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arXiv:1903.03136 · Physical Review Applied

Secret-Key Distillation across a Quantum Wiretap Channel under Restricted Eavesdropping

Ziwen Pan, Kaushik Parasuram Seshadreesan, William Clark, Mark R. Adcock, Ivan B. Djordjevic, Jeffrey H. Shapiro, Saikat Guha

Published Aug 17, 2020• 39 citations
arXivHTMLPDF

Abstract

The theory of quantum cryptography aims to guarantee unconditional information-theoretic security against an omnipotent eavesdropper. In many practical scenarios, however, the assumption of an all-powerful adversary is excessive and can be relaxed considerably. In this paper we study secret-key distillation across a lossy and noisy quantum wiretap channel between Alice and Bob, with a separately parameterized realistically lossy quantum channel to the eavesdropper Eve. We show that under such restricted eavesdropping, the key rates achievable can exceed the secret-key-distillation capacity against an unrestricted eavesdropper in the quantum wiretap channel. Furthermore, we show upper bounds on the key rates based on the relative entropy of entanglement. This simple restricted eavesdropping model is widely applicable, for example, to free-space quantum optical communication, where realistic collection of light by Eve is limited by the finite size of her optical aperture. Future work will include calculating bounds on the amount of light Eve can collect under various realistic scenarios.

