It is well known that quantum computers, when fully realized, pose a threat to most cryptosystems deployed today. On the other hand, quantum information is also known to enhance classical cryptography, in terms of improved security and efficiency. Surprisingly, quantum information can also provide guarantees that are completely impossible to attain classically. The class of quantum cryptographic primitives called unclonable primitives fall into this category, with quantum money being a canonical example. Intuitively, quantum money allows a bank to distribute currency in the form of quantum states that provably resist counterfeiting due to the no-cloning theorem of quantum mechanics. This is in sharp contrast to classical information, for which there is no fundamental barrier that prevents its duplication. This work focusses on another up-and-coming unclonable primitive referred to as secure key leasing (SKL). This is a notion that allows to encode secret keys into a quantum state that can be temporarily leased. For example, it allows decryption keys of a public-key encryption scheme to be leased, enabling the recipient to decrypt ciphertexts while it possesses the quantum state. Later, the recipient can provide a proof of deletion which ensures that they have effectively ``lost'' access to the leased key. SKL is especially useful for software distributors that wish to provide trial period access. It allows them to provide access to their service via leased quantum keys, where they can incentivize timely deletion using a refund. In more detail, this dissertation studies SKL schemes in the setting of collusion, where multiple users can be leased independently generated quantum keys that provide access to the same underlying secret-key. It involves the study of meaningful notions of collusion-resistant security in this context, which are more realistic for real world applications than schemes secure in the standalone (single-key/single-user) setting. Then, new constructions are provided to realize these notions, with an emphasis on utilizing standard/well-understood cryptographic assumptions. Another major focus of the work is on providing modular approaches to constructing collusion-resistant SKL. In this light, novel compilers for different variants of the primitive are motivated and explored in detail.
It is well known that quantum computers, when fully realized, pose a threat to most cryptosystems deployed today. On the other hand, quantum information is also known to enhance classical cryptography, in terms of improved security and efficiency. Surprisingly, quantum information can also provide guarantees that are completely impossible to attain classically. The class of quantum cryptographic primitives called unclonable primitives fall into this category, with quantum money being a canonical example. Intuitively, quantum money allows a bank to distribute currency in the form of quantum states that provably resist counterfeiting due to the no-cloning theorem of quantum mechanics. This is in sharp contrast to classical information, for which there is no fundamental barrier that prevents its duplication. This work focusses on another up-and-coming unclonable primitive referred to as secure key leasing (SKL). This is a notion that allows to encode secret keys into a quantum state that can be temporarily leased. For example, it allows decryption keys of a public-key encryption scheme to be leased, enabling the recipient to decrypt ciphertexts while it possesses the quantum state. Later, the recipient can provide a proof of deletion which ensures that they have effectively ``lost'' access to the leased key. SKL is especially useful for software distributors that wish to provide trial period access. It allows them to provide access to their service via leased quantum keys, where they can incentivize timely deletion using a refund. In more detail, this dissertation studies SKL schemes in the setting of collusion, where multiple users can be leased independently generated quantum keys that provide access to the same underlying secret-key. It involves the study of meaningful notions of collusion-resistant security in this context, which are more realistic for real world applications than schemes secure in the standalone (single-key/single-user) setting. Then, new constructions are provided to realize these notions, with an emphasis on utilizing standard/well-understood cryptographic assumptions. Another major focus of the work is on providing modular approaches to constructing collusion-resistant SKL. In this light, novel compilers for different variants of the primitive are motivated and explored in detail.
Inspired by the no-cloning theorem in quantum theory, a variety of quantum cryptographic primitives with unclonable functionalities, such as secure key leasing and copy protection, have been proposed and attracted significant attention. However, trapdoor functions (TDFs), fundamental primitives in public-key cryptography, have not been extensively studied in these areas. In this work, we initiate a study of TDFs in both secure key leasing and copy protection settings. We first introduce the definition of TDFs with secure key leasing (TDF-SKL), which enables leasing and deleting of quantum trapdoors. We formalize TDF-SKL both with and without domain sampler, and give a construction of TDF-SKL without domain sampler based on the LWE assumption and a construction of TDF-SKL with domain sampler based on any standard PKE schemes combined with hinting pseudorandom generators [Koppula and Waters, CRYPTO 2019]. Next, we define TDFs with copy protection (TDF-CP), where the inversion functionality is copy protected by a quantum trapdoor. We establish a construction of TDF-CP assuming indistinguishability obfuscation and the LWE assumption, following a modular framework of copy protection proposed by Ananth and Behera [CRYPTO 2024]. We also present applications of TDF-SKL and TDF-CP. Existing constructions of public-key encryption with secure key leasing (PKE-SKL) and single-decryptor encryption (SDE) suffer from a critical vulnerability: quantum decryption keys may be destroyed after decrypting maliciously chosen ciphertexts. We construct PKE-SKL schemes and SDE schemes with robust quantum decryption keys that remain reusable after decrypting arbitrary ciphertexts from TDF-SKL and TDF-CP, respectively.
