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Journal of Modern Optics

Eavesdropping Strategies and Rejected-data Protocols in Quantum Cryptography

Stephen Mark Barnett, B. Hüttner, Simon J. D. Phoenix

Published Dec 1, 1993• 45 citations
Publisher

Abstract

We show that rejected-data protocols for quantum cryptography are secure against generalized intercept/resend strategies of an eavesdropper provided that the legitimate users of the communication channel use at least three bases. We discuss the connection between this result and the recently-developed protocol based on violations of a suitably-constructed Bell-type inequality for single particles. We also give a new estimate of the probability that an eavesdropper remains undetected under the original protocol and thereby show that the optimal strategies available to an eavesdropper are further limited to those which randomize the errors between the sub-ensembles of data. This result also has implications for the way in which the legitimate users of the channel choose their test data.

DOI
10.1080/09500349314552491

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We show that rejected-data protocols for quantum cryptography are secure against generalized intercept/resend strategies of an eavesdropper provided that the legitimate users of the communication channel use at least three bases. We discuss the connection between this result and the recently-developed protocol based on violations of a suitably-constructed Bell-type inequality for single particles. We also give a new estimate of the probability that an eavesdropper remains undetected under the original protocol and thereby show that the optimal strategies available to an eavesdropper are further limited to those which randomize the errors between the sub-ensembles of data. This result also has implications for the way in which the legitimate users of the channel choose their test data.
A generalization of the quantum cryptographic protocol by Bennett and Brassard is discussed, using three conjugate bases, i.e., six states. By calculating the optimal mutual information between sender and eavesdropper it is shown that this scheme is safer against eavesdropping on single qubits than the one based on two conjugate bases. We also address the question for a connection between the maximal classical correlation in a generalized Bell inequality and the intersection of mutual informations between sender/receiver and sender/eavesdropper.
We consider the Bennett-Brassard cryptographic scheme, which uses two conjugate quantum bases. An eavesdropper who attempts to obtain information on qubits sent in one of the bases causes a disturbance to qubits sent in the other basis. We derive an upper bound to the accessible information in one basis, for a given error rate in the conjugate basis. Independently fixing the error rates in the conjugate bases, we show that both bounds can be attained simultaneously by an optimal eavesdropping probe. The probe interaction and its subsequent measurement are described explicitly. These results are combined to give an expression for the optimal information an eavesdropper can obtain for a given average disturbance when her interaction and measurements are performed signal by signal. Finally, the relation between quantum cryptography and violations of Bell's inequalities is discussed.
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.
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.
Today's Classical cryptographic algorithms will fail against the quantum cryptosystems. In this paper, Security protocols are reviewed with analysis of intercept-resend, faked-state and light pulse attacks and eavesdropper strategies to gain the information transferred in between communication channel. The quantum cryptography is providing absolute security against the above stated attacking environment. That is the reason for using the concepts of quantum mechanics with cryptographic algorithms to achieve the utmost security. This paper is focusing on review to the key distribution techniques used for protecting the communication. We found that the communication is successfulif we use privacy amplification, authentication, and Bell's inequalities.