We perform a comprehensive analysis of practical quantum cryptography (QC) systems implemented in actual physical environments via either free-space or fiber-optic cable quantum channels for ground-ground, ground-satellite, air-satellite and satellite-satellite links. (1) We obtain universal expressions for the effective secrecy capacity and rate for QC systems taking into account three important attacks on individual quantum bits, including explicit closed-form expressions for the requisite amount of privacy amplification. Our analysis also includes the explicit calculation in detail of the total cost in bits of continuous authentication, thereby obtaining new results for actual ciphers of finite length. (2) We perform for the first time a detailed, explicit analysis of all systems losses due to propagation, errors, noise, etc. as appropriate to both optical fiber cable- and satellite communications-based implementations of QC. (3) We calculate for the first time all system load costs associated to classical communication and computational constraints that are ancillary to, but essential for carrying out, the pure QC protocol itself. (4) We introduce an extended family of generalizations of the Bennett-Brassard (BB84) QC protocol that equally provide unconditional secrecy but allow for the possibility of optimizing throughput rates against specific cryptanalytic attacks. (5) We obtain universal predictions for maximal rates that can be achieved with practical system designs under realistic environmental conditions. (6) We propose a specific QC system design that includes the use of a novel method of high-speed photon detection that may be able to achieve very high throughput rates for actual implementations in realistic environments.
We perform a comprehensive analysis of practical quantum cryptography (QC) systems implemented in actual physical environments via either free-space or fiber-optic cable quantum channels for ground-ground, ground-satellite, air-satellite and satellite-satellite links. (1) We obtain universal expressions for the effective secrecy capacity and rate for QC systems taking into account three important attacks on individual quantum bits, including explicit closed-form expressions for the requisite amount of privacy amplification. Our analysis also includes the explicit calculation in detail of the total cost in bits of continuous authentication, thereby obtaining new results for actual ciphers of finite length. (2) We perform for the first time a detailed, explicit analysis of all systems losses due to propagation, errors, noise, etc. as appropriate to both optical fiber cable- and satellite communications-based implementations of QC. (3) We calculate for the first time all system load costs associated to classical communication and computational constraints that are ancillary to, but essential for carrying out, the pure QC protocol itself. (4) We introduce an extended family of generalizations of the Bennett-Brassard (BB84) QC protocol that equally provide unconditional secrecy but allow for the possibility of optimizing throughput rates against specific cryptanalytic attacks. (5) We obtain universal predictions for maximal rates that can be achieved with practical system designs under realistic environmental conditions. (6) We propose a specific QC system design that includes the use of a novel method of high-speed photon detection that may be able to achieve very high throughput rates for actual implementations in realistic environments.
We perform a comprehensive analysis of practical quantum cryptography (QC) systems implemented in actual physical environments via either free-space or fiber-optic cable quantum channels for ground-ground, ground-satellite, air-satellite and satellite-satellite links. (1) We obtain the complete universal expressions for the effective secrecy capacity and rate for QC systems taking into account the most general attacks on individual quantum bits, including explicit closed-form expressions for the necessary and sufficient amount of privacy amplification. Our analysis also includes the explicit calculation in detail of the total cost in bits of continuous authentication, thereby obtaining new results for actual ciphers of finite length. (2) We perform for the first time a detailed, explicit analysis of all systems losses due to propagation, errors, noise, etc. as appropriate to both optical fiber cable- and satellite communications-based implementations of QC. (3) We calculate for the first time all system load costs associated to classical communication and computational constraints that are ancillary to, but essential for carrying out, the pure QC protocol itself. (4) We introduce an extended family of generalizations of the Bennett-Brassard (BB84) QC protocol that equally provide unconditional secrecy but allow for the possibility of optimizing throughput rates against specific cryptanalytic attacks. (5) We obtain universal predictions for maximal rates that can be achieved with practical system designs under realistic environmental conditions. (6) We propose a specific QC system design that includes the use of a novel method of high-speed photon detection that may be able to achieve very high throughput rates for actual implementations in realistic environments.
Quantum cryptography has attracted much recent attention due to its potential for providing secret communications that cannot be decrypted by any amount of computational effort. This is the first analysis of the secrecy of a practical implementation of the BB84 protocol that simultaneously takes into account and presents the full set of analytical expressions for effects due to the presence of pulses containing multiple photons in the attenuated output of the laser, the finite length of individual blocks of key material, losses due to error correction, privacy amplification, and authentication, errors in polarization detection, the efficiency of the detectors, and attenuation processes in the transmission medium. The analysis addresses eavesdropping attacks on individual photons rather than collective attacks in general. Of particular importance is the first derivation of the necessary and sufficient amount of privacy amplification compression to ensure secrecy against the loss of key material which occurs when an eavesdropper makes optimized individual attacks on pulses containing multiple photons. It is shown that only a fraction of the information in the multiple photon pulses is actually lost to the eavesdropper.
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.
