses equally. The VOA utilized in experiment to attenuate signals dynamically was Intensity Modulator (IM). We had implemented weak + vacuum protocol on a modified commercial QKD system over a 25 km of telecom fibers with an unconditionally secure key rate of 6.2931×10-4 per pulse. Conclusion: By making simple modifications to a commercial quantum key distribution system, we could achieve much better performance with substantially higher key generation rate and longer distance than QKD system without decoy state.
In the age of information and globalisation, secure communication as well as the protection of sensitive data against unauthorised access are of utmost importance. Quantum cryptography currently provides the only way to exchange a cryptographic key between two parties in an unconditionally secure fashion. Owing to losses and noise of today's optical fibre and detector technology, at present quantum cryptography is limited to distances below a few 100 km. In principle, larger distances could be subdivided into shorter segments, but the required quantum repeaters are still beyond current technology. An alternative approach for bridging larger distances is a satellite-based system, that would enable secret key exchange between two arbitrary points on the globe using free-space optical communication. The aim of the presented experiment was to investigate the feasibility of satellite-based global quantum key distribution. In this context, a free-space quantum key distribution experiment over a real distance of 144 km was performed. The transmitter and the receiver were situated in 2500 m altitude on the Canary Islands of La Palma and Tenerife, respectively. The small and compact transmitter unit generated attenuated laser pulses, that were sent to the receiver via a 15-cm optical telescope. The receiver unit for polarisation analysis and detection of the sent pulses was integrated into an existing mirror telescope designed for classical optical satellite communications. To ensure the required stability and efficiency of the optical link in the presence of atmospheric turbulence, the two telescopes were equipped with a bi-directional automatic tracking system. Still, due to stray light and high optical attenuation, secure key exchange would not be possible using attenuated pulses in connection with the standard BB84 protocol. The photon number statistics of attenuated pulses follows a Poissonian distribution. Hence, by removing a photon from all pulses containing two or more photons, an eavesdropper could measure its polarisation without disturbing the polarisation state of the remaining pulse. In this way, he can gain information about the key without introducing detectable errors. To protect against such attacks, the presented experiment employed the recently developed method of using additional "decoy" states, i.e., the the intensity of the pulses created by the transmitter were varied in a random manner. By analysing the detection probabilities of the different pulses individually, a photon-number-splitting attack can be detected. Thanks to the decoy-state analysis, the secrecy of the resulting quantum key could be ensured despite the Poissonian nature of the emitted pulses. For a channel attenuation as high as 35 dB, a secret key rate of up to 250 bit/s was achieved. Our outdoor experiment was carried out under real atmospheric conditions and with a channel attenuation comparable to an optical link from ground to a satellite in low earth orbit. Hence, it definitely shows the feasibility of satellite-based quantum key distribution using a technologically comparatively simple system.
In this paper we analyze the feasibility of performing Quantum Key Distribution (QKD), in Earth-satellite up and downlinks and in intersatellite links, with two quantum cryptography protocols: BB84 and SARG04, and with two implementation options: with and without decoy states. As real measurements in these scenarios are not possible yet, the objective is to obtain results as realistic as possible to support the design of future satellite missions performing QKD. Therefore, we use realistic values for the optical hardware and take into account usual atmospheric conditions. In the same line, we assume specific types of attacks, namely the photon number splitting and the intercept-resend with unambiguous discrimination attacks, which could likely be the main threat to the first satellite-based QKD applications. A lower bound on the key generation rate of SARG04 with two decoy states is presented. The optimum signal- and decoy-states mean photon numbers for each protocol and each distance are also computed. The resulting values for the signal-state are larger than those often employed. We show that it may be possible to establish QKD with LEO (Low Earth Orbit) and, under certain circumstances, with MEO (Medium Earth Orbit) satellites, but not with GEO (Geostationary) ones. Furthermore, we obtain that the optimum signal-state mean photon number for SARG04 with two decoy states is almost independent of the link distance, which greatly facilitates its use in a real scenario.
Quantum Key Distribution (QKD) enables the sharing of cryptographic keys secured by quantum mechanics. The BB84 protocol assumes single-photon sources, but practical systems rely on weak coherent pulses vulnerable to Photon-Number-Splitting (PNS) attacks. The Gottesman-Lo-Lütkenhaus-Preskill (GLLP) framework addresses these imperfections, deriving secure key rate bounds under limited PNS scenarios. The decoy-state protocol further improves performance by refining single-photon yield estimates, but still considers multi-photon states as insecure, thereby limiting intensities and constraining key rate and distance. More recently, finite-key security bounds for decoy-state QKD have been extended to address general attacks, ensuring security against adversaries capable of exploiting arbitrary strategies. In this work, we focus on a specific class of attacks, the generalized PNS attack, and demonstrate that higher pulse intensities can be securely used by employing Bayesian inference to estimate key parameters directly from observed data. By raising the pulse intensity to 10 photons, we achieve a 50-fold increase in key rate and a 62.2% increase in operational range (about 200 km) compared to the decoy-state protocol. Furthermore, we accurately model after-pulsing using a Hidden Markov Model (HMM) and reveal inaccuracies in decoy-state calculations that may produce erroneous key-rate estimates. While this methodology does not address all possible attacks, it provides a new approach to security proofs in QKD by shifting from worst-case assumption analysis to observation-dependent inference, advancing the reach and efficiency of discrete-variable QKD protocols.