This dissertation is composed of the results of our investigation in quantum cryptography - a new topic in computer security. The goal of this study is to explore useful schemes for quantum cryptographic communications. The focus of our study is an investigation into quantum cryptographic protocols based on quantum-mechanical uncertainty principle and Bell's inequality. First, we use the theory of quadrature phase amplitudes and quantum homodyne detection to establish a new quantum key distribution protocol which relies on an optical coupler. In this work we propose, for the first time, the use of this theory in quantum cryptography. Second, we investigate Ekert's protocol using Bell's theorem. The contents in this investigation is not new, but we use our calculation to prove that Ekert's protocol is true for both photon-based and spin- |-particle-bcised systems. Third, we study a quantum coherence key distribution constructed using Bennett and Brassard's protocol. The information theory of the system is used to study the scenario where eavesdropping occurs. Finally, we explore the theory of quantum nondemolition detection (QND) to investigate the results when eavesdropping occurs. A calculation for the QND, using parametric frequency conversion, is given for two different quantum cryptographic systems. Our study is undertaken with the aid of some knowledge of physics, therefore, before our main results are presented, we introduce some useful physics which may help readers understand the contents of our work.
This dissertation is composed of the results of our investigation in quantum cryptography - a new topic in computer security. The goal of this study is to explore useful schemes for quantum cryptographic communications. The focus of our study is an investigation into quantum cryptographic protocols based on quantum-mechanical uncertainty principle and Bell's inequality. First, we use the theory of quadrature phase amplitudes and quantum homodyne detection to establish a new quantum key distribution protocol which relies on an optical coupler. In this work we propose, for the first time, the use of this theory in quantum cryptography. Second, we investigate Ekert's protocol using Bell's theorem. The contents in this investigation is not new, but we use our calculation to prove that Ekert's protocol is true for both photon-based and spin- |-particle-bcised systems. Third, we study a quantum coherence key distribution constructed using Bennett and Brassard's protocol. The information theory of the system is used to study the scenario where eavesdropping occurs. Finally, we explore the theory of quantum nondemolition detection (QND) to investigate the results when eavesdropping occurs. A calculation for the QND, using parametric frequency conversion, is given for two different quantum cryptographic systems. Our study is undertaken with the aid of some knowledge of physics, therefore, before our main results are presented, we introduce some useful physics which may help readers understand the contents of our work.
Abstract The application of the principles of quantum mechanics to cryptography has led to a respectable new dimension in confidential communication. As a result of these developments, it is now possible to construct cryptographic communication systems which detect unauthorized eavesdropping should it occur, and which give a incontestable guarantee of no eavesdropping should it not occur. Here several protocols for such communication systems are explored. We first examine quantum bit commitment protocols which are proven as not being unconditionally secure, then, we take a look at proposed protocols which are constructed to disprove the proofs claiming that unconditionally secure quantum bit commitment protocols are impossible.
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 rapid advancement of quantum computing poses a significant threat to classical cryptographic systems that rely on the computational hardness of mathematical problems such as integer factorization and discrete logarithm problems. In this context, quantum cryptography has emerged as a promising paradigm for secure communication based on the fundamental principles of quantum mechanics rather than on computational assumptions. This paper presents a comprehensive review of quantum cryptography, with a particular focus on Quantum Key Distribution (QKD), the most mature application. The study discusses the theoretical foundations of quantum security, including superposition, entanglement, and the No-cloning theorem, which collectively enable eavesdropping detection and guarantee information-theoretic security. Furthermore, the review examines major QKD protocols, such as BB84 and E91, as well as their advanced variants designed to address practical vulnerabilities and enhance performance. Recent progress in real-world implementations, including fiber-optic networks, free-space communication, and satellite-based systems such as the Micius satellite, is also analyzed. In addition, the paper highlights critical challenges related to scalability, hardware limitations, and security loopholes arising from imperfect devices. Finally, emerging research directions, including hybrid cryptographic frameworks that integrate quantum and post-quantum approaches, are discussed to provide insights into the future of secure communication. This review aims to provide a structured, up-to-date understanding of quantum cryptography, bridging the gap between theoretical developments and practical implementations, and emphasizing its crucial role in shaping next-generation cybersecurity systems.
The demands for secure communication systems have been growing rapidly as technologies in computer networks advance. However, classical cryptography employed in network systems is only secure when malicious users do not have enough computational power to break the security in a practical amount of time. Quantum cryptography provides theoretically unbreakable security since its security relies on quantum mechanical properties. This dissertation resolves the weakness of classical cryptography in computer networks by developing novel cryptographic schemes. First, a new encryption scheme, quantum commutative encryption (QCE), has been developed by utilizing quantum superposition states. The analysis of possible attacks to the developed encryption scheme, the advantages of the developed scheme, and the requirements to utilize the developed scheme in a communication system are presented. Also, an example of realization with current technologies is shown.
Considering all the characteristics of the developed encryption scheme, a key distribution protocol, two authentication protocols, secret sharing scheme, and the possible practical application of the secret sharing scheme are designed by making use of the developed encryption scheme. This dissertation also discusses the security analysis for each developed scheme. All developed quantum cryptographic schemes are theoretically unbreakable and can be realized with current technologies.
The main contributions of this dissertation are not only the proposal of novel schemes, but also a demonstration of how quantum mechanical properties can be utilized in computer engineering/science.
Cryptography is used for the secure communication in which two parties are involved. The most popular cryptographic issue is the transmission of confidential messages. The privacy is maintained using the cryptographic protocol. The security of quantum cryptography relies more on physics including quantum mechanics and statistics rather than on solving mathematical problems. A well-known application of quantum cryptography is quantum key distribution (QKD) that is used to establish communication by generating cryptographic keys. Moreover, it is based on the Heisenberg uncertainty principle that ensures the security and prevents from eavesdropping. Basically, quantum cryptography with faint laser pulses, polarization coding, phase coding, and frequency coding have been discussed.
Cryptographic protocols can be classified by the type of security against eavesdropping which they provide. There exist mathematically secure schemes whose security relies on mathematical proofs (like the Vernam cipher discussed below) or conjectures (like public key RSA encryption) about the complexity of deciphering the message without possessing the correct key. The majority of current secure public Internet connections rely on such schemes. Alternatively, a cryptographic setup may provide a physically secure method for communicating. In these setups the security is provided by the physical laws governing the communication protocol. Here we first discuss a provably secure classical communication protocol and then quantum methods for distributing the necessary keys. The BB84 protocol relies on the impossibility of perfectly distinguishing non-orthogonal quantum states from one copy of the quantum system. The scheme was invented in 1984 and is the first of its kind. In contrast, the Ekert91 protocol makes use of Bell correlations between entangled pairs of photons. These correlations are destroyed when Eve attempts to make a measurement on one of the particles but also when imperfections, such as decoherence processes, affect the scheme. As long as no such “elements of reality” are introduced, and Bell correlations violating local realism can be generated by Alice and Bob, no eavesdropper can be present. One-time pads and the Vernam cipher The Vernam cipher is a cryptographic protocol which allows the encryption and decryption protocol to be publicly known. The security of the protocol relies entirely on the key which is private and not publicly known. Alice and Bob share identical n -bit secret key strings (one-time pad).