A realistic quantum cryptographic system must function in the presence of the noise and channel loss inevitable in any practical transmission. We examine the effects of these channel limitations on the security and throughput of a class of quantum cryptographic protocols known as four-state or BB84 protocols. Provable unconditional security against eavesdropping, which is the principal feature of quantum cryptography, can be achieved despite minor channel defects, albeit at a reduced transmission throughput. We present a semiempirical relation between the fully secure throughput and the loss and noise levels in the channel. According to this relation, an implementation of BB84 utilizing commercially available detectors can reach throughputs as high as 104-105 secure bits per second over a practical channel of reasonable quality.
A realistic quantum cryptographic system must function in the presence of the noise and channel loss inevitable in any practical transmission. We examine the effects of these channel limitations on the security and throughput of a class of quantum cryptographic protocols known as four-state or BB84 protocols. Provable unconditional security against eavesdropping, which is the principal feature of quantum cryptography, can be achieved despite minor channel defects, albeit at a reduced transmission throughput. We present a semiempirical relation between the fully secure throughput and the loss and noise levels in the channel. According to this relation, an implementation of BB84 utilizing commercially available detectors can reach throughputs as high as 104-105 secure bits per second over a practical channel of reasonable quality.
A realistic quantum cryptographic system must function in the presence of noise and channel loss inevitable in any practical transmission. We examine the effects of these channel limitations on the security and throughput of a class of quantum cryptographic protocols known as four-state, or BB84. Provable unconditional security against eavesdropping, which is the principal feature of quantum cryptography, can be achieved despite minor channel defects, albeit at a reduced transmission throughput. We present a semi-empirical relation between the fully-secure throughput and the loss and noise levels in the channel. According to this relation, a particular implementation of BB84, based on the frequency-division multiplexing scheme and utilizing commercially available detectors, can reach throughputs as high as 104 - 105 secure bits per second over a practical channel of reasonable quality.
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.
A number of questions associated with practical implementations of quantum cryptography systems having to do with unconditional secrecy, computational loads and effective secrecy rates in the presence of perfect and imperfect sources are discussed. The different types of unconditional secrecy, and their relationship to general communications security, are discussed in the context of quantum cryptography. In order to actually carry out a quantum cryptography protocol it is necessary that sufficient computational resources be available to perform the various processing steps, such as sifting, error correction, privacy amplification and authentication. We display the full computer machine instruction requirements needed to support a practical quantum cryptography implementation. We carry out a numerical comparison of system performance characteristics for implementations that make use of either weak coherent sources of light or perfect single photon sources, for eavesdroppers making individual attacks on the quantum channel characterized by different levels of technological capability. We find that, while in some circumstances it is best to employ perfect single photon sources, in other situations it is preferable to utilize weak coherent sources. In either case the secrecy level of the final shared cipher is identical, with the relevant distinguishing figure-of-merit being the effective throughput rate.
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 peculiar properties of quantum mechanics enable possibilities not allowed by classical physics. In particular, two parties can generate a random, secret key at a distance, even though an eavesdropper can do anything permitted by the laws of physics. Measuring the quantum properties of the signals generating the key, would ultimately change them, and thus reveal the eavesdropper’s presence. This exchange of a random, secret key is known as quantum cryptography.\n\nQuantum cryptography can be, and has been proven unconditionally secure using perfect devices. However, when quantum cryptography is implemented, one must use components available with current technology. These are usually imperfect. Although the security of quantum cryptography has been proven for components with certain imperfections, the question remains: can quantum cryptography be implemented in a provable, unconditionally secure way, using components available with current technology? This thesis contains both a theoretical, and an experimental contribution to the answer of this question. On the experimental side, components used in, and complete quantum cryptography systems have been carefully examined for security loopholes. In particular, it turned out that two commercial quantum cryptography systems contained loopholes, which would allow an eavesdropper to capture the full secret key, without exposing her presence. Furthermore, this detector control attack could be implemented with current technology. The attack is applicable against a variety of quantum cryptography implementations and protocols.\n\nThe theoretical contribution consists of security proofs for quantum cryptography in a very general setting. Precisely, the security is proven with arbitrary individual imperfections in the source and detectors. These proofs should make it possible to use a wide array of imperfect devices in implementations of quantum cryptography.\n\nFinally, a secure detection scheme is proposed, immune to the detector control attack and compatible with those security proofs. Therefore, if this scheme is implemented correctly, it offers provable security.
In real fiber-optic quantum cryptography systems, the avalanche photodiodes are not perfect, the source of quantum states is not a single-photon one, and the communication channel is lossy. For these reasons, key distribution is impossible under certain conditions for the system parameters. A simple analysis is performed to find relations between the parameters of real cryptography systems and the length of the quantum channel that guarantee secure quantum key distribution when the eavesdropper’s capabilities are limited only by fundamental laws of quantum mechanics while the devices employed by the legitimate users are based on current technologies. Critical values are determined for the rate of secure real-time key generation that can be reached under the current technology level. Calculations show that the upper bound on channel length can be as high as 300 km for imperfect photodetectors (avalanche photodiodes) with present-day quantum efficiency (η ≈ 20%) and dark count probability (p dark ∼ 10−7).