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Security Issues of Quantum Cryptographic Systems with Imperfect Detectors

Viacheslav Burenkov

Published Jun 1, 2015• 1 citation
OpenAlex

Abstract

The laws of quantum physics can be used to secure communications between two distant parties in a scheme called quantum key distribution (QKD), even against a technologically unlimited eavesdropper. While the theoretical security of QKD has been proved rigorously, current implementations of QKD are generally insecure. In particular, mathematical models of devices, such as detectors, do not accurately describe their real-life behaviour. Such seemingly insignificant discrepancies can compromise the security of the entire scheme, especially as novel detector technologies are being developed with little regard for potential vulnerabilities.In this thesis, we study how detector imperfections can impact the security of QKD and how to overcome such technological limitations. We first analyze the security of a high-speed QKD system with finite detector dead time tau. We show that the previously reported sifting approaches are not guaranteed to be secure in this regime. More specifically, Eve can induce a basis-dependent detection efficiency at the receiver's end. Modified key sifting schemes that are basis-independent, and thus secure in the presence of dead time and an active eavesdropper, are discussed and compared. It is shown that the maximum key generation rate is 1/(2tau) for passive basis selection, and 1/tau for active basis selection. The security analysis is also extended to the decoy state BB84 protocol.We then study a relatively new type of single-photon detector called the superconducting nanowire single-photon detector (SNSPD), and discover some unexpected behaviour. We report an afterpulsing effect present when the SNSPD is operated in the high bias current regime. In our standard set-up, the afterpulsing is most likely to occur at around 180 ns following a detection event, for both real counts and dark counts. We characterize the afterpulsing behaviour and speculate that it is not due to the SNSPD itself but rather the associated read-out circuit. We also report and examine a short-lived enhancement of detection efficiency during the recovery of the SNSPD, as well as a longer dead time than previously thought. These findings should be of interest not only to the QKD community but also researchers using SNSPDs in other applications.

