Multi-Copy Security in Quantum Cryptography and More

arXiv:2510.12626 · quant-ph, cs.CR · Submitted 2025-10-14 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Today's paper: "Multi-Copy Security in Quantum Cryptography and More".

Mira: As a fastidious and diligent researcher,

Kai: First, who's behind it and why it matters.

Paper summary: Kai: So, reflecting on the title "Multi-Copy Security in Quantum Cryptography and More," it seems the authors are positioning this work as a comprehensive tool rather than just a single result about one specific primitive.

Mira: That's right; they’re not just focusing on quantum coins or encryption but using that generic compiler to show how security properties can be upgraded across different cryptographic primitives (<ref:2510.12626#pg0>).

Lev: From my perspective, the real impact is establishing a rigorous security baseline for what a multi-copy secure scheme actually needs to satisfy in terms of anti-piracy guarantees before we even think about hardware.

Kai: Exactly, Lev; it’s about setting the standard for what constitutes acceptable security in this domain, which is crucial when we try to move these concepts from theory into physical reality.

Mira: The implication is that if functional encryption assumptions hold, then multi-copy security becomes a more accessible construction for building practical quantum applications (<ref:2510.12626#pg0>).

Lev: If the underlying assumptions are too strong, those constructions might be beautiful but impossible to realize with current error correction techniques, which is a real limitation we have to keep in mind.

Kai: That’s fair; the paper provides the theoretical structure, but it leaves us with the engineering challenge of realizing that structure physically.

Mira: Ultimately, "Multi-Copy Security in Quantum Cryptography and More" shows how combining quantum principles with generic compilation can lead to constructions that satisfy multi-copy security requirements (<ref:2510.12626#pg0>).

Lev: And I think the most significant contribution is providing a concrete path forward for error correction researchers by showing what kind of security we're aiming for when designing physical systems.

Conclusion: Kai: So, looking at the title and who wrote this paper, it sounds like they're really trying to build a universal toolbox for making quantum cryptography more robust.

Mira: That’s right; the focus isn't on one specific algorithm but on that compiler itself, showing how existing security features can be systematically layered onto new constructions.

Lev: From my side, the implication is that if this compiler works as described, it means we can use a wider variety of established primitives to build secure systems without having to invent entirely new security layers for every application.

Kai: Exactly, and when you think about the real-world implications for hardware, it suggests a more standardized way to approach building quantum devices that need high levels of copying resistance.

Mira: The authors are essentially providing a framework where we can take what we already have in terms of collusion resistance and upgrade it to handle the physical realities of multi-copy security.

Lev: I think this could really help error correction teams because it gives them a structured way to determine if their current error-correcting codes can be adapted to support these higher security guarantees.

Kai: It’s exciting because it moves us from proving one specific scheme secure to having a general method for upgrading many different types of quantum schemes.

Mira: And the authors are laying the groundwork for what they call "upgradable quantum coins," which seems like a very practical concept for things like digital cash in a quantum environment.

Lev: If we can use this compiler, it opens up possibilities where we might be able to design more resilient physical protocols that are less susceptible to copying errors during transmission or storage.

Alper C¸ akan, Vipul Goyal, Fuyuki Kitagawa, Ryo Nishimaki, Takashi Yamakawa

Carnegie Mellon University · NTT Research & Carnegie Mellon University

quant-ph, cs.CR

Submitted: 2025-10-14

Updated: 2026-10-05

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 92/100

The gist: As a fastidious and diligent researcher, I have meticulously analyzed these excerpts from the arXiv paper "Multi-Copy Security in Quantum Cryptography and More." The material outlines a significant

Key concepts

Generic Compiler: A tool designed to take existing cryptographic building blocks, which already offer some resistance against copying, and transform them into schemes that guarantee security even when multiple copies of the data are present. It automates the process of upgrading security levels.
Multi-Copy Security: A property ensuring a cryptographic scheme remains secure even if an adversary possesses multiple identical copies of the encrypted or signed data. This is achieved by leveraging quantum principles, specifically preventing unauthorized copying via the no-cloning theorem.
One-Way Functions (OWFs): Mathematical functions that are easy to compute in one direction but extremely difficult to reverse without specific secret information. The paper assumes these exist as a fundamental building block necessary for upgrading security properties across different cryptographic schemes.

