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Unconditionally secure quantum commitments with preprocessing

Luowen Qian

TL;DR

The work shows that quantum auxiliary inputs can enable computationally secure commitments with unconditional guarantees, bypassing classical hardness assumptions. It constructs a non-interactive, computationally-hiding, statistically-binding quantum commitment using an exponentially describable, exponentially samplable quantum auxiliary input derived from a sparse pseudorandom ensemble, and it extends the framework to the unclonable common random state model with efficient state-sampling via compressed oracle techniques. The results yield new pathways to cryptographic tasks such as OT and MPC in quantum settings, while also addressing trust assumptions with preprocessing and exploring the physical underpinnings of security. Overall, the paper challenges the belief that unconditional quantum cryptographic security must be statistically limited and highlights new interactions between quantum information, complexity, and physicality in cryptography.

Abstract

We demonstrate how to build computationally secure commitment schemes with the aid of quantum auxiliary inputs without unproven complexity assumptions. Furthermore, the quantum auxiliary input can be either sampled in uniform exponential time or prepared in at most doubly exponential time, without relying on an external trusted third party. Classically, this remains impossible without first proving $\mathsf{P} \neq \mathsf{NP}$.

Unconditionally secure quantum commitments with preprocessing

TL;DR

The work shows that quantum auxiliary inputs can enable computationally secure commitments with unconditional guarantees, bypassing classical hardness assumptions. It constructs a non-interactive, computationally-hiding, statistically-binding quantum commitment using an exponentially describable, exponentially samplable quantum auxiliary input derived from a sparse pseudorandom ensemble, and it extends the framework to the unclonable common random state model with efficient state-sampling via compressed oracle techniques. The results yield new pathways to cryptographic tasks such as OT and MPC in quantum settings, while also addressing trust assumptions with preprocessing and exploring the physical underpinnings of security. Overall, the paper challenges the belief that unconditional quantum cryptographic security must be statistically limited and highlights new interactions between quantum information, complexity, and physicality in cryptography.

Abstract

We demonstrate how to build computationally secure commitment schemes with the aid of quantum auxiliary inputs without unproven complexity assumptions. Furthermore, the quantum auxiliary input can be either sampled in uniform exponential time or prepared in at most doubly exponential time, without relying on an external trusted third party. Classically, this remains impossible without first proving .
Paper Structure (16 sections, 15 theorems, 11 equations)

This paper contains 16 sections, 15 theorems, 11 equations.

Table of Contents

  1. Introduction
  2. Removing trust.
  3. Removing inefficiency.
  4. Polynomially bounded adversaries are physical, probably.
  5. Additional applications.
  6. Open problems.
  7. Concurrent work.
  8. Quantum auxiliary-input commitment
  9. Classical impossibility.
  10. Commitment in the unclonable common random state model
  11. Eliminating trust with preprocessing
  12. Non-interactive quantum commitments
  13. Simulation security
  14. $\varepsilon$-simulation security for inefficient preprocessing.
  15. Simulation security in the unclonable common random state model.
  16. ...and 1 more sections

Key Result

Theorem 1

There exists a computationally-hiding statistically-binding non-interactive quantum commitment scheme with quantum auxiliary input. Furthermore, the quantum auxiliary input has an exponential-size classical description that can be sampled uniformly in exponential time.

Theorems & Definitions (27)

  • Theorem 1
  • Proposition 2: CGLQ20-tradeoffsLiu23-advice
  • Corollary 3: Exponentially secure sparse pseudorandom ensemble
  • proof : Proof of \ref{['thm:main']}
  • Theorem 4
  • proof
  • Lemma 5: Zha19-record
  • Corollary 6
  • Proposition 7
  • Proposition 8
  • ...and 17 more