In our modern era of telecommunications and the Internet, information has become a valuable commodity. Sometimes it must therefore be protected against theft - in this case, loss of secret information to an eavesdropper. Most of today's transactions are protected using encryption unproven to be secure against a computational attack by a classical computer and, in fact, the standardly used encryption algorithms are provably vulnerable to the mind-boggling parallelism of a quantum computer, should one ever be physically realized. Enter quantum cryptography. Underlying nearly all forms of encryption is the necessity for a truly secret key, a random string of zeros and ones; the basic notion of quantum cryptography is to employ single photon transmissions (or the closest attainable approximation to these) to distribute the random key material, while removing the threat of an undetected eavesdropper. Now, nearly twenty years since the seminal quantum cryptography paper by Bennett and Brassard (Bennett C H and Brassard G 1984 Proc. IEEE Int. Conf. on Computers, Systems, and Signal Processing (Bangalore) (New York: IEEE) pp 175-9), we take a look at several state-of-the-art implementations, and glimpse how future quantum cryptosystems might look. We start with papers from three of the world's leading experimental quantum cryptography efforts: Stucki et al and Bethune and Risk describe working systems for quantum key distribution (QKD) over telecommunications fibres (at 1550 nanometres and 1300 nanometres, respectively). The former's achievement of quantum key exchange over 67 kilometres of optical fibre is a world record, as is the experimental demonstration by Hughes et al of daylight free-space QKD over a 10 km atmospheric range. Next, Lütkenhaus and Jahma explore the possible vulnerabilities of such systems (which employ attenuated laser pulses instead of actual single photon states) to conceivable future eavesdropping technologies. Enzer et al have implemented a totally new protocol, using polarization-entangled photons, which in some circumstances can tolerate higher error rates than the traditional one of Bennett and Brassard; moreover, the use of entanglement provides a means of `automatic source verification'. Finally, looking to the future, Elliott gives a provocative view of how these technologies may be merged into network operation, and Shapiro describes a method to combine a novel source of entangled photons with a means to transfer the photons' quantum state to trapped-atom quantum memories. If realized, these systems could presage the world's first quantum network. Focus on Quantum Cryptography Contents Quantum key distribution over 67 km with a plug&play system D Stucki, N Gisin, O Guinnard, G Ribordy and H Zbinden Autocompensating quantum cryptography Donald S Bethune and William P Risk Practical free-space quantum key distribution over 10 km in daylight and at night Richard J Hughes, Jane E Nordholt, Derek Derkacs and Charles G Peterson Quantum key distribution with realistic states: photon-number statistics in the photon-number splitting attack Norbert Lütkenhaus and Mika Jahma Entangled-photon six-state quantum cryptography Daphna G Enzer, Phillip G Hadley, Richard J Hughes, Charles G Peterson and Paul G Kwiat Building the quantum network Chip Elliott Architectures for long-distance quantum teleportation Jeffrey H Shapiro Ground to satellite secure key exchange using quantum cryptography J G Rarity, P R Tapster, P M Gorman and P Knight Method for decoupling error correction from privacy amplification Hoi-Kwong Lo Paul G Kwiat University of Illinois at Urbana-Champaign, USA
One of the most fascinating recent developments in research has been how different disciplines have become more and more interconnected. So much so that fields as disparate as information theory and fundamental physics have combined to produce ideas for the next generation of computing and secure information technologies, both of which have far reaching consequences. For more than fifty years Moore's law, which describes the trend of the transistor's size shrinking by half every two years, has proven to be uncannily accurate. However, the computing industry is now approaching a fundamental barrier as the size of a transistor approaches that of an individual atom and the laws of physics and quantum mechanics take over. Rather then look at this as the end, quantum information science has emerged to ask the question of what additional power and functionality might be realized by harnessing some of these quantum effects. This thesis presents work on the sub-field of quantum cryptography which seeks to use quantum means in order to assure the security of ones communications. The beauty of quantum cryptographic methods are that they can be proven secure, now and indefinitely into the future, relying solely on the validity of the laws of physics for their proofs of security. This is something which is impossible for nearly all current classical cryptographic methods to claim. \n \nThe thesis begins by examining the first implementation of an entangled quantum key distribution system over two free-space optical links. This system represents the first test-bed of its kind in the world and while its practical importance in terrestrial applications is limited to a smaller university or corporate campus, the system mimics the setup for an entangled satellite system aiding in the study of distributing entangled photons from an orbiting satellite to two earthbound receivers. Having completed the construction of a second free-space link and the automation of the alignment system, I securely distribute keys to Alice and Bob in two distant locations separated by 1,575 m with no direct line-of-sight between them. I examine all of the assumptions necessary for my claims of security, something which is particularly important for moving these systems out of the lab and into commercial industry. I then go on to describe the free-space channel over which the photons are sent and the implementation of each of the major system components. I close with a discussion of the experiment which saw raw detected entangled photon rates of 565 s^{-1} and a quantum bit error rate (QBER) of 4.92% resulting in a final secure key rate of 85 bits/s. Over the six hour night time experiment I was able to generate 