The security of the B92 protocol using single photon polarization states against an individual attack over a realistic channel is estimated. We calculated an upper bound of Eve's information and clarified the region where B92 over a realistic channel is secure against any individual attack.
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.
The security of two-state quantum-key distribution against individual attack is estimated when the channel has losses and noises. We assume that Alice and Bob use two nonorthogonal single-photon polarization states. To make our analysis simple, we propose a modified B92 protocol in which Alice and Bob make use of inconclusive results, and Bob performs a kind of symmetrization of received states. Using this protocol, Alice and Bob can estimate Eve's information gain as a function of a few parameters that reflect the imperfections of devices, or Eve's disturbance. In some parameter regions, Eve's maximum information gain shows counterintuitive behavior, namely, it decreases as the amount of disturbances increases. For a small noise rate, Eve can extract perfect information in the case where the angle between Alice's two states is small or large, while she cannot extract perfect information for intermediate angles. We also estimate the secret key gain, which is the net growth of the secret key per pulse. We show the region where the modified B92 protocol over a realistic channel is secure against individual attack.
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.
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 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.
Secure communication has always been a key concern while sharing information between two parties. Traditional and lightweight cryptography primitives and protocols are insecure against quantum attacks. The objective of cryptography is to ensure confidentiality, integrity, authentication and non-repudiation between both parties. Quantum key distribution is a safe and sound method for communication between two parties to share their information. However early applications with applied limitations lead to open ambiguities, permitting an eavesdropper to breach the security of quantum cryptographic system. This research proposes a framework for quantum key distribution using B92 protocol. The B92 protocol allows two different users A to share their polarized photons with high security and without any interruption of Eavesdropper. While B92 protocol generates a secrete key, that is known to just sender and receiver. The use of QuVis framework can provide this secure communication and photons are transferred to Bob securely without any Eavesdropper.