In this work we study the (superposition-based, or QS2) quantum security of public key encryption schemes, originally initiated by Boneh and Zhandry (CRYPTO 2013, for a classical challenge indistinguishability phase) and imprioved by Gagliardoni et al. (CRYPTO 2016, for the symmetric key case). For public key encryption schemes, no notion of quantum security with a quantum indistinguishability phase exists. In this work we close this gap by using so-called type-2 operators for encrypting the challenge message. This brings non-trivial obstacles: On the one hand, public key encryption schemes typically cannot recover the randomness during decryption. On the other hand, many real-world schemes suffer from a small probability of decryption failures. Nevertheless, we identify a class of encryption schemes, which we call recoverable, that allow to avoid decryption failures given knowledge of the original encryption randomness, and we show that for these schemes the type-2 operator can be efficiently implemented even without knowledge of the secret key. This means that, for the public key case, type-2 operators are actually very natural. We also observe that many real-world quantum-resistant schemes, including many NIST candidates, are of this type. Equipped with these results, we (1) give the first quantum security notion (qINDqCPA) for public key encryption with a quantum indistinguishability phase, (2) prove that the canonical LWE-based encryption scheme achieves our security notion, (3) show that our notion is strictly stronger than existing security notions, (4) study the general classification of quantum-resistant public key encryption schemes, and (5) compare our results to a concurrent and independent work by Chevalier et al. (2020).
In this work we study the (superposition-based, or QS2) quantum security of public key encryption schemes, originally initiated by Boneh and Zhandry (CRYPTO 2013, for a classical challenge indistinguishability phase) and imprioved by Gagliardoni et al. (CRYPTO 2016, for the symmetric key case). For public key encryption schemes, no notion of quantum security with a quantum indistinguishability phase exists. In this work we close this gap by using so-called type-2 operators for encrypting the challenge message. This brings non-trivial obstacles: On the one hand, public key encryption schemes typically cannot recover the randomness during decryption. On the other hand, many real-world schemes suffer from a small probability of decryption failures. Nevertheless, we identify a class of encryption schemes, which we call recoverable, that allow to avoid decryption failures given knowledge of the original encryption randomness, and we show that for these schemes the type-2 operator can be efficiently implemented even without knowledge of the secret key. This means that, for the public key case, type-2 operators are actually very natural. We also observe that many real-world quantum-resistant schemes, including many NIST candidates, are of this type. Equipped with these results, we (1) give the first quantum security notion (qINDqCPA) for public key encryption with a quantum indistinguishability phase, (2) prove that the canonical LWE-based encryption scheme achieves our security notion, (3) show that our notion is strictly stronger than existing security notions, (4) study the general classification of quantum-resistant public key encryption schemes, and (5) compare our results to a concurrent and independent work by Chevalier et al. (2020).
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.
In 2013, Boneh and Zhandry introduced the notion of indistinguishability (IND) in chosen plaintext (CPA) and chosen ciphertext (CCA) attacks by a quantum adversary which is given superposition access to an oracle for encryption and decryption queries but is restricted to classical queries in the challenge phase. In this paper we define IND-CPA and IND-CCA notions for symmetric encryption schemes where the adversary has full quantum superposition access to the oracle, and give constructions that achieve these security notions. Our results are formulated in the concrete security framework.
Quantum computing is a significant threat to classical public-key cryptography. In strong "quantum access" security models, numerous symmetric-key cryptosystems are also vulnerable. We consider classical encryption in a model which grants the adversary quantum oracle access to encryption and decryption, but where the latter is restricted to non-adaptive (i.e., pre-challenge) queries only. We define this model formally using appropriate notions of ciphertext indistinguishability and semantic security (which are equivalent by standard arguments) and call it QCCA1 in analogy to the classical CCA1 security model. Using a bound on quantum random-access codes, we show that the standard PRF-based encryption schemes are QCCA1-secure when instantiated with quantum-secure primitives. We then revisit standard IND-CPA-secure Learning with Errors (LWE) encryption and show that leaking just one quantum decryption query (and no other queries or leakage of any kind) allows the adversary to recover the full secret key with constant success probability. In the classical setting, by contrast, recovering the key requires a linear number of decryption queries. The algorithm at the core of our attack is a (large-modulus version of) the well-known Bernstein-Vazirani algorithm. We emphasize that our results should not be interpreted as a weakness of these cryptosystems in their stated security setting (i.e., post-quantum chosen-plaintext secrecy). Rather, our results mean that, if these cryptosystems are exposed to chosen-ciphertext attacks (e.g., as a result of deployment in an inappropriate real-world setting) then quantum attacks are even more devastating than classical ones.