DOI
10.1103/physrevapplied.14.024044

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The theory of quantum cryptography aims to guarantee unconditional information-theoretic security against an omnipotent eavesdropper. In many practical scenarios, however, the assumption of an all-powerful adversary is excessive and can be relaxed considerably. In this paper we study secret-key distillation across a lossy and noisy quantum wiretap channel between Alice and Bob, with a separately parameterized realistically lossy quantum channel to the eavesdropper Eve. We show that under such restricted eavesdropping, the key rates achievable can exceed the secret-key-distillation capacity against an unrestricted eavesdropper in the quantum wiretap channel. Furthermore, we show upper bounds on the key rates based on the relative entropy of entanglement. This simple restricted eavesdropping model is widely applicable, for example, to free-space quantum optical communication, where realistic collection of light by Eve is limited by the finite size of her optical aperture. Future work will include calculating bounds on the amount of light Eve can collect under various realistic scenarios.
Quantum cryptography provides absolute security against an all-powerful eavesdropper (Eve). However, in practice Eve's resources may be restricted to a limited aperture size so that she cannot collect all paraxial light without alerting the communicating parties (Alice and Bob). In this paper we study a quantum wiretap channel in which the connection from Alice to Eve is lossy, so that some of the transmitted quantum information is inaccessible to both Bob and Eve. For a pureloss channel under such restricted eavesdropping, we show that the key rates achievable with a two-mode squeezed vacuum state, heterodyne detection, and public classical communication assistance-given by the Hashing inequality-can exceed the secret key distillation capacity of the channel against an omnipotent eavesdropper. We report upper bounds on the key rates under the restricted eavesdropping model based on the relative entropy of entanglement, which closely match the achievable rates. For the pure-loss channel under restricted eavesdropping, we compare the secret-key rates of continuous-variable (CV) quantum key distribution (QKD) based on Gaussian-modulated coherent states and heterodyne detection with the discrete variable (DV) decoystate BB84 QKD protocol based on polarization qubits encoded in weak coherent laser pulses.
The conventional omnipotent eavesdropper assumption in quantum cryptography study can be too strict for some realistic scenarios. In this paper, we study the secret key distillation over a satellite-to-satellite free space optics channel in which we assume that the eavesdropper (Eve) is restricted in her ability of power collection due to the limited size of her aperture but can change the position of her aperture to gain advantages over the communication parties (Alice and Bob) and we determine the achievable key rate lower and upper bounds with respect to different scenarios. We first study the case where Eve is behind Bob and we prove that the optimal eavesdropping strategy for her in long-distance transmission case is to place her aperture on the beam transmission axis and set Bob-to-Eve distance equal to Alice-to-Bob distance. We also show that the achievable key rate would be characterized by a Bessel function integral related to Eve's position in a short-distance transmission case. We then investigate the case where Eve is before Bob and show similar results with Eve's and Bob's roles exchanged.
Quantum cryptography is the study of unconditional information security against an all-powerful eavesdropper in secret key distillation. However, the assumption of an omnipotent eavesdropper is too strict for some realistic implementations. In this paper, we study the realistic application model of secret key distillation over a satellite-to-satellite free-space channel in which we impose a reasonable restriction on the eavesdropper by setting an exclusion zone around the legitimate receiver as a defense strategy. We first study the case where the eavesdropper’s aperture size is unlimited so their power is only restricted by the exclusion zone. Then, we limit Eve’s aperture to a finite size and study the straightforward case when her aperture is in the same plane of Bob’s, investigating how an exclusion zone can help improve security. Correspondingly, we determine the secret key rate lower bounds as well as upper bounds. Furthermore, we also apply our results on specific discrete variable (DV) and continuous variable (CV) protocols for comparison. We show that, by putting reasonable restrictions on the eavesdropper through the realistic assumptions of an inaccessible exclusion zone, we can significantly increase the key rate in comparison to those without and do so with relatively lower transmission frequency. We conclude that this model is suitable for extended analysis in many light-gathering scenarios and for different carrier wavelengths.
Conventionally, unconditional information security has been studied by quantum cryptography although the assumption of an omnipotent eavesdropper is too strict for some realistic implementations. In this paper, we study the realistic secret key distillation over a satellite-to-satellite free space optics channel where we assume a limited-sized aperture eavesdropper (Eve) in the same plane of the legitimate receiver (Bob) and determine the secret key rate (SKR) lower bounds correspondingly. We first study the input power dependency without assumptions on Bob's detection scheme before optimizing the input power to determine lower bounds as functions of transmission distances, center frequency or Eve aperture radius. Then we calculate analytical expressions regarding the SKR lower bound and upper bound as transmission distance goes to infinity. We also incorporate specific discrete variable (DV) and continuous variable (CV) protocols for comparison. We demonstrate that significantly higher SKR lower bounds can be achieved compared to traditional unrestricted Eve scenario.
Quantum cryptography studies the unconditional information security against an all-powerful eavesdropper in secret key distillation. However the assumption of an omnipotent eavesdropper is too strict for some realistic implementations. In this paper we study the realistic application model of secret key distillation over satellite-to-satellite free space channel in which we impose a reasonable restriction on the eavesdropper by setting an exclusion zone around the legitimate receiver as a defense strategy. We first study the case where the eavesdropper's aperture size is unlimited so her power is only restricted by the exclusion zone. Then we limit Eve's aperture to a finite size and study the straightforward case when her aperture is in the same plane of Bob, investigating how an exclusion zone can help improve security. Correspondingly, we determine the secret key rate lower bounds as well as upper bounds. Further more, we also apply our results on specific discrete variable (DV) and continuous variable (CV) protocols for comparison. We show that by putting reasonable restrictions on the eavesdropper through the realistic assumptions of an inaccessible exclusion zone, we can increase the key rate in comparison to those without and do so with relatively lower transmission frequency. We conclude that this model is suitable for extended analysis in many light gathering scenarios and for different carrier wavelengths.
Research on optimal eavesdropping models under practical conditions will help to evaluate realistic risk when employing a quantum key distribution system for secure information transmission. Intuitively, fiber loss will lead to the optical energy leaking to the environment, rather than harvested by the eavesdropper, which also limits the eavesdropping ability while improving the quantum key distribution system performance in practical use. However, defining the optimal eavesdropping model in the presence of lossy fiber is difficult because the channel is beyond the control of legitimate partners and the leaked signal is undetectable. Here we investigate how the fiber loss influences the eavesdropping ability based on a teleportation-based collective attack model, which requires two distant stations and a shared entanglement source. We find that if the distributed entanglement is limited due to the practical loss, the optimal attack occurs when the two teleportation stations are merged to one and placed close to the transmitter site, which performs similar to the entangling-cloning attack but with a reduced wiretapping ratio. Assuming Eve uses the best available hollow-core fiber, the secret key rate in the practical environment can be 20--40% higher than that under ideal eavesdropping. While if the entanglement distillation technology is mature enough to provide high quality of distributed entanglement, the two teleportation stations should be distantly separated for better eavesdropping performance, where the eavesdropping can even approach the optimal collective attack. Under the current level of entanglement purification technology, the unavoidable fiber loss can still greatly limit the eavesdropping ability as well as enhance the secret key rate and transmission distance of the realistic system, which promotes the development of quantum key distribution systems in practical application scenarios.