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A Practical Protocol for Quantum Oblivious Transfer from One-Way Functions

Eleni Diamanti, Alex B. Grilo, Adriano Innocenzi, Pascal Lefebvre, Verena Yacoub, Álvaro Yángüez

TL;DR

This work tackles the problem of obtaining simulation-secure quantum oblivious transfer from computational assumptions (one-way functions) in the plain model, with a focus on practical feasibility. The authors introduce a noise-tolerant QOT protocol that mirrors quantum-key-distribution resources, achieving substantial resource efficiency by reducing required BB84 states to roughly $10^6$ per OT and enabling multiple OTs per protocol run. The technical core combines a novel Equivocal and Relaxed-Extractable Commitment (ERE-Commitment) with a streamlined equivocal compiler, augmented by linear error-correcting codes and privacy amplification to tolerate experimental imperfections. Security is established via simulation-based proofs leveraging equivocation and extraction concepts, Watrous rewinding, and careful hybrids, yielding a protocol suitable for realistic implementation in MPC-related quantum cryptography. The approach promises practical near-term deployment by lowering quantum resource needs, accounting for errors, and providing a clear distillation path for multiple OT keys from a single quantum run.

Abstract

We present a new simulation-secure quantum oblivious transfer (QOT) protocol based on one-way functions in the plain model. With a focus on practical implementation, our protocol surpasses prior works in efficiency, promising feasible experimental realization. We address potential experimental errors and their correction, offering analytical expressions to facilitate the analysis of the required quantum resources. Technically, we achieve simulation security for QOT through an equivocal and relaxed-extractable quantum bit commitment.

A Practical Protocol for Quantum Oblivious Transfer from One-Way Functions

TL;DR

This work tackles the problem of obtaining simulation-secure quantum oblivious transfer from computational assumptions (one-way functions) in the plain model, with a focus on practical feasibility. The authors introduce a noise-tolerant QOT protocol that mirrors quantum-key-distribution resources, achieving substantial resource efficiency by reducing required BB84 states to roughly per OT and enabling multiple OTs per protocol run. The technical core combines a novel Equivocal and Relaxed-Extractable Commitment (ERE-Commitment) with a streamlined equivocal compiler, augmented by linear error-correcting codes and privacy amplification to tolerate experimental imperfections. Security is established via simulation-based proofs leveraging equivocation and extraction concepts, Watrous rewinding, and careful hybrids, yielding a protocol suitable for realistic implementation in MPC-related quantum cryptography. The approach promises practical near-term deployment by lowering quantum resource needs, accounting for errors, and providing a clear distillation path for multiple OT keys from a single quantum run.

Abstract

We present a new simulation-secure quantum oblivious transfer (QOT) protocol based on one-way functions in the plain model. With a focus on practical implementation, our protocol surpasses prior works in efficiency, promising feasible experimental realization. We address potential experimental errors and their correction, offering analytical expressions to facilitate the analysis of the required quantum resources. Technically, we achieve simulation security for QOT through an equivocal and relaxed-extractable quantum bit commitment.
Paper Structure (24 sections, 21 theorems, 32 equations, 7 algorithms)

This paper contains 24 sections, 21 theorems, 32 equations, 7 algorithms.

Table of Contents

  1. Introduction
  2. Background and our results
  3. Technical overview
  4. Related works
  5. Paper Organisation
  6. Preliminaries and Definitions
  7. Notation
  8. Bit commitment
  9. Security against malicious receiver.
  10. Security against malicious sender.
  11. Leftover hash lemma
  12. Watrous Rewinding Lemma
  13. Error resilience
  14. Equivocal Commitment
  15. Relaxed statistical binding
  16. ...and 9 more sections

Key Result

lemma 1

Let $\rho_{XE}$ be a hybrid state and $h(r,x): \{0,1\}^m \times \{0,1\}^n \rightarrow \{0,1\}^{\ell}$ a two-universal hash function, with $r$ uniformly distributed over $\mathcal{R}$. Then, $K = h(r,x)$ satisfies:

Theorems & Definitions (46)

  • definition 1: Computational hiding
  • definition 2: Equivocality
  • definition 3: Statistical binding
  • definition 4: $\eta$-relaxed statistical binding
  • definition 5: $\chi$-relaxed extractability
  • definition 6: Quantum conditional min-entropy Ren05
  • lemma 1: Leftover Hash Lemma with Quantum Side Information Ren05
  • lemma 2: Conditional min-entropy BF12
  • lemma 3: Rewinding lemma with small perturbations Wat05
  • theorem 1
  • ...and 36 more