Quantum cryptography cannot prevent eavesdropping, but any eavesdropping attempt can be detected by the legitimate users of the communication channel. This is because eavesdropping affects the quantum state of the information carriers and results in an abnormal error rate. In this paper, we analyze various eavesdropping techniques, which may be either translucent or opaque to the transmitted photons, and we estimate the error rate above which the key distribution is deemed unsafe and should be abandoned.
Quantum cryptography cannot prevent eavesdropping, but any eavesdropping attempt can be detected by the legitimate users of the communication channel. This is because eavesdropping affects the quantum state of the information carriers and results in an abnormal error rate. In this paper, we analyze various eavesdropping techniques, which may be either translucent or opaque to the transmitted photons, and we estimate the error rate above which the key distribution is deemed unsafe and should be abandoned.
All existing quantum cryptosystems use nonorthogonal states as the carriers of information. Nonorthogonal states cannot be cloned (duplicated) by an eavesdropper. As a result, any eavesdropping attempt must introduce errors in the transmission, and, therefore, can be detected by the legal users of the communication channel. Orthogonal states are not used in quantum cryptography, since they can be faithfully cloned without altering the transmitted data. We present a cryptographic scheme based on orthogonal states, which also assures the detection of any eavesdropper.
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.
The recent application of the principles of quantum mechanics to cryptography has led to a remarkable new dimension in secret communication.Quantum Cryptography uses the principles of Quantum Mechanics to implement a cryptographic system.The key problem which is solved by using quantum techniques is that of eavesdropping detection.Conventional secret-key cryptography techniques require the communication of a secret key prior to message exchange.Quantum principles can be used to detect eavesdropping probabilistically when it occurs.The bits are represented as qubits, physically modeled by photons, and communicated over a quantum channel.The polarization states of photons represent 0's and 1's.As a result of these new developments, it is now possible to construct cryptographic communication systems which detect unauthorized eavesdropping should it occur, and which give a guarantee of no eavesdropping should it not occur.
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 present a mathematical physics analysis of entangled translucent eavesdropping in quantum cryptography, based on the recent work of Ekert, Huttner, Palma, and Peres. 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 new 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.