arXiv subjects

Alper Çakan

Publications and source records attributed to Alper Çakan.

7 recordsLinked to original sources

arXiv2026

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

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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arXiv2026

Public-Key Quantum Fire and Key-Fire From Classical Oracles

Quantum fire is a distribution of quantum states that can be efficiently cloned, but cannot be efficiently converted into a classical string. First considered by Nehoran and Zhandry (ITCS'24) and later formalized by Bostanci, Nehoran, Zhandry (STOC'25), quantum fire has strong applications and implications in cryptography, along with important connections to physics and complexity. However, constructing and proving the security of quantum fire so far has been elusive. Nehoran and Zhandry gave a construction relative to an inefficient quantum oracle. Later, Bostanci et al gave a candidate construction based on group actions, however, even in the oracle model they could only conjecture the security of their scheme, and were not able to prove security. In this work, we give a construction of public-key quantum fire relative to a classical oracle and prove its security unconditionally. Going further, we introduce two stronger notions that generalize it: Quantum key-fire where the clonable fire states serve as keys, and interactive (i.e. LOCC) security for quantum (key-)fire. We give a construction of quantum key-fire relative to a classical oracle and unconditionally prove that it satisfies interactive security for any unlearnable functionality. As a result, we also obtain the first classical oracle separations between various notions in physics and cryptography: *** A computational separation between two fundamental principles of quantum mechanics: No-cloning and no-teleportation, which are equivalent in information-theoretically. *** A separation between copy-protection security (Aaronson, CCC'09) and LOCC leakage-resilience security (Cakan, Goyal, Liu-Zhang, Ribeiro, TCC'24). *** A separation between computational no-cloning security and no-learning security, two notions introduced recently by Fefferman, Ghosh, Sinha, Yuen (ITCS'26).

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arXiv2025

Multi-Copy Security in Unclonable Cryptography

Unclonable cryptography leverages the quantum no-cloning principle to copy-protect cryptographic functionalities. While most existing works address the basic single-copy security, the stronger notion of multi-copy security remains largely unexplored. We introduce a generic compiler that upgrades collusion-resistant unclonable primitives to achieve multi-copy security, assuming only one-way functions. Using this framework, we obtain the first multi-copy secure constructions of public-key quantum money (termed quantum coins), single-decryptor encryption, unclonable encryption, and more. We also introduce an extended notion of quantum coins, called upgradable quantum coins, which allow weak (almost-public) verification under weaker assumptions and can be upgraded to full public verification under stronger assumptions by the bank simply publishing additional classical information. Along the way, we give a generic compiler that upgrades single-copy secure single-decryptor encryption to a collusion-resistant one, assuming the existence of functional encryption, and construct the first multi-challenge secure unclonable encryption scheme, which we believe are of independent interest.

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arXiv2025

How to Copy-Protect Malleable-Puncturable Cryptographic Functionalities Under Arbitrary Challenge Distributions

A quantum copy-protection scheme (Aaronson, CCC 2009) encodes a functionality into a quantum state such that given this state, no efficient adversary can create two (possibly entangled) quantum states that are both capable of running the functionality. There has been a recent line of works on constructing provably-secure copy-protection schemes for general classes of schemes in the plain model, and most recently the recent work of Çakan and Goyal (IACR Eprint, 2025) showed how to copy-protect all cryptographically puncturable schemes with pseudorandom puncturing points. In this work, we show how to copy-protect even a larger class of schemes. We define a class of cryptographic schemes called malleable-puncturable schemes where the only requirement is that one can create a circuit that is capable of answering inputs at points that are unrelated to the challenge in the security game but does not help the adversary answer inputs related to the challenge. This is a flexible generalization of puncturable schemes, and can capture a wide range of primitives that was not known how to copy-protect prior to our work. Going further, we show that our scheme is secure against arbitrary high min-entropy challenge distributions whereas previous work has only considered schemes that are punctured at pseudorandom points.

