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

Information investigation for B92 protocol in quantum cryptography

Ming Zou, Guoping Zhang

Published Jan 11, 2005• 4 citations
Publisher

Abstract

In this paper, we simulate the quantum channel with a binary symmetric channel and a binary erasure channel, a series channel and a Markovian chain channel in classical information theory, then calculate respectively the mutual information between the signal's deliverer, the legal receiver and the eavesdropper, the bit error rate during propagating the signals with the theory about the quantum measurement channel and the quantum information theory. For B92 protocol, a simple quantum cryptography distribution scheme, we study the bound and the property of mutual information obtained by the legal receiver and the eavesdropper, seek the relationship between the bit error rates and the eavesdropper's way, in two cases of the opaque eavesdropping and the translucent eavesdropping. A new criteria for checking the eavesdropper and ensuring the legal correspondent is estimated. Furthermore, the comparison in bit error rates caused respectively in two different measuring ways indicates that POVM is better than the standard measurement by the way of orthogonal projecting for reducing the bit error rate and increasing effective communication.

DOI
10.1117/12.569663

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In this paper, we simulate the quantum channel with a binary symmetric channel and a binary erasure channel, a series channel and a Markovian chain channel in classical information theory, then calculate respectively the mutual information between the signal's deliverer, the legal receiver and the eavesdropper, the bit error rate during propagating the signals with the theory about the quantum measurement channel and the quantum information theory. For B92 protocol, a simple quantum cryptography distribution scheme, we study the bound and the property of mutual information obtained by the legal receiver and the eavesdropper, seek the relationship between the bit error rates and the eavesdropper's way, in two cases of the opaque eavesdropping and the translucent eavesdropping. A new criteria for checking the eavesdropper and ensuring the legal correspondent is estimated. Furthermore, the comparison in bit error rates caused respectively in two different measuring ways indicates that POVM is better than the standard measurement by the way of orthogonal projecting for reducing the bit error rate and increasing effective communication.
The security of B92 protocol was studied in the terms of single basis with the probability and the information theory.The relation between the optimal eavesdropping angle and the signal probability was obtained.The mutual information among Alice,Bob and Eve was calculated with the theory of Markovian chain series channel.The results of comparison with the conclusion in the case of POVM eavesdropping show that Eve can guess the quantum bit with higher probability by single basis,and the average mutual information obtained by single basis is rather high.The conclusion offers a new criterion for cheking Eve.
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.
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.
We present a mathematical physics analysis of entangled translucent eavesdropping in quantum cryptography, based on the recent work of Ekert, Huttner, Palma, and Peres [Phys. Rev. A 50, 1047 (1994)]. The key generation procedure involves the transmission, interception, and reception of two nonorthogonal photon polarization states. At the receiving end, a positive operator valued measure (POVM) is employed in the measurement process. The eavesdropping involves an information-maximizing von Neumann--type projective measurement. We propose a design for a receiver that is an all-optical realization of the POVM, using a Wollaston prism, a mirror, two beam splitters, a polarization rotator, and three photodetectors. We present a quantitative analysis of the receiver. We obtain closed-form algebraic expressions for the error rates and mutual information, expressed in terms of the POVM-receiver error rate and the angle between the carrier polarization states. We also prove a significant result, namely, that in the entangled translucent eavesdropping approach, the unsafe error rate based on standard mutual information comparisons is equivalent to the maximum allowable error rate based on perfect mutual information for the eavesdropper. In this case, the above unsafe error rate is in fact not overly conservative.