A mix of physics, mathematics, and computer science, the study of quantum information seeks to understand and utilize the information that can be held in the state of a quantum system. Quantum cryptography is then the study of various cryptographic protocols on the information in a quantum system. One of the goals we may have is to verify the integrity of quantum data, a process called quantum message authentication. In this thesis, we consider two quantum message authentication schemes, the Clifford code and the trap code. While both of these codes have been previously proven secure, they have not been proven secure in the simulator model, with an efficient simulation. We offer a new class of simulator that is efficient, so long as the adversary is efficient, and show that both of these codes can be proven secure using the efficient simulator. The efficiency of the simulator is typically a crucial requirement for a composable notion of security. The main results of this thesis have been accepted to appear in the Proceedings of the 9th International Conference on Information Theoretic Security (ICITS 2016).
A mix of physics, mathematics, and computer science, the study of quantum information seeks to understand and utilize the information that can be held in the state of a quantum system. Quantum cryptography is then the study of various cryptographic protocols on the information in a quantum system. One of the goals we may have is to verify the integrity of quantum data, a process called quantum message authentication. In this thesis, we consider two quantum message authentication schemes, the Clifford code and the trap code. While both of these codes have been previously proven secure, they have not been proven secure in the simulator model, with an efficient simulation. We offer a new class of simulator that is efficient, so long as the adversary is efficient, and show that both of these codes can be proven secure using the efficient simulator. The efficiency of the simulator is typically a crucial requirement for a composable notion of security. The main results of this thesis have been accepted to appear in the Proceedings of the 9th International Conference on Information Theoretic Security (ICITS 2016).
Quantum networking is the study of transmitting data that uses quantum mechanics principles (quantum messages).This thesis describes an algorithm that detects when an adversary maliciously modifies a quantum message (an integrity attack).The algorithm is analyzed in terms of its ability to detect an integrity attack and its efficiency in terms of classical computational complexity and the number of quantum basic gates used.It is rigorously compared to the Clifford code quantum message authentication (QMA) scheme.It offers a trade-off compared to the Clifford code QMA scheme in terms of integrity attack detection versus efficiency: reduced detection rates and improved efficiency.The new algorithm is conjectured to satisfy a more lax alternative definition of QMA.As a consequence of developing this new algorithm, a novel method for unranking permutations of multisets is also presented.
To the field of cryptography, quantum mechanics is a game changer. The exploitation of quantum mechanical properties through the manipulation of quantum information, the information encoded in the state of quantum systems, would allow many protocols in use today to be broken as well as lead to the expansion of cryptography to new protocols. In this thesis, quantum encryption, i.e. encryption schemes for quantum data, is defined, along with several definitions of security, broadly divisible into semantic security and ciphertext indistinguishability, which are proven equivalent, in analogy to the foundational result by Goldwasser and Micali. Private- and public-key quantum encryption schemes are also constructed from quantum-secure cryptographic primitives, and their security is proven. Most of the results are in the joint paper Computational Security of Quantum Encryption, to appear in the 9th International Conference on Information Theoretic Security (ICITS2016).
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.
The phenomenal progress in quantum technologies over the past decades has laid the groundwork for the construction of quantum networks, which will channel the power of quantum theory to guarantee secure and efficient communication, computation, and much more. This thesis studies the notion of trust in quantum networks. In our information age, protecting the security or anonymity of data is a key requirement. We investigate certain protocols that are fundamental to the operation and applications of quantum networks, and propose ways to test and analyse their security, in spite of adversarial intervention. Our focus is on practical methods of verifying the untrusted components, which could be incorporated into realistic networks in the near future. To begin, we propose a protocol for authenticated communication of quantum messages, by verifying the entanglement required for quantum teleportation in an experimentally feasible way. We model the performance of our scheme in the presence of noise. Furthermore, we explore such an authenticated teleportation in the one-sided device-independent scenario, where some devices used for verification may be corrupted. We derive error-tolerant self- testing bounds and extend our results to a realistic experimental setting, demonstrating the compatibility of our protocol with state-of-the-art technology. We then study anonymity, an essential feature for communication across networks. Combining the power of classical and quantum subroutines, we build a practical protocol for anonymous communication of quantum messages, without the need to trust the players in our network, their computational power, or the entanglement they share. We end by considering the verification of graph states distributed across a network of possibly dishonest players, applying our scheme to specific graph states that are central to quantum communication and computation schemes.
Authentication is a well-studied area of classical cryptography: a sender A and a receiver B sharing a classical secret key want to exchange a classical message with the guarantee that the message has not been modified or replaced by a dishonest party with control of the communication line. In this paper we study the authentication of messages composed of quantum states. We give a formal definition of authentication in the quantum setting. Assuming A and B have access to an insecure quantum channel and share a secret, classical random key, we provide a non-interactive scheme that enables A to both encrypt and authenticate an m qubit message by encoding it into m+s qubits, where the error probability decreases exponentially in the security parameter s. The scheme requires a secret key of size 2m+O(s). To achieve this, we give a highly efficient protocol for testing the purity of shared EPR pairs. It has long been known that learning information about a general quantum state will necessarily disturb it. We refine this result to show that such a disturbance can be done with few side effects, allowing it to circumvent cryptographic protections. Consequently, any scheme to authenticate quantum messages must also encrypt them. In contrast, no such constraint exists classically. This reasoning has two important consequences: It allows us to give a lower bound of 2m key bits for authenticating m qubits, which makes our protocol asymptotically optimal. Moreover, we use it to show that digitally signing quantum states is impossible.
Quantum cryptography offers a way of key agreement, which is unbreakable by any external adversary. Authentication is of crucial importance, as perfect secrecy is worthless if the identity of the addressee cannot be ensured before sending important information. Message authentication has been studied thoroughly, but no approach seems to be able to explicitly counter meet-in-the-middle impersonation attacks. The goal of this paper is the development of an authentication scheme being resistant against active adversaries controlling the communication channel. The scheme is built on top of a key-establishment protocol and is unconditionally secure if built upon quantum cryptographic key exchange. In general, the security is the same as for the key-agreement protocol lying underneath.