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arXiv:quant-ph/0611235 · Physical Review A

Complete physical simulation of the entangling-probe attack on the Bennett-Brassard 1984 protocol

Taehyun Kim, Ingo Stork genannt Wersborg, Franco N. C. Wong, Jeffrey H. Shapiro

Published Apr 25, 2007• 31 citations
arXivHTMLPDF

Abstract

We have used deterministic single-photon two-qubit quantum logic to implement the most powerful individual-photon attack against the Bennett-Brassard 1984 (BB84) quantum key distribution protocol. Our measurement results, including physical source and gate errors, are in good agreement with theoretical predictions for the R\'enyi information obtained by Eve as a function of the errors she imparts to Alice and Bob's sifted key bits. The current experiment is a physical simulation of a true attack, because Eve has access to Bob's physical receiver module. Nevertheless, the physical simulation allows investigation of the fundamental security limit of the BB84 protocol against eavesdropping in the presence of realistic physical errors, and it affords the opportunity to study the effectiveness of error correction and privacy amplification when the BB84 protocol is attacked.

DOI
10.1103/physreva.75.042327

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•Mar 24, 2004•0 citations
We have used deterministic single-photon two-qubit quantum logic to implement the most powerful individual-photon attack against the Bennett-Brassard 1984 (BB84) quantum key distribution protocol. Our measurement results, including physical source and gate errors, are in good agreement with theoretical predictions for the R'enyi information obtained by Eve as a function of the errors she imparts to Alice and Bob's sifted key bits. The current experiment is a physical simulation of a true attack, because Eve has access to Bob's physical receiver module. Nevertheless, the physical simulation allows investigation of the fundamental security limit of the BB84 protocol against eavesdropping in the presence of realistic physical errors, and it affords the opportunity to study the effectiveness of error correction and privacy amplification when the BB84 protocol is attacked.
The Fuchs-Peres-Brandt (FPB) probe realizes the most powerful individual attack on Bennett-Brassard 1984 quantum key distribution (BB84 QKD) by means of a single controlled-NOT (CNOT) gate. This paper describes a complete physical simulation of the FPB-probe attack on polarization-based BB84 QKD using a deterministic CNOT constructed from single-photon two-qubit quantum logic. Adding polarization-preserving quantum nondemolition measurements of photon number to this configuration converts the physical simulation into a true deterministic realization of the FPB attack.
We investigate the security of quantum key distribution with entangled photons, focusing on the two-photon variation of the Bennett-Brassard 1984 (BB84) protocol proposed in 1992 by Bennett, Brasard, and Mermin (BBM92). We present a proof of security which applies to realistic sources, and to untrustable sources which can be placed outside the labs of the two receivers. The proof is restricted to individual eavesdropping attacks, and assumes that the detection apparatus is trustable. We find that the average collision probability for the BBM92 protocol is the same as that of the BB84 protocol with an ideal single-photon source. This indicates that there is no analog in BBM92 to photon splitting attacks, and that the source can be placed between the two receivers without changing the form of the collision probability. We then compare the communication rate of both protocols as a function of distance, and show that BBM92 has potential for much longer communication distances, up to 170 km, in the presence of realistic experimental imperfections. Finally, we propose a scheme based on entanglement swapping that can lead to even longer distance communication. The limiting factor in this scheme is the channel loss, which imposes very slow communication rates at longer distances.
It is argued that the BB84 (Bennett–Brassard 1984) protocol of quantum key distribution has a vulnerability similar to the well-known vulnerability of the B92 (Bennett 1992) protocol in the presence of losses. The quantum circuit and design are first reviewed for an optimized entangling probe attacking the BB84 protocol of quantum key distribution and yielding maximum information to the probe. Probe photon polarization states become optimally entangled with the signal states on their way between the legitimate transmitter and receiver. Although standard von Neumann projective measurements of the probe yield maximum information on the pre-privacy amplified key, if instead the probe measurements are performed with a certain positive operator valued measure, then the measurement results are unambiguous, at least some of the time, resulting in complete information gain by the probe for sufficient loss in the key distribution channel.
An attempt to eavesdrop on a quantum cryptographic channel reveals itself through errors it inevitably introduces into the transmission. We investigate the relationship between the induced error rate and the maximum amount of information the eavesdropper can extract, in both the two-state B92 [B92 refers to the work of C. H. Bennett, Phys. Rev. Lett. 68, 3121 (1992)] and the four-state BB84 [BB84 refers to the work of C. H. Bennett and G. Brassard, in Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing, Bangalore, India (IEEE, New York, 1984), pp. 175--179] quantum cryptographic protocols. In each case, the optimal eavesdropping method that on average yields the most information for a given error rate is explicitly constructed. Analysis is limited to eavesdropping strategies where each bit of the quantum transmission is attacked individually and independently from other bits. Subject to this restriction, however, we believe that all attacks not forbidden by physical laws are covered. Unlike previous work, the eavesdropper's advantage is measured in terms of Renyi (rather than Shannon) information, and with respect only to bits received error-free by Bob (rather than all bits). This alters both the maximum extractable information and the optimal eavesdropping attack. The result can be used directly at the privacy amplification stage of the protocol to accomplish secure communication over a noisy channel.
In this thesis, we analyze the security of the Bennett 1992 quantum key-distribution protocol (B92 protocol) over a realistic channel assuming that bit values are encoded in single photon polarization states. First, we study the security of the B92 protocol against individual attack. In the individual attack, eavesdropper (Eve) interacts a qubit emitted by the sender (Alice) with her probe system followed by a measurement on each probe. To make our analysis simple, we propose a modified B92 protocol. Using this protocol, Alice and the receiver (Bob) can estimate Eve's information gain as a function of a few parameters that reflect the imperfections of devices or Eve's disturbance. We find a counter-intuitive behavior of Eve's maximum information gain, i.e., it decreases as the amount of disturbances increases. We also estimate the secret key gain that is the net growth of the secret key per one pulse. We show the region where the modified B92 protocol over a realistic channel is secure against individual attack. Next, we study the unconditional security of the B92 protocol, which is the security against any attack. To prove the security, we first propose a protocol that is unconditionally secure and can be reduced to the B92 protocol. This protocol employs the entanglement distillation protocol (EDP) based on a filtering operation and the Calderbank-Shor-Steane (CSS) quantum error correcting codes. The bit errors and the phase errors, which have to be estimated for the EDP based on the CSS codes, are correlated after the filtering operation, and we can bound the amount of phase errors from the observed bit errors by an estimation method involving nonorthogonal measurements. The angle between the two states shows a trade-off between accuracy of the estimation and robustness to noises. We show a way to run the unconditionally secure B92.