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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Knowledge of error-correcting protocol helps in individual eavesdropping

D. B. Horoshko

Published Jun 15, 2007• 1 citation
Publisher

Abstract

The quantum key distribution protocol ΒΒ84 combined with the repetition protocol for error correction are analyzed from the viewpoint of security against individual eavesdropping empowered by quantum memory. We show that a mere knowledge of the error correction protocol changes the optimal attack and provides the eavesdropper with additional information about the generated key.

DOI
10.1117/12.752649

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The quantum key distribution protocol ΒΒ84 combined with the repetition protocol for error correction are analyzed from the viewpoint of security against individual eavesdropping empowered by quantum memory. We show that a mere knowledge of the error correction protocol changes the optimal attack and provides the eavesdropper with additional information about the generated key.
Security of quantum key distribution (QKD) protocols rely solely on quantum physics laws, namely, on the impossibility to distinguish between non-orthogonal quantum states with absolute certainty. Due to this, a potential eavesdropper cannot extract full information from the states stored in their quantum memory after an attack despite knowing all the information disclosed during classical post-processing stages of QKD. Here, we introduce the idea of encrypting classical communication related to error-correction in order to decrease the amount of information available to the eavesdropper and hence improve the performance of quantum key distribution protocols. We analyze the applicability of the method in the context of additional assumptions concerning the eavesdropper's quantum memory coherence time and discuss the similarity of our proposition and the quantum data locking (QDL) technique.
An attempt to eavesdrop 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, both in the two-state B92 and the four-state BB84 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 form other bits. Subject to this restriction, however, we believe that all attacks not forbidden by physical laws are included. Unlike previous work, the eavesdropper's advantage is measured in terms of Renyi information, and with respect only to bits received error-free by Bob. 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.
[Shortened abstract:] This thesis investigates the importance of quantum memory in quantum cryptography, concentrating on quantum key distribution schemes. In the hands of an eavesdropper -- a quantum memory is a powerful tool, putting in question the security of quantum cryptography; Classical privacy amplification techniques, used to prove security against less powerful eavesdroppers, might not be effective when the eavesdropper can keep quantum states for a long time. In this work we suggest a possible direction for approaching this problem. We define strong attacks of this type, and show security against them, suggesting that quantum cryptography is secure. We start with a complete analysis regarding the information about a parity bit (since parity bits are used for privacy amplification). We use the results regarding the information on parity bits to prove security against very strong eavesdropping attacks, which uses quantum memories and all classical data (including error correction codes) to attack the final key directly. In the hands of the legitimate users, a quantum memory is also a useful tool. We suggest a new type of quantum key distribution scheme where quantum memories are used instead of quantum channels. This scheme is especially adequate for networks of many users. The use of quantum memory also allows reducing the error rate to improve large scale quantum cryptography, and to enable the legitimate users to work with reasonable error rate.
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.
We consider the security of the BB84 (Bennett and Brassard 1984 Proc. IEEE Int. Conf. on Computers, Systems, and Signal Processing pp 175–9), six-state (Bruß 1998 Phys. Rev. Lett. 81 3018 ) and SARG04 (Scarani et al 2004 Phys. Rev. Lett. 92 057901 ) quantum key distribution protocols when the eavesdropper does not have access to a quantum memory. In this case, Eve’s most general strategy is to measure her ancilla with an appropriate positive operator-valued measure designed to take advantage of the post-measurement information that will be released during the sifting phase of the protocol. After an optimization on all the parameters accessible to Eve, our method provides us with new bounds for the security of six-state and SARG04 against a memoryless adversary. In particular, for the six-state protocol we show that the maximum quantum bit error ratio for which a secure key can be extracted is increased from 12.6% (for collective attacks) to 20.4% with the memoryless assumption.