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arXiv2024

How to Delete Without a Trace: Certified Deniability in a Quantum World

Is it possible to comprehensively destroy a piece of quantum information, so that nothing is left behind except the memory of whether one had it at one point? For example, various works, most recently Morimae, Poremba, and Yamakawa (TQC 2024), show how to construct a signature scheme with certified deletion where a user who deletes a signature on m cannot later produce a signature for m. However, in all of the existing schemes, even after deletion the user is still able keep irrefutable evidence that m was signed, and thus they do not fully capture the spirit of deletion. In this work, we initiate the study of certified deniability in order to obtain a more comprehensive notion of deletion. Certified deniability uses a simulation-based security definition, ensuring that any information the user has kept after deletion could have been learned without being given the deleteable object to begin with; meaning that deletion leaves no trace behind! We define and construct two non-interactive primitives that satisfy certified deniability in the quantum random oracle model: signatures and non-interactive zero-knowledge arguments (NIZKs). As a consequence, for example, it is not possible to delete a signature/NIZK and later provide convincing evidence that it used to exist. Notably, our results utilize uniquely quantum phenomena to bypass the celebrated result of Pass (CRYPTO, 2003) showing that deniable NIZKs are impossible even in the random oracle model.

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arXiv2024

Unclonable Cryptography with Unbounded Collusions and Impossibility of Hyperefficient Shadow Tomography

Quantum no-cloning theorem gives rise to the intriguing possibility of quantum copy protection where we encode a program or functionality in a quantum state such that a user in possession of k copies cannot create k+1 copies, for any k. Introduced by Aaronson (CCC'09) over a decade ago, copy protection has proven to be notoriously hard to achieve. Previous work has been able to achieve copy-protection for various functionalities only in restricted models: (i) in the bounded collusion setting where k -> k+1 security is achieved for a-priori fixed collusion bound k (in the plain model with the same computational assumptions as ours, by Liu, Liu, Qian, Zhandry [TCC'22]), or, (ii) only k -> 2k security is achieved (relative to a structured quantum oracle, by Aaronson [CCC'09]). In this work, we give the first unbounded collusion-resistant (i.e. multiple-copy secure) copy-protection schemes, answering the long-standing open question of constructing such schemes, raised by multiple previous works starting with Aaronson (CCC'09). More specifically, we obtain the following results. - We construct (i) public-key encryption, (ii) public-key functional encryption, (iii) signature and (iv) pseudorandom function schemes whose keys are copy-protected against unbounded collusions in the plain model (i.e. without any idealized oracles), assuming (post-quantum) subexponentially secure iO and LWE. - We show that any unlearnable functionality can be copy-protected against unbounded collusions, relative to a classical oracle. - As a corollary of our results, we rule out the existence of hyperefficient quantum shadow tomography, * even given non-black-box access to the measurements, assuming subexponentially secure iO and LWE, or, * unconditionally relative to a quantumly accessible classical oracle, and hence answer an open question by Aaronson (STOC'18).

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arXiv2023

Computational Quantum Secret Sharing

Quantum secret sharing (QSS) allows a dealer to distribute a secret quantum state among a set of parties so that certain subsets can reconstruct the secret, while unauthorized subsets obtain no information. While QSS was introduced over twenty years ago, previous works focused only on existence of perfectly secure schemes, and the share size of the known schemes is exponential even for access structures computed by polynomial size monotone circuits. This stands in contrast to the classical case, where efficient computationally-secure schemes have been long known for all access structures in $\mathsf{monotone~P}$, and one can even obtain shares which are much shorter than the secret which is impossible with perfect security. In this work, we initiate the study of computationally-secure QSS and show that computational assumptions help significantly in building QSS schemes. We present a simple compiler and use it to obtain a large variety results: We construct polynomial-time QSS schemes under standard assumptions for a rich class of access structures. This includes many access structures for which previous results in QSS required exponential share size. We also construct QSS schemes for which the size of the shares is significantly smaller than the size of the secret. As in the classical case, this is impossible with perfect security. We also use our compiler to obtain results beyond computational QSS. In the information-theoretic setting, we improve the share size of perfect QSS schemes for a large class of access structures to $1.5^{n+o(n)}$, improving upon best known schemes and matching the best known result for general access structures in the classical case. Finally, we show construct efficient schemes for all access structures in $\mathsf{P}$ and $\mathsf{NP}$ when the quantum secret sharing scheme is given multiple of copies of the secret.

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