We propose the first error-tolerant secure key leasing (SKL) for public-key encryption. As with SKL in prior works, our protocol consists of a lessor and lessee. In the protocol, the lessor encodes its secret key into quantum states and leases the key to the lessee. Then, the lessor can ask the lessee to return the secret key at a later point. The lessor is able to check whether the lessee has returned its key honestly. However, our protocol works even when the leased secret key is subject to noise. The lessee decrypts the ciphertext correctly, and the lessor verifies the return of the secret key correctly when the amount of error is below a certain threshold. Our improved protocol does not change the encoding of the secret key, and thus adds no overhead to the quantum information processing. Our most significant result is a framework to analyze the trade-off between robustness against error and security. We bridge the security of the error-tolerant SKL and that of the error-tolerant certified deletion with shortened codes, which is a relatively less explored concept in coding theory.
The emergence of quantum computing has provided new paradigms for cryptography. On the one hand, it poses significant new threats to existing classically cryptographic systems, requiring the community to define new security models that capture what a quantum adversary can do. On the other hand, it gives us new tools to design cryptographic protocols, with weaker assumptions than in the classical world, or even protocols that are impossible classically. In this survey, we first give an overview of new security definitions for classical cryptography, considering quantum adversaries who can either only use local quantum computation (post-quantum security), or even send quantum messages and in particular have access to oracle in superposition (quantum security). We explore these new notions through the examples of commitments, zero-knowledge proofs, encryption, and signatures. Then, we present what is arguably the most famous application of quantum cryptography: quantum key distribution (QKD) protocols that take advantage of unique properties of quantum mechanics to provide secure communication unconditionally. We also explore cryptography beyond QKD, focusing on unclonable cryptography: a family of cryptographic functionalities, built with quantum states, and designed to be resistant to counterfeit by leveraging the “no-cloning” theorem. We examine in particular quantum money, but also the recent notions of unclonable encryption and copy-protection, including related variants. By presenting a comprehensive survey of these topics, this paper aims to provide a thorough understanding of the current landscape and future potential of quantum cryptography.
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.
Fundamental principles of quantum mechanics have inspired many new research directions, particularly in quantum cryptography. One such principle is quantum no-cloning which has led to the emerging field of revocable cryptography. Roughly speaking, in a revocable cryptographic primitive, a cryptographic object (such as a ciphertext or program) is represented as a quantum state in such a way that surrendering it effectively translates into losing the capability to use this cryptographic object. All of the revocable cryptographic systems studied so far have a major drawback: the recipient only receives one copy of the quantum state. Worse yet, the schemes become completely insecure if the recipient receives many identical copies of the same quantum state - a property that is clearly much more desirable in practice. While multi-copy security has been extensively studied for a number of other quantum cryptographic primitives, it has so far received only little treatment in context of unclonable primitives. Our work, for the first time, shows the feasibility of revocable primitives, such as revocable encryption and revocable programs, which satisfy multi-copy security in oracle models. This suggest that the stronger notion of multi-copy security is within reach in unclonable cryptography more generally, and therefore could lead to a new research direction in the field.
Fundamental principles of quantum mechanics have inspired many new research directions, particularly in quantum cryptography. One such principle is quantum no-cloning which has led to the emerging field of revocable cryptography. Roughly speaking, in a revocable cryptographic primitive, a cryptographic object (such as a ciphertext or program) is represented as a quantum state in such a way that surrendering it effectively translates into losing the capability to use this cryptographic object. All of the revocable cryptographic systems studied so far have a major drawback: the recipient only receives one copy of the quantum state. Worse yet, the schemes become completely insecure if the recipient receives many identical copies of the same quantum state -- a property that is clearly much more desirable in practice. While multi-copy security has been extensively studied for a number of other quantum cryptographic primitives, it has so far received only little treatment in context of unclonable primitives. Our work, for the first time, shows the feasibility of revocable primitives, such as revocable encryption and revocable programs, which satisfy multi-copy security in oracle models. This suggest that the stronger notion of multi-copy security is within reach in unclonable cryptography more generally, and therefore could lead to a new research direction in the field.