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arXiv:1309.2711

Intrinsic-Correlation Quantum Key Generation

Kim Fook Lee, Yong Meng Sua

Published Sep 11, 2013• 1 citation
arXivHTMLPDF

Abstract

A new conceptual key generation scheme is presented by using intrinsic quantum correlations of single photons between Alice and Bob. The intrinsic bi-partite correlation functions allow key bit to be generated through high level communication language i.e. a key bit is directly encoded to shared correlation functions not to the state and detection of a photon at Bob does not mean key bit. These make the scheme robust against intercept-resend attack because Alice and Bob can always check the errors in their measurements and reveal the presence of Eve in their channel without leaking any key bit information. The laser source is located in the middle of Alice and Bob, consists of two modes (x,y), relatively random phase-modulated $(\pm \fracπ{2})$ weak coherent states combined in a perfect 50/50 beam splitter. The scheme is strictly relied on the perfect beam splitter and mean photon number less than 1, where more than one photon in a coherent pulse will introduce more errors in Bob even without the presence of Eve. From the percentage of errors in Bob, we can estimate the amount of information will be leaked to Eve in the photon-number splitting attack. This scheme can preserve the randomness of phase-randomized light source for doubling the communication distance as in original Ekert's protocol and providing the raw key generation rate a factor of 2 higher than weak coherent light protocols.