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The laws of quantum physics can be used to secure communications between two distant parties in a scheme called quantum key distribution (QKD), even against a technologically unlimited eavesdropper. While the theoretical security of QKD has been proved rigorously, current implementations of QKD are generally insecure. In particular, mathematical models of devices, such as detectors, do not accurately describe their real-life behaviour. Such seemingly insignificant discrepancies can compromise the security of the entire scheme, especially as novel detector technologies are being developed with little regard for potential vulnerabilities.In this thesis, we study how detector imperfections can impact the security of QKD and how to overcome such technological limitations. We first analyze the security of a high-speed QKD system with finite detector dead time tau. We show that the previously reported sifting approaches are not guaranteed to be secure in this regime. More specifically, Eve can induce a basis-dependent detection efficiency at the receiver's end. Modified key sifting schemes that are basis-independent, and thus secure in the presence of dead time and an active eavesdropper, are discussed and compared. It is shown that the maximum key generation rate is 1/(2tau) for passive basis selection, and 1/tau for active basis selection. The security analysis is also extended to the decoy state BB84 protocol.We then study a relatively new type of single-photon detector called the superconducting nanowire single-photon detector (SNSPD), and discover some unexpected behaviour. We report an afterpulsing effect present when the SNSPD is operated in the high bias current regime. In our standard set-up, the afterpulsing is most likely to occur at around 180 ns following a detection event, for both real counts and dark counts. We characterize the afterpulsing behaviour and speculate that it is not due to the SNSPD itself but rather the associated read-out circuit. We also report and examine a short-lived enhancement of detection efficiency during the recovery of the SNSPD, as well as a longer dead time than previously thought. These findings should be of interest not only to the QKD community but also researchers using SNSPDs in other applications.
The security of a high speed quantum key distribution system with finite detector dead time τ is analyzed. When the transmission rate becomes higher than the maximum count rate of the individual detectors (1/τ), security issues affect the algorithm for sifting bits. Analytical calculations and numerical simulations of the Bennett-Brassard BB84 protocol are performed. We study Rogers et al.'s protocol (introduced in "Detector dead-time effects and paralyzability in high-speed quantum key distribution," New J. Phys. 9 (2007) 319) in the presence of an active eavesdropper Eve who has the power to perform an intercept-resend attack. It is shown that Rogers et al.'s protocol is no longer secure. More specifically, Eve can induce a basis-dependent detection efficiency at the receiver's end. Modified key sifting schemes that are secure in the presence of dead time and an active eavesdropper are then introduced. We analyze and compare these secure sifting schemes for this active Eve scenario, and calculate and simulate their key generation rate. It is shown that the maximum key generation rate is 1/(2τ) for passive basis selection, and 1/τ for active basis selection. The security analysis for finite detector dead time is also extended to the decoy state BB84 protocol.
The security of a high speed quantum key distribution system with finite detector dead time τ\tauτ is analyzed. When the transmission rate becomes higher than the maximum count rate of the individual detectors (1/τ1/\tau1/τ), security issues affect the scheme for sifting bits. Analytical calculations and numerical simulations of the Bennett-Brassard BB84 protocol are performed. We study Rogers et al.'s scheme (further information is available in [D. J. Rogers, J. C. Bienfang, A. Nakassis, H. Xu, and C. W. Clark, New J. Phys.~{\bf 9}, 319 (2007)]) in the presence of an active eavesdropper Eve who has the power to perform an intercept-resend attack. It is shown that Rogers et al.'s scheme is no longer guaranteed to be secure. More specifically, Eve can induce a basis-dependent detection efficiency at the receiver's end. Modified key sifting schemes that are basis-independent and thus secure in the presence of dead time and an active eavesdropper are then introduced. We analyze and compare these secure sifting schemes for this active Eve scenario, and calculate and simulate their key generation rate. It is shown that the maximum key generation rate is 1/(2τ)1/(2\tau)1/(2τ) for passive basis selection, and 1/τ1/\tau1/τ for active basis selection. The security analysis for finite detector dead time is also extended to the decoy state BB84 protocol for one particular secure sifting scheme.
Quantum key distribution (QKD) allows for provably secure key distribution between two trusted parties. Because the security and performance of QKD protocols rely on devices that behave according to specific assumptions, idealized or inaccurate assumptions about device behavior can introduce security loopholes. Real devices can never be perfectly characterized, and their performance metrics are always subject to certain error margins, which must be accounted for in a rigorous theoretical analysis. Only recently have rigorous finite-size results allowed for imperfect characterizations of devices (where device parameter have uncertainty margins) - an advance yet to be considered in experimental implementations of the BB84 protocol. In this work, we prove the security and analyze the performance of an implementation of the BB84 protocol using single photons generated by a semiconductor quantum dot light source in combination with dynamic polarization-state encoding. We consider the presence of incompletely characterized devices by accounting for imperfections in the single-photon source (in terms of finite g(2)(0)) as well as the receiver (non-ideal beam-splitters, finite detector efficiencies, and dark counts), all with error margins. The resulting protocol implementation shows competitive performance, paving the way towards practical and loop-hole free implementations of QKD.
The rules of quantum mechanics makes it possible to exchange a secret key at a distance. This is called quantum key distribution (QKD). In theory the key exchange can be made completely secure. Real QKD implementations however, has numerous imperfections. Luckily one has also been able to prove the security of QKD with a large variety of imperfections. The field of QKD has matured over the recent years, and it has now reached commercial applications with photons as the quantum bits, and optical fibers as the quantum channel. Today there are at least three commercial vendors of QKD-systems. We live in the times of quantum hacking. Researchers has begun the task of breaking the security of QKD-systems. Many new imperfections has been discovered, some of which might be used to break the security of QKD. This thesis is a study of the detector efficiency mismatch loophole. Most QKD-systems require two detectors, and it is virtually impossible to make two identical detectors with the exact same efficiency. What is worse, it turns out that the eavesdropper can often control the relative efficiencies of the two detectors trough some domain, for instance by controlling the timing, the frequency or the spacial mode of the photons. This can in turn be used by the eavesdropper to gain information about the secret key. Previously the best known attack would compromise security if the detector efficiency mismatch of about 1:15. Here the current attacks on systems with detector efficiency mismatch are improved to compromise security for a mismatch of about 1:4. This is less than the mismatch found in a commercial QKD-system, so the attack could in principle be used to eavesdrop on this QKD-system. One might try to close the loophole by modifying the implementation. One suggestion is the four state Bob. The problem is that this patch will in turn open other loopholes, and one of these loopholes reopen the detector efficiency mismatch loophole. One can remove Eves information about the key by doing a sufficient amount of extra privacy amplification. Here a general security bound is presented, quantifying the required amount of extra privacy amplification to remove Eve's information about the key. The proof is more general than the previous security proof, and is valid for any basis dependent, possibly lossy, linear optical imperfections in the channel and receiver/detectors. Since this is more realistic assumptions for a QKD-implementation, the proof represents a major step of closing the loophole in real devices.
Decoy-state quantum key distribution (QKD) is the most widely adopted approach for overcoming the limitations of imperfect single-photon sources. However, existing security proofs typically either neglect important device imperfections or rely on assumptions that are difficult to justify in realistic high-speed implementations, such as the independent and identically distributed nature of the emitted signals. In this work, we combine and extend several recent theoretical advances to provide a comprehensive analytical finite-key security proof for decoy-state QKD that simultaneously incorporates multiple practically relevant transmitter and receiver imperfections, including state-preparation flaws, bit and basis side-channel leakage and correlations, setting-independent intensity fluctuations, and detection-efficiency mismatches.
Quantum cryptography or quantum key distribution (QKD) applies fundamental laws of quantum physics to guarantee secure communication. The security of quantum cryptography was proven in the last decade. Many security analyses are based on the assumption that QKD system components are idealized. In practice, inevitable device imperfections may compromise security unless these imperfections are well investigated.\n\nA highly attenuated laser pulse which gives a weak coherent state is widely used in QKD experiments. A weak coherent state has multi-photon components, which opens up a security loophole to the sophisticated eavesdropper. With a small adjustment of the hardware, we will prove that the decoy state method can close this loophole and substantially improve the QKD performance. We also propose a few practical decoy state protocols, study statistical fluctuations and perform experimental demonstrations. Moreover, we will apply the methods from entanglement distillation protocols based on two-way classical communication to improve the decoy state QKD performance. Furthermore, we study the decoy state methods for other single photon sources, such as triggering parametric down-conversion (PDC) source. Note that our work, decoy state protocol, has attracted a lot of scientific and media interest. The decoy state QKD becomes a standard technique for prepare-and-measure QKD schemes.\n\nAside from single-photon-based QKD schemes, there is another type of scheme based on entangled photon sources. A PDC source is commonly used as an entangled photon source. We propose a model and post-processing scheme for the entanglement-based QKD with a PDC source. Although the model is proposed to study the entanglement-based QKD, we emphasize that our generic model may also be useful for other non-QKD experiments involving a PDC source. By simulating a real PDC experiment, we show that the entanglement-based QKD can achieve longer maximal secure distance than the single-photon-based QKD schemes.\n\nWe propose a time-shift attack that exploits the efficiency mismatch of two single photon detectors in a QKD system. This eavesdropping strategy can be realized by current technology. We will also discuss counter measures against the attack and study the security of a QKD system with efficiency mismatch detectors.