Attainable Unconditional Security for Shared-Key Cryptosystems

Preserving the privacy of private communication is a fundamental concern of computing addressed by encryption. Information-theoretic reasoning models unconditional security where the strength of the results does not depend on computational hardness or unproven results. Usually the information leaked on the message by the ciphertext is used to measure the privacy of a communication, with perfect secrecy when the leakage is zero. However this is hard to achieve in practice. An alternative measure is the equivocation, intuitively the average number of message/key pairs that could have produced a given ciphertext. We show a theoretical bound on equivocation called max-equivocation and show that this generalizes perfect secrecy when achievable, and provides an alternative measure when perfect secrecy is not. We derive bounds for max-equivocation for symmetric encoder functions and show that max-equivocation is achievable when the entropy of the ciphertext is minimized. We show that max-equivocation easily accounts for key re-use scenarios, and that large keys relative to the message perform very poorly under equivocation. We study encoders under this new perspective, deriving results on their achievable maximal equivocation and showing that some popular approaches such as Latin squares are not optimal. We show how unicity attacks can be naturally modeled, and how breaking encoder symmetry improves equivocation. We present some algorithms for generating encryption functions that are practical and achieve 90-95% of the theoretical best, improving with larger message spaces

Universal Optimality of Apollonian Cell Encoders

Preserving privacy of private communication against an attacker is a fundamental concern of computer science security. Unconditional encryption considers the case where an attacker has unlimited computational power, hence no complexity result can be relied upon for encryption. Optimality criteria are defined for the best possible encryption over a general collection of entropy measures. This paper introduces Apollonian cell encoders, a class of shared-key cryptosystems that are proven to be universally optimal. In addition to the highest possible security for the message, Apollonian cell encoders prove to have perfect secrecy on their key allowing unlimited key reuse. Conditions for the existence of Apollonian cell encoders are presented, as well as a constructive proof. Further, a compact representation of Apollonian cell encoders is presented, allowing for practical implementation

Quantum Cryptography Beyond Quantum Key Distribution

Quantum cryptography is the art and science of exploiting quantum mechanical effects in order to perform cryptographic tasks. While the most well-known example of this discipline is quantum key distribution (QKD), there exist many other applications such as quantum money, randomness generation, secure two- and multi-party computation and delegated quantum computation. Quantum cryptography also studies the limitations and challenges resulting from quantum adversaries---including the impossibility of quantum bit commitment, the difficulty of quantum rewinding and the definition of quantum security models for classical primitives. In this review article, aimed primarily at cryptographers unfamiliar with the quantum world, we survey the area of theoretical quantum cryptography, with an emphasis on the constructions and limitations beyond the realm of QKD.Comment: 45 pages, over 245 reference

Practical unconditionally secure signature schemes and related protocols

The security guarantees provided by digital signatures are vital to many modern applications such as online banking, software distribution, emails and many more. Their ubiquity across digital communications arguably makes digital signatures one of the most important inventions in cryptography. Worryingly, all commonly used schemes – RSA, DSA and ECDSA – provide only computational security, and are rendered completely insecure by quantum computers. Motivated by this threat, this thesis focuses on unconditionally secure signature (USS) schemes – an information theoretically secure analogue of digital signatures. We present and analyse two new USS schemes. The first is a quantum USS scheme that is both information-theoretically secure and realisable with current technology. The scheme represents an improvement over all previous quantum USS schemes, which were always either realisable or had a full security proof, but not both. The second is an entirely classical USS scheme that uses minimal resources and is vastly more efficient than all previous schemes, to such an extent that it could potentially find real-world application. With the discovery of such an efficient classical USS scheme using only minimal resources, it is difficult to see what advantage quantum USS schemes may provide. Lastly, we remain in the information-theoretic security setting and consider two quantum protocols closely related to USS schemes – oblivious transfer and quantum money. For oblivious transfer, we prove new lower bounds on the minimum achievable cheating probabilities in any 1-out-of-2 protocol. For quantum money, we present a scheme that is more efficient and error tolerant than all previous schemes. Additionally, we show that it can be implemented using a coherent source and lossy detectors, thereby allowing for the first experimental demonstration of quantum coin creation and verification

Implementation of Quantum Key Distribution Protocols

As a wide spectrum of the human activity rapidly transitions to a digital environment, the need for secure and efficient communication intensifies. The currently used public key distribution cryptosystems, such as the Rivest-Shamir-Adleman (RSA) protocol, source their security from the computational difficulty of certain mathematical problems. While widely successful, the security these cryptosystems offer remains heuristic and the development of Quantum computers may render them obsolete. The security that Quantum Key Distribution (QKD) guarantees, stems not from the mathematical complexity of the encryption algorithms but from the laws of Quantum Physics. Implementations of QKD protocols, however, rely on imperfect instruments and devices for information encoding, transmission and detection. Device imperfections limit the rate of information exchange and introduce vulnerabilities which can be exploited by a potential eavesdropper. This work explores practical aspects of QKD as it matures beyond proof-of-principle experiments, focusing on the Measurement Device Independent - QKD, a novel Quantum Communication protocol that offers an exceptional balance between security and efficiency. At the heart of the MDI-QKD lies the Hong-Ou-Mandel (HOM) interference which characterizes the indistinguishability of the photon states that the communicating parties independently send. This study examines the HOM interference in a realistic lab environment and concludes that exceptional interference visibility can be achieved using typical commercially available optical devices and detectors, further demonstrating the applicability of the MDI-QKD protocol. An important limiting factor for every Quantum Communication protocol is the transmission medium. Fiber - based optical networks suffer significant losses that prohibit Quantum Communication beyond metropolitan scales. While Free Space communication is an attractive alternative for long distance communication, is susceptible to losses due to the atmospheric Turbulence of the channel. As a means to improve the key generation efficiency, this work examines and experimentally demonstrates the Prefixed-Threshold Real Time Selection (P-RTS) scheme, which improves the free-space communication efficiency by rejecting detections that occur while the channel transmittance drops below a predetermined threshold