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Secure Quantum Encryption

Michael St-Jules

Published Jan 1, 2016• 1 citation
Publisher

Abstract

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).

DOI
10.20381/ruor-329

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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).
We call quantum security the area of IT security dealing with scenarios where one or more parties have access to quantum hardware. This encompasses both the fields of post-quantum cryptography (that is, traditional cryptography engineered to be resistant against quantum adversaries), and quantum cryptography (that is, security protocols designed to be natively run on a quantum infrastructure, such as quantum key distribution). Moreover, there exist also hybrid models, where traditional cryptographic schemes are somehow `mixed' with quantum operations in certain scenarios. Even if a fully-fledged, scalable quantum computer has yet to be built, recent results and the pace of research in its realization call for attention, lest we suddenly find ourselves one day with an obsolete security infrastructure. For this reason, in the last two decades research in quantum security has experienced an exponential growth in interest and investments. In this work, we propose the first systematic classification of quantum security scenarios, and for each of them we recall the main tools and results, as well as presenting new ones. We achieve this goal by identifying four distinct quantum security classes, or domains, each of them encompassing the security notions and constructions related to a particular scenario. We start with the class QS0, which is `classical cryptography' (meaning that no quantum scenario is considered), where we present some classical constructions and results as a preliminary step. Regarding post-quantum cryptography, we introduce the class QS1, where we discuss in detail the problems arising when designing a classical cryptographic object meant to be resistant against adversaries with local quantum computing power, and we provide a classification of the possible quantum security reductions in this scenario when considering provable security. Moreover, we present results about the quantum security and insecurity of the Fiat-Shamir transformation (a useful tool used to turn interactive identification schemes into digital signatures), and ORAMs (protocols used to outsource a database in a private way). In respect to hybrid classical-quantum models, in the security class QS2 we discuss in detail the possible scenarios where these scenarios arise, and what a correct formalization should be in terms of quantum oracle access. We also provide a novel framework for the quantum security (both in terms of indistinguishability and semantic security) of secret-key encryption schemes, and we give explicit secure constructions, as well as impossibility results. Finally, in the class QS3 we consider all those cryptographic constructions designed to run natively on quantum hardware. We give constructions for quantum encryption schemes (both in the secret- and public-key scenario), and we introduce transformations for obtaining such schemes by conceptually simpler schemes from the class QS2. Moreover, we introduce a quantum version of ORAM, called quantum ORAM (QORAM), aimed at outsourcing in a private way a database composed of quantum data. In proposing a suitable security model and an explicit construction for QORAMs, we also introduce a technique of independent interest which models a quantum adversary able to extract information from a quantum system without disturbing it `too much'. We believe that the framework we introduce in this work will be a valuable tool for the scientific community in addressing the challenges arising when formalizing sound constructions and notions of security in the quantum world.
Quantum cryptography represents a revolutionary paradigm shift in secure communication by leveraging the principles of quantum mechanics to guarantee unbreakable encryption. Unlike classical cryptographic methods dependent on computational hardness, quantum cryptography exploits quantum phenomena such as superposition and entanglement to provide provable security against eavesdropping. This paper explores fundamental quantum cryptographic protocols, their operational principles, and recent advances that enable practical deployment. We further discuss challenges, implementation issues, and the future scope of quantum key distribution (QKD) technologies in securing global communication infrastructures
We investigate the definition of security for encryption scheme in quantum context. We systematically define the indistinguishability and semantic security for quantum public-key and private-key encryption schemes, and for computational security, physical security and information-theoretic security. Based on our definition, we present a necessary and sufficient condition that leads to information-theoretic indistinguishability for quantum encryption scheme. The equivalence between the indistinguishability and semantic security of quantum encryption scheme is also proved.
Quantum computing, based on the principles of quantum mechanics, is rapidly gaining momentum as a promising field of information technology.However, with the growing capabilities of quantum computing comes a new level of cybersecurity.Quantum-secure cryptography is emerging as a response to the potential threats posed by quantum computers to traditional cryptographic methods.The main goal of quantum-secure cryptography is to ensure the security of data in information systems, as quantum computing becomes more and more accessible.In this study, we thoroughly studied the essence of quantum-secure cryptography, its fundamental principles and applications.We have explored the advantages and limitations of this new cryptographic paradigm and discussed the potential challenges that arise in the context of its implementation.In addition, we analyzed the current state of research in the field of quantum-secure cryptography and highlighted the prospects for further development of this intriguing technology.We have researched potential threats and possible ways to solve them.Additionally, we reviewed a quantum risk assessment methodology that helps identify and manage threats in the context of quantum security.Finally, we trace existing examples and recent developments in the field of quantum-secure cryptography, revealing their potential to improve information security in the future.Overall, the research allows for a better understanding of the importance and prospects of quantum-secure cryptography in today's digital world.
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).