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Multi-Copy Security in Unclonable Cryptography

Alper Çakan, Vipul Goyal, Fuyuki Kitagawa, Ryo Nishimaki, Takashi Yamakawa

TL;DR

The paper presents a general compiler that upgrades collusion resistant unclonable primitives to multi copy secure variants under standard one way functions. By instantiating this compiler with existing mini schemes, it achieves first multi copy secure constructions for public key quantum money (quantum coins), single decryptor encryption, and unclonable encryption, including an upgradable quantum coin model. A key technical tool is a purification based compiler that relates mixed state queries to purified state copies, and a suite of hybrids and probabilistic state constructions to prove security. The framework also yields a cascade of auxiliary results such as a generic compiler from single key SDE to collusion resistant SDE via functional encryption, and a multi challenge to multi copy transformation for UE, all under minimal assumptions like OWFs and in some cases indistinguishability obfuscation. Collectively, the work expands the landscape of multi copy secure unclonable cryptography and provides practically relevant constructions under standard cryptographic assumptions.

Abstract

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.

Multi-Copy Security in Unclonable Cryptography

TL;DR

The paper presents a general compiler that upgrades collusion resistant unclonable primitives to multi copy secure variants under standard one way functions. By instantiating this compiler with existing mini schemes, it achieves first multi copy secure constructions for public key quantum money (quantum coins), single decryptor encryption, and unclonable encryption, including an upgradable quantum coin model. A key technical tool is a purification based compiler that relates mixed state queries to purified state copies, and a suite of hybrids and probabilistic state constructions to prove security. The framework also yields a cascade of auxiliary results such as a generic compiler from single key SDE to collusion resistant SDE via functional encryption, and a multi challenge to multi copy transformation for UE, all under minimal assumptions like OWFs and in some cases indistinguishability obfuscation. Collectively, the work expands the landscape of multi copy secure unclonable cryptography and provides practically relevant constructions under standard cryptographic assumptions.

Abstract

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.
Paper Structure (87 sections, 53 theorems, 47 equations, 3 figures)

This paper contains 87 sections, 53 theorems, 47 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Multi-copy security.
  3. Collusion-resistance.
  4. Why multi-copy security?
  5. Our Results
  6. Quantum Coins
  7. Upgradable quantum coins.
  8. Single-Decryptor Encryption.
  9. Unclonable Encryption
  10. Other Applications
  11. Related Work
  12. Anonymous public key quantum money.
  13. Comparison with PRV24.
  14. Comparison with ITC:AnaMutPor25.
  15. Organization
  16. ...and 72 more sections

Key Result

Theorem 1

Suppose that there is a QPT algorithm $\mathsf{GenState}$ that takes a classical input $z$ and a classical randomness $rand\in\{0, 1\}^{r}$, and outputs a pure quantum state $\ket{\phi_{z,rand}}$ fully determined by $z$ and $rand$. For a pseudorandom state (PRS) key $k$ for $\lambda$-qubit output st

Figures (3)

  • Figure 1: The description of $\mathsf{RE}[\mathsf{one}.\mathsf{pk}]$
  • Figure 2: The description of reduction $\mathcal{R}_0$
  • Figure 3: The description of $\mathsf{R}\mathsf{M}$

Theorems & Definitions (112)

  • Theorem 1: Informal
  • Definition 1: Pseudorandom Function (PRF)
  • Definition 2: Puncturable PRF
  • Theorem 2: JACM:GolGolMic86AC:BonWat13PKC:BoyGolIva14CCS:KPTZ13
  • Definition 3: Indistinguishability Obfuscation
  • Definition 4: Functional Encryption
  • Definition 5: Adaptive Security for PKFE
  • Definition 6: Quantum algorithms with classically determined outputs
  • Lemma 1: zhandry2019record
  • Lemma 2: C:BonZha13
  • ...and 102 more