Terminology

Unclonable Encryption — 18× in this paper
Verification — 18× in this paper · explained in 2 episodes
Single-Decryptor Encryption — 15× in this paper
Trace — 6× in this paper · explained in 2 episodes
Trace Distance — 3× in this paper · explained in 3 episodes
Fidelity — 2× in this paper · explained in 2 episodes
Consistency — 1× in this paper · explained in 3 episodes
Core — 1× in this paper · explained in 2 episodes
Generative AI — 1× in this paper · explained in 2 episodes
Shadow Tomography — 1× in this paper · explained in 4 episodes

Summary

As a fastidious and diligent researcher, I have meticulously analyzed these excerpts from the arXiv paper Multi-Copy Security in Quantum Cryptography and More. The material outlines a significant advancement in cryptographic primitives by introducing a generic compiler capable of upgrading existing security properties to achieve multi-copy security, leveraging the quantum no-cloning principle.

Here is a detailed and comprehensive summary combining the provided information:

This paper focuses on developing robust cryptographic schemes that resist unauthorized copying, specifically through the lens of unclonable cryptography, which fundamentally relies on the quantum no-cloning principle. The central contribution is a generic compiler designed to systematically upgrade existing primitives—those possessing collusion resistance—into schemes that achieve multi-copy security.

Generic Compiler for Upgrading Security: The authors introduce a generic compiler that takes existing primitives (like those providing collusion resistance) and upgrades them to provide multi-copy security. This process is predicated on the assumption of the existence of One-Way Functions (OWFs).
Expanded Primitive Security: By applying this framework, the paper achieves several groundbreaking constructions:

Public-Key Quantum Money (Quantum Coins): The compiler yields the first multi-copy secure constructions for quantum coins.
Single-Decryptor Encryption (SDE): It provides a method to upgrade single-copy secure encryption schemes to multi-copy secure ones.
Unclonable Encryption (UE): The framework is used to construct unclonable encryption schemes that satisfy multi-copy security requirements.

Upgradable Quantum Coins: The authors introduce an extended concept called upgradable quantum coins, demonstrating a scheme that satisfies both correctness and upgradability, specifically with respect to certain security assumptions (S1 = subexp − PKE and S2 = subexp − PKE, subspace-hiding obfuscation).
Upgrading Collusion Resistance: A key technical step involves applying the compiler to convert a collusion-resistant SDE scheme into a multi-copy secure one (as detailed in Section 8.5).

The paper establishes rigorous security guarantees based on specific underlying assumptions:

Theorem 17: Assuming the existence of polynomially secure indistinguishability obfuscation (Indistinguishability Obfuscation) and One-Way Functions (OWFs), the authors prove the existence of a public-key SDE scheme that simultaneously satisfies three critical security properties against copying:
Multi-copy strong anti-piracy security.
Multi-copy strong search anti-piracy security.
Multi-copy identical-challenge search anti-piracy security.
Theorem 19: Under the same assumptions (polynomially secure indistinguishability obfuscation and OWFs), an unclonable encryption (UE) scheme is constructed that guarantees multi-copy search security.
Theorem 20: This theorem provides a constructive link for UE schemes. It states that if a UE scheme with a classical key generation algorithm exists that satisfies multi-copy search security, then there also exists an equivalent UE scheme possessing both multi-copy search security and the property of having identical encryption and decryption keys.
Theorem 18: This theorem establishes a relationship between SDE and UE security: If an SDE is already collusion-resistant and satisfies identical-challenge search anti-piracy, then the resulting UE scheme will be multi-challenge search secure.

The analysis delves into the practical characteristics of these constructed schemes:

Classical Key Generation: The authors note that the multi-copy search secure UE scheme constructed in Section 9.3 possesses a classical key generation algorithm.
Key Identity: Corollary 8 explicitly confirms the existence of an unclonable encryption scheme with multi-copy search security that features identical encryption and decryption keys.

The paper is heavily supported by a series of corollaries that explore the existence of various quantum coin schemes under different assumptions, including:

Subspace-Hiding Obfuscation: Used in conjunction with collision-resistant hash functions to construct public-key quantum coins (Corollary 5).
Public-Key Mini-schemes: Also contribute to the existence proofs for public-key quantum coins (Corollary 4).

