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arXiv:2608.18841

Copy-Protection with Correlated Challenges: Point Functions and More via Decisional Coset Monogamy

Amit Behera, Alper Çakan, Vipul Goyal

quant-phcs.CRSubmitted Aug 19, 2026• Announced Aug 20, 2026• 0 citations
v1 · Aug 19, 2026v2 · Oct 1, 2026
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Abstract

Copy-protection encodes a functionality in a reusable quantum state that cannot be split into two states (freeloader adversaries) which remain simultaneously useful. Prior plain-model results handle only independently sampled challenges; the more natural identical-challenge notion, also tied to unclonable bits and copy-protection of point functions, has remained open. We strengthen these definitions and prove plain-model security for our new stronger notions. For single-decryptor encryption (SDE) we define correlated challenge security, show it implies all previous SDE notions including identical-challenge security, and prove that the construction of Kitagawa and Yamakawa (TCC'25) achieves it assuming iO and one-way functions. We also nearly fully characterize the relations among prior SDE notions. For general functionalities we define correlated challenge unclonable puncturable obfuscation (UPO), allowing arbitrary correlations among challenge points and puncturing bits plus auxiliary information before and after splitting, and requiring only conditionally uniform bits and $λ^c$ average conditional min-entropy in each point separately (thus, in particular, the points may be identical). Assuming post-quantum iO and quantum-hard LWE, we construct correlated UPO for polynomial-size keyed circuits with input length at least $λ^c$, answering an open question of Ananth, Behera, Huang, Kitagawa, Yamakawa (EUROCRYPT'26) and of Cakan-Goyal (EUROCRYPT'26). We also obtain the first plain-model copy protection for point functions, $k$-point functions, and compute-and-compare programs, and identical-challenge copy protection for general puncturable functionalities.