1,612,239 bits of secure key. \n \nWith a successful QKD experiment completed, this thesis then turns to the problem of improving the technology to make it more practical by increasing the key rate of the system and thus the speed at which it can securely encrypt information. It does so in three different ways, involving each of the major disciplines comprising the system: measurement hardware, source technology, and software post-processing. First, I experimentally investigate a theoretical proposal for biasing the measurement bases in the QKD system showing a 79% improvement in the secret key generated from the same raw key rates. Next, I construct a second generation entangled photon source with rates two orders of magnitude higher than the previous source using the idea of a Sagnac interferometer. More importantly, the new source has a QBER as low as 0.93% which is not only important for the security of the QKD system but will be required for the implementation of a new cryptographic primitive later. Lastly, I study the free-space link transmission statistics and the use of a signal-to-noise ratio (SNR) filter to improve the key rate by 25.2% from the same amount of raw key. The link statistics have particular relevance for a current project with the Canadian Space Agency to exchange a quantum key with an orbiting satellite - a project which I have participated in two feasibility studies for. \n \nWanting to study the usefulness of more recent ideas in quantum cryptography this thesis then looks at the first experimental implementation of a new cryptographic primitive called oblivious transfer (OT) in the noisy storage model. This primitive has obvious important applications as it can be used to implement a secure identification scheme provably secure in a quantum scenario. Such a scheme could one day be used, for example, to authenticate a user over short distances, such as at ATM machines, which have proven to be particularly vulnerable to hacking and fraud. Over a four hour experiment, Alice and Bob measure 405,642,088 entangled photon pairs with an average QBER of 0.93% allowing them to create a secure OT key of 8,939,150 bits. As a first implementer, I examine many of the pressing issues currently preventing the scheme from being more widely adopted such as the need to relax the dependance of the OT rate on the loss of the system and the need to extend the security proof to cover a wider range of quantum communication channels and memories. It is important to note that OT is fundamentally different than QKD for security as the information is never physically exchanged over the communication line but rather the joint equality function f(x) = f(y) is evaluated. Thus, security in QKD does not imply security for OT. \n \nFinally, this thesis concludes with the construction and initial alignment of a second generation free-space quantum receiver, useful for increasing the QKD key rates, but designed for a fundamental test of quantum theory namely a Svetlichny inequality violation. Svetlichny's inequality is a generalization of Bell's inequality to three particles where any two of the three particles maybe be non-locally correlated. Even so, a violation of Svetlichny's inequality shows that certain quantum mechanical states are incompatible with this restricted class of non-local yet realistic theories. Svetlichny's inequality is particularly important because while there has been an overwhelming number of Bell experiments performed testing two-body correlations, experiments on many-body systems have been few and far between. Experiments of this type are particularly valuable to explore since we live in a many-body world. The new receiver incorporates an active polarization analyzer capable of switching between measurement bases on a microsecond time-scale through the use of a Pockels cell while maintaining measurements of a high fidelity. Some of the initial alignment and analysis results are detailed including the final measured contrasts of 1:25.2 and 1:22.6 in the rectilinear and diagonal bases respectively.
The purpose of the article was to theoretically determine harmonised criteria for the applicability of quantum key distribution for the protection of critical infrastructure, taking into account the long-term risk of decryption by adversaries possessing quantum computational resources and traffic archiving capabilities. The methodology relied on a theoretical systems analysis of three Quantum Key Distribution subsystems – sources, detectors, and channels (fibre/free space) – complemented by simplified models of the link budget and bit error probability. A concise scenario analysis was conducted for banking networks, energy systems, and government communications, taking into account scalability, compatibility, and cost. The main results showed that laser intensity stability of 1-2% and higher detector efficiencies – 60-70% for Avalanche Photodiodes and 80-90% for Superconducting Nanowire Single-Photon Detectors – extended practical distances and reduced errors. Without trusted nodes in fibre, 150-200 km was achievable; for urban Free-Space Optics lines, 5-20 km was optimal, while longer distances required network segmentation or satellite segments. Architecturally, it was justified that: for banks – rings with trusted nodes and Free-Space Optics reserve; for energy systems – dual fibre channels “control centre-substation” with a local key cache; for government communications – segmented domains with interagency gateways and satellite redundancy. In all scenarios, a Quantum Key Distribution + Post-Quantum Cryptography hybrid with short key rotation and operational countermeasures against attacks on detectors and channels was appropriate, confirming practical suitability for urban and regional networks. The practical significance lay in providing engineering teams in banking, energy, and government communications with ready-made architectural profiles – from rings and dual fibre channels to segmented domains – with Key Management System/Hardware Security Module integration, definition of Service Level Objective/Service Level Agreement, and phased roadmaps. For regulators and operators, this formed a basis for updating requirements and audits, as well as for planning redundancy (Free-Space Optics/satellite) and Total Cost of Ownership categories