We analyse the information obtained by an eavesdropper during the various stages of a quantum cryptographic protocol associated with key distribution. We provide both an upper and a lower limit on the amount of information that may have leaked to the eavesdropper at the end of the key distribution procedure. These limits are restricted to intercept/resend eaves-dropping strategies. The upper one is higher than has been estimated so far, and should be taken into account in order to guarantee the secrecy of the final key, which is subsequently obtained via the so-called privacy amplification.
We analyse the information obtained by an eavesdropper during the various stages of a quantum cryptographic protocol associated with key distribution. We provide both an upper and a lower limit on the amount of information that may have leaked to the eavesdropper at the end of the key distribution procedure. These limits are restricted to intercept/resend eaves-dropping strategies. The upper one is higher than has been estimated so far, and should be taken into account in order to guarantee the secrecy of the final key, which is subsequently obtained via the so-called privacy amplification.
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.
With the increasing security demands of nextgeneration communication standards and the looming threat posed by quantum computers to traditional encryption methods, quantum key distribution (QKD) has emerged as a promising solution in domains such as military, government, and finance, with significant potential for further commercialization. Although QKD is theoretically unconditional secure, practical implementations often face vulnerabilities arising from imperfections in channels and devices, as well as inherent characteristics of QKD protocols. This paper investigates the probability of eavesdropping from the perspective of error rates using probabilistic analysis. Such an approach not only facilitates the detection of potential eavesdropping but also helps estimate the amount of leaked information, providing a basis for subsequent countermeasures like privacy amplification. Additionally, the probabilistic analysis sheds light on the robustness of communication channels with varying quality against eavesdropping attempts.
In order to be practically useful, quantum cryptography must not only provide a guarantee of secrecy, but it must provide this guarantee with a useful, sufficiently large throughput value. The standard result of generalized privacy amplification yields an upper bound only on the average value of the mutual information available to an eavesdropper. Unfortunately this result by itself is inadequate for cryptographic applications. A naive application of the standard result leads one to incorrectly conclude that an acceptable upper bound on the mutual information has been achieved. It is the pointwise value of the bound on the mutual information, associated with the use of some specific hash function, that corresponds to actual implementations. We provide a fully rigorous mathematical derivation that shows how to obtain a cryptographically acceptable upper bound on the actual, pointwise value of the mutual information. Unlike the bound on the average mutual information, the value of the upper bound on the pointwise mutual information and the number of bits by which the secret key is compressed are specified by two different parameters, and the actual realization of the bound in the pointwise case is necessarily associated with a specific failure probability. The constraints amongst these parameters, and the effect of their values on the system throughput, have not been previously analyzed. We show that the necessary shortening of the key dictated by the cryptographically correct, pointwise bound, can still produce viable throughput rates that will be useful in practice.
Employing the fundamental laws of quantum physics, Quantum Key Distribution (QKD) promises the unconditionally secure distribution of cryptographic keys. However, in practical realisations, a QKD protocol is only secure, when the quantum bit error rate introduced by an eavesdropper unavoidably exceeds the system error rate. This condition guarantees that an eavesdropper cannot disguise his presence by simply replacing the original transmission line with a less faulty one. Unfortunately, this condition also limits the possible distance between the communicating parties, Alice and Bob, to a few hundred kilometers. To overcome this problem, we design a QKD protocol which allows Alice and Bob to distinguish system errors from eavesdropping errors. If they are able to identify the origin of their errors, they can detect eavesdropping even when the system error rate exceeds the eavesdropping error rate. To achieve this, the proposed protocol employs an alternative encoding of information in two-dimensional photon states. Errors manifest themselves as quantum bit and as index transmission errors with a distinct correlation between them in case of intercept-resend eavesdropping. As a result, Alice and Bob can tolerate lower eavesdropping and higher system error rates without compromising their privacy.
We present and analyze a quantum key distribution protocol based on sending entangled N-qubit states instead of single-qubit ones as in the trail-blazing scheme by Bennett and Brassard 1984 (BB84). Since the qubits are sent and acknowledged individually, an eavesdropper is limited to accessing them one by one. In an intercept-resend attack, this fundamental restriction allows one to make the eavesdropper's information on the transmitted key vanish if even one of the qubits is not intercepted. The implied upper bound 1∕(2N) for this information is further shown not to be the lowest, as the information can be reduced to less than 30% of that in the BB84 scheme in the case N=2. In general, the protocol is at least as secure as BB84.