Improvements for AI systems

As a diligent researcher, I have analyzed this paper, Multi-Copy Security in Unclonable Cryptography. The core contribution is the development of a generic compiler that upgrades existing single-copy secure primitives (like Single-Decryptor Encryption or Unclonable Encryption) into multi-copy secure schemes by leveraging one-way functions (OWFs), Functional Encryption (FE), and other quantum cryptographic tools.

Here are the specific improvements to AI systems and what the improved system can achieve:

)

Improvement Focus: Multi-Copy Secure Unclonable Encryption (UE) for Robust Data Protection.
Specific Improvement: Implement a generic compiler that transforms single-copy secure UE into multi-copy search secure UE, assuming the existence of polynomially secure Indistinguishability Obfuscation (iO) and OWFs.
System Capability: The resulting AI system will be able to generate quantum states (ciphertexts) whose security guarantees hold even if an adversary possesses multiple copies of the same ciphertext generated under independent randomness. This is critical for scenarios involving distributed data storage or multi-party access where a single copy might be compromised, but multiple copies are held by different entities.
Improvement Focus: Multi-Copy Secure Quantum Money (Quantum Coins).
Specific Improvement: Apply the compiler to existing subspace-hiding obfuscation and OWF based public-key mini-schemes to construct Quantum Coins where all honest banknotes are identical pure states, satisfying multi-copy strong anti-piracy and search security.
System Capability: The AI system can manage a quantum asset (like a digital token or cryptocurrency) that is protected against duplication attempts by an adversary who has access to multiple copies of the underlying state, ensuring that any attempt to clone the asset fails with high probability.
Improvement Focus: Upgradable Quantum Coins for Evolving Cryptographic Standards.
Specific Improvement: Construct Upgradable Quantum Coins where security transitions from a weaker assumption (e.g., almost-public setting) to a stronger, fully public key quantum money scheme by simply publishing additional classical information (a single value).
System Capability: This AI system can operate in dynamic environments where cryptographic assumptions evolve. It can start with a less secure, but practical, verification method and upgrade its security posture to the highest standard as new cryptographic primitives become available, without needing a complete overhaul of the underlying scheme.
Improvement Focus: Enhancing Search Security for Single-Decryptor Encryption (SDE).
Specific Improvement: Utilize the generic compiler to upgrade single-key secure SDE schemes into collusion-resistant SDE schemes, which subsequently satisfy strong search anti-piracy security under the assumption of a puncturable PRF.
System Capability: The AI system can protect sensitive decryption keys (which are themselves quantum states) against adversaries who collaborate (collusion resistance) and attempt to find an alternative decryption method using multiple copies of those keys, ensuring that only one valid decryption key can be successfully found.

Abstract

Unclonable cryptography uses the quantum no-cloning principle to achieve security guarantees that are impossible in a classical world. Most existing works, however, consider only single-key security. The few works that achieve collusion-resistance rely on techniques highly tailored to their applications. Moreover, multi-copy security, where an adversary receives identical copies of a pure state, remains largely open. In this work, we develop a toolset of generic compilers and technical lemmata for collusion-resistance and multi-copy security. We first show how classical functional encryption can upgrade single-key quantum protection of decryption keys to collusion-resistant security, covering copy-protection, secure leasing, and leakage resilience. We then give a purification compiler that upgrades collusion-resistant state-query games with classically determined outputs to multi-copy security, assuming only one-way functions. Along the way, we develop a collusion-resistant one-way-to-hiding lemma, a quantum-state analogue of the small-range-distributions lemma, and a quantum pigeonhole lemma for entangled adversaries. We also construct the first deterministic signatures with quantum-query security and show that strong search security implies identical-challenge security for collusion-resistant single-decryptor encryption. Using these tools, we obtain the first public-key quantum coins, multi-copy secure single-decryptor encryption and unclonable encryption, and collusion-resistant secure key leasing with a fully classical vendor. Our quantum coins and plain-model search-secure UE use indistinguishability obfuscation and one-way functions, while our QROM UE achieves indistinguishability security unconditionally. Finally, we obtain multi-copy secure LOCC leakage-resilient public-key encryption, making progress towards quantum key-fire in the plain model.