DOI
10.48550/arxiv.1309.2711

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A new conceptual key generation scheme is presented by using intrinsic quantum correlations of single photons between Alice and Bob. The intrinsic bi-partite correlation functions allow key bit to be generated through high level communication language i.e. a key bit is directly encoded to shared correlation functions not to the state and detection of a photon at Bob does not mean key bit. These make the scheme robust against intercept-resend attack because Alice and Bob can always check the errors in their measurements and reveal the presence of Eve in their channel without leaking any key bit information. The laser source is located in the middle of Alice and Bob, consists of two modes (x,y), relatively random phase-modulated (±π2)(\pm \fracπ{2})(±2π​) weak coherent states combined in a perfect 50/50 beam splitter. The scheme is strictly relied on the perfect beam splitter and mean photon number less than 1, where more than one photon in a coherent pulse will introduce more errors in Bob even without the presence of Eve. From the percentage of errors in Bob, we can estimate the amount of information will be leaked to Eve in the photon-number splitting attack. This scheme can preserve the randomness of phase-randomized light source for doubling the communication distance as in original Ekert's protocol and providing the raw key generation rate a factor of 2 higher than weak coherent light protocols.
We present a scheme for key distribution based on bi-partite correlation of single photons. Alice keeps an ancilla photon and sends a signal photon to Bob, where intrinsic bi-partite correlation of these photons is obtained through first order intensity correlation in their detectors. The key bits are distributed through sharing four bi-partite correlation functions and photon counting. The scheme consists of two parts; first, Alice prepares deterministic photon states and Bob measures the photon states based on his random choice on correlation functions. Second, Alice guesses Bob's choice of correlation functions and sets the key bits by sending out photon states. Bob verifies the key bits through the photon states regardless Alice made a right or wrong guess. We called this key distribution scheme as prepare-measure-guess-verify (PMGV) protocol. We discuss the protocol by using a highly attenuated laser light, and then point out the advantages of using a fiber based correlated photon-pair to achieve better performance in security, communication distance and success rate of key distribution.
We propose a class of quantum cryptography protocols that are robust against photon-number-splitting attacks (PNS) in a weak coherent-pulse implementation. We give a quite exhaustive analysis of several eavesdropping attacks on these schemes. The honest parties (Alice and Bob) use present-day technology, in particular an attenuated laser as an approximation of a single-photon source. The idea of the protocols is to exploit the nonorthogonality of quantum states to decrease the information accessible to Eve due to the multiphoton pulses produced by the imperfect source. The distance at which the key distribution becomes insecure due to the PNS attack is significantly increased compared to the existing schemes. We also show that strong-pulse implementations, where a strong pulse is included as a reference, allow for key distribution robust against photon-number-splitting attacks.
We have implemented an experimental setup in order to demonstrate the feasibility of time-coding protocols for quantum key distribution. Alice produces coherent 20-ns faint pulses of light at 853 nm. They are sent to Bob with delay 0 ns (encoding bit 0) or 10 ns (encoding bit 1). Bob directs at random the received pulses to two different arms. In the first one, a 300 ps resolution Si photon counter allows Bob to precisely measure the detection times of each photon in order to establish the key. Comparing them with the emission times of the pulses sent by Alice allows one to evaluate the quantum bit error rate (QBER). The minimum obtained QBER is 1.62%. The possible loss of coherence in the setup can be exploited by Eve to eavesdrop the line. Therefore, the second arm of Bob setup is a Mach-Zehnder interferometer with a 10 ns propagation delay between the two paths. Contrast measurement of the output beams allows one to measure the autocorrelation function of the received pulses that characterizes their average coherence. In the case of an ideal setup, the value expected with the pulses sent by Alice is 0.576. The experimental value of the pulses autocorrelation function is found to be 0.541. Knowing the resulting loss of coherence and the measured QBER, one can evaluate the mutual information between Alice and Eve and the mutual information between Alice and Bob, in the case of intercept-resend attacks and in the case of attacks with intrication. With our values, Bob has an advantage on Eve of 0.43 bit per pulse. The maximum possible QBER corresponding to equal informations for Bob and Eve is 5.8%. With the usual attenuation of fibres at 850 nm, it shows that secure key distribution is possible up to a distance of 2.75 km, which is sufficient for local links.
Quantum-based cryptographic protocols are often said to enjoy security guaranteed by the fundamental laws of physics. However, even carefully designed quantum-based cryptographic schemes may be susceptible to subtle attacks that are outside the original design. As an example, we give attacks against a recently proposed ``secure communication using mesoscopic coherent states'', which employs mesoscopic states, rather than single-photon states. Our attacks can be used either as a known-plaintext attack or in the case where the plaintext has not been randomized. One of our attacks requires beamsplitters and the replacement of a lossy channel by a lossless one. It is successful provided that the original loss in the channel is so big that Eve can obtain 2k2^k2k copies of what Bob receives, where kkk is the length of the seed key pre-shared by Alice and Bob. In addition, substantial improvements over such an exhaustive key search attack can be made, whenever a key is reused. Furthermore, we remark that, under the same assumption of a known or non-random plaintext, Grover's exhaustive key search attack can be applied directly to "secure communication using mesoscopic coherent states", whenever the channel loss is more than 50 percent. Therefore, as far as information-theoretic security is concerned, optically amplified signals necessarily degrade the security of the proposed scheme, when the plaintext is known or non-random. Our attacks apply even if the mesoscopic scheme is used only for key generation with a subsequent use of the key for one-time-pad encryption. Studying those attacks can help us to better define the risk models and parameter spaces in which quantum-based cryptographic schemes can operate securely. Finally, we remark that our attacks do not affect standard protocols such as Bennett-Brassard BB84 protocol or Bennett B92 protocol, which rely on single-photon signals.
In elaborating on the multiple-photon absorption attack on Ekert protocol proposed in arXiv:1011.4740, we show that it can be used in other entanglement-based protocols, in particular the BBM92 protocol. In this attack, the eavesdropper (Eve) is assumed to be in control of the source, and she sends pulses correlated in polarization (but not entangled) containing several photons at frequencies for which only multiple-photon absorptions are possible in Alice's and Bob's detectors. Whenever the photons stemming from one pulse are dispatched in such a way that the number of photons is insufficient to trigger a multiple-photon absorption in either channel, the pulse remains undetected. We show that this simple feature is enough to reproduce the type of statistics on the detected pulses that are considered as indicating a secure quantum key distribution, even though the source is actually a mixture of separable states. The violation of Bell inequalities measured by Alice and Bob increases with the order of the multiple-photon absorption that Eve can drive into their detectors, while the measured quantum bit error rate decreases as a function of the same variable. We show that the attack can be successful even in the simplest case of a two-photon absorption or three-photon absorption attack, and we discuss possible countermeasures, in particular the use of a fair sampling test.
Quantum-key distribution (QKD) schemes employing quantum communication links are typically based on the transmission of weak optical pulses over optical fibers to setup a secret key between the transmitting and receiving nodes. Alice transmits optically a random bit stream to the receiver (Bob) through the photon polarizations or the quadrature components of the lightwaves associated with the photons, with a secret key remaining implicitly embedded therein. However, during the above transmission, some eavesdropper (Eve) might attempt to tap the passing-by photons from the optical fiber links to extract the key. In one of the popular QKD schemes, along with signal pulses, some additional decoy pulses are transmitted by Alice, while Eve might use photon-number splitting (PNS) for eavesdropping. In a typical PNS scheme, (i) the optical pulses with single photon are blocked by Eve, (ii) from the optical pulses with two photons, one photon is retained by Eve to carry out eavesdropping operation and the other is retransmitted to Bob, and (iii) all other pulses with more than two photons are retransmitted by Eve to Bob without retaining any photon from them. Extensive theoretical research has been carried out on such QKD schemes, by employing information-theoretic approach along with computer simulations and experimental studies. We present a novel event-by-event impairment enumeration approach to evaluate the overall performance of one such QKD scheme analytically with due consideration to the physical layer of the quantum communication links. The proposed approach monitors the impairments of the propagating optical pulses event-by-event at all possible locations along the optical fiber link using statistical approach, and provides estimates of the realizable key generation rate, while assuring an adequate yield ratio between signal and decoy pulses for the detection of possible eavesdropping.