Large-scale quantum computing poses a major threat to classical public-key cryptography. Recently, strong “quantum access” security models have shown that numerous symmetric-key cryptosystems are also vulnerable. In this paper, we consider classical encryption in a model that grants the adversary quantum oracle access to encryption and decryption, but where we restrict the latter to non-adaptive (i.e., pre-challenge) queries only. We formalize this model using appropriate notions of ciphertext indistinguishability and semantic security (which are equivalent by standard arguments) and call it QCCA 1 in analogy to the classical CCA 1 security model. We show that the standard pseudorandom function ( PRF )-based encryption schemes are QCCA 1 -secure when instantiated with quantum-secure primitives. Our security proofs use a strong bound on quantum random-access codes with shared randomness. Revisiting plain IND − CPA -secure Learning with Errors ( LWE ) encryption, we show that leaking only a single quantum decryption query (and no other leakage or queries of any kind) allows the adversary to recover the full secret key with constant success probability. Information-theoretically, full recovery of the key in the classical setting requires at least a linear number of decryption queries. Our results thus challenge the notion that LWE is unconditionally “just as secure” quantumly as it is classically. The algorithm at the core of our attack is a new variant of the well-known Bernstein–Vazirani algorithm. Finally, we emphasize that our results should not be interpreted as a weakness of these cryptosystems in their stated security setting (i.e., post-quantum chosen-plaintext secrecy). Rather, our results mean that, if these cryptosystems are exposed to chosen-ciphertext attacks (e.g., as a result of deployment in an inappropriate real-world setting) then quantum attacks are even more devastating than classical ones.
It is an important question to find constructions of quantum cryptographic protocols which rely on weaker computational assumptions than classical protocols. Recently, it has been shown that oblivious transfer and multi-party computation can be constructed from one-way functions, whereas this is impossible in the classical setting in a black-box way. In this work, we study the question of building quantum public-key encryption schemes from one-way functions and even weaker assumptions. Firstly, we revisit the definition of IND-CPA security to this setting. Then, we propose three schemes for quantum public-key encryption from one-way functions, pseudorandom function-like states with proof of deletion and pseudorandom function-like states, respectively.
Inner-product functional encryption (IPFE) is an exciting paradigm for non-interactively computing on encrypted data where a master secret key can be used to derive decryption keys associated with certain inner-product functions in such a way that the decryption operation reveals an inner-product result, and nothing else. Over the decades, all efforts regarding existing IPFE schemes have been dedicated to extending them to multi-input/multi-client scenarios, understanding the security concepts that can be achieved, and identifying a multitude of practical use cases. However, in the event of key compromise, a common issue in real-world applications, the existing IPFE schemes are unable to guarantee the confidentiality of past encryptions. This paper introduces a novel variant of IPFE that supports key updates, called updatable IPFE, potentially opening up a new avenue of research to address the common key exposure problem. In this setting, any sender can initiate the transition to the next period by computing a new public key and a special update. The special update can be processed by the system administrator and the receiver to compute the next-period master secret key and the next-period decryption key, respectively. If done honestly, future (regular) ciphertexts generated with the new public key can be decrypted with the new decryption key, but ciphertexts from the past cannot be decrypted with the new decryption key. To formally illustrate this, we formalize the notion of the indistinguishability-based security under chosen randomness chosen plaintext attacks (IND-CR-CPA). We further propose the first efficient construction of updatable IPFE in the standard model, based on Learning with Errors (LWE) assumption with polynomial modulus-to-noise rate. Finally, we conduct a comprehensive performance evaluation of our updatable IPFE, and the experimental results demonstrate its computational efficiency, making it a viable solution for real-world applications.