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Copy-protection encodes a functionality in a reusable quantum state that cannot be split into two states (freeloader adversaries) which remain simultaneously useful. Prior plain-model results handle only independently sampled challenges; the more natural identical-challenge notion, also tied to unclonable bits and copy-protection of point functions, has remained open. We strengthen these definitions and prove plain-model security for our new stronger notions. For single-decryptor encryption (SDE) we define correlated challenge security, show it implies all previous SDE notions including identical-challenge security, and prove that the construction of Kitagawa and Yamakawa (TCC'25) achieves it assuming iO and one-way functions. We also nearly fully characterize the relations among prior SDE notions. For general functionalities we define correlated challenge unclonable puncturable obfuscation (UPO), allowing arbitrary correlations among challenge points and puncturing bits plus auxiliary information before and after splitting, and requiring only conditionally uniform bits and λcλ^cλc average conditional min-entropy in each point separately (thus, in particular, the points may be identical). Assuming post-quantum iO and quantum-hard LWE, we construct correlated UPO for polynomial-size keyed circuits with input length at least λcλ^cλc, answering an open question of Ananth, Behera, Huang, Kitagawa, Yamakawa (EUROCRYPT'26) and of Cakan-Goyal (EUROCRYPT'26). We also obtain the first plain-model copy protection for point functions, kkk-point functions, and compute-and-compare programs, and identical-challenge copy protection for general puncturable functionalities.
By leveraging the no-cloning principle of quantum mechanics, unclonable cryptography enables us to achieve novel cryptographic protocols that are otherwise impossible classically. Two most notable examples of unclonable cryptography are quantum copy-protection and unclonable encryption. Most known constructions rely on the quantum random oracle model (as opposed to the plain model), in which all parties have access in superposition to a powerful random oracle. Despite receiving a lot of attention in recent years, two important open questions still remain: copy-protection of point functions in the plain model, which is usually considered as feasibility demonstration, and unclonable encryption with unclonable indistinguishability security in the plain model. A core ingredient of these protocols is the so-called monogamy-of-entanglement property. Such games allow quantifying the correlations between the outcomes of multiple non-communicating parties sharing entanglement in a particular context. Specifically, we define the games between a challenger and three players in which the first player is asked to split and share a quantum state between the two others, who are then simultaneously asked a question and need to output the correct answer. In this work, by relying on previous works of Coladangelo, Liu, Liu, and Zhandry (Crypto'21) and Culf and Vidick (Quantum'22), we establish a new monogamy-of-entanglement property for subspace coset states, which allows us to progress towards the aforementioned goals. However, it is not sufficient on its own, and we present two conjectures that would allow first to show that copy-protection of point functions exists in the plain model, with different challenge distributions (including arguably the most natural ones), and then that unclonable encryption with unclonable indistinguishability security exists in the plain model. We believe that our new monogamy-of-entanglement to be of independent interest, and it could be useful in other applications as well. To highlight this last point, we leverage our new monogamy-of-entanglement property to show the existence of a tokenized signature scheme with a new security definition, called unclonable unforgeability.
By leveraging the no-cloning principle of quantum mechanics, unclonable cryptography enables us to achieve novel cryptographic protocols that are otherwise impossible classically. Two most notable examples of unclonable cryptography are copy-protection (CP) and unclonable encryption (UE). Most known constructions rely on the QROM (as opposed to the plain model). Despite receiving a lot of attention in recent years, two important open questions still remain: CP for point functions in the plain model, which is usually considered as feasibility demonstration, and UE with unclonable indistinguishability security in the plain model. A core ingredient of these protocols is the so-called monogamy-of-entanglement (MoE) property. Such games allow quantifying the correlations between the outcomes of multiple non-communicating parties sharing entanglement in a particular context. Specifically, we define the games between a challenger and three players in which the first player is asked to split and share a quantum state between the two others, who are then simultaneously asked a question and need to output the correct answer. In this work, by relying on previous works [CLLZ21, CV22], we establish a new MoE property for subspace coset states, which allows us to progress towards the aforementioned goals. However, it is not sufficient on its own, and we present two conjectures that would allow first to show that CP of point functions exists in the plain model, with different challenge distributions, and then that UE with unclonable indistinguishability security exists in the plain model. We believe that our new MoE to be of independent interest, and it could be useful in other applications as well. To highlight this last point, we leverage our new MoE property to show the existence of a tokenized signature scheme with a new security definition, called unclonable unforgeability.
Unclonable cryptography is concerned with leveraging the no-cloning principle to build cryptographic primitives that are otherwise impossible to achieve classically. Understanding the feasibility of unclonable encryption, one of the key unclonable primitives, satisfying indistinguishability security in the plain model has been a major open question in the area. So far, the existing constructions of unclonable encryption are either in the quantum random oracle model or are based on new conjectures. We present a new approach to unclonable encryption via a reduction to a novel question about nonlocal quantum state discrimination: how well can non-communicating -- but entangled -- players distinguish between different distributions over quantum states? We call this task simultaneous state indistinguishability. Our main technical result is showing that the players cannot distinguish between each player receiving independently-chosen Haar random states versus all players receiving the same Haar random state. We leverage this result to present the first construction of unclonable encryption satisfying indistinguishability security, with quantum decryption keys, in the plain model. We also show other implications to single-decryptor encryption and leakage-resilient secret sharing.
We study a novel question about nonlocal quantum state discrimination: how well can non-communicating - but entangled - players distinguish between different distributions over quantum states? We call this task simultaneous state indistinguishability. Our main technical result is to show that the players cannot distinguish between each player receiving independently-chosen Haar random states versus all players receiving the same Haar random state. We show that this question has implications to unclonable cryptography, which leverages the no-cloning principle to build cryptographic primitives that are classically impossible to achieve. Understanding the feasibility of unclonable encryption, one of the key unclonable primitives, satisfying indistinguishability security in the plain model has been a major open question in the area. So far, the existing constructions of unclonable encryption are either in the quantum random oracle model or are based on new conjectures. We leverage our main result to present the first construction of unclonable encryption satisfying indistinguishability security, with quantum decryption keys, in the plain model. We also show other implications to single-decryptor encryption and leakage-resilient secret sharing. These applications present evidence that simultaneous Haar indistinguishability could be useful in quantum cryptography.
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.
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.