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Two-Server Oblivious Transfer for Quantum Messages

Masahito Hayashi, Seunghoan Song

TL;DR

Two‐server oblivious transfer protocols for quantum messages are proposed for the first time and it is shown that no existing method works even under the above two‐server assumption.

Abstract

Oblivious transfer is considered as a cryptographic primitive task for quantum information processing over quantum network. Although it is possible with two servers, any existing protocol works only with classical messages. We propose two-server oblivious transfer protocols for quantum messages.

Two-Server Oblivious Transfer for Quantum Messages

TL;DR

Two‐server oblivious transfer protocols for quantum messages are proposed for the first time and it is shown that no existing method works even under the above two‐server assumption.

Abstract

Oblivious transfer is considered as a cryptographic primitive task for quantum information processing over quantum network. Although it is possible with two servers, any existing protocol works only with classical messages. We propose two-server oblivious transfer protocols for quantum messages.
Paper Structure (19 sections, 8 theorems, 32 equations, 2 figures, 1 table)

This paper contains 19 sections, 8 theorems, 32 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Definitions of various concepts
  3. Correctness and complexity
  4. User and server secrecy
  5. Blind and visible settings
  6. Outline of obtained protocols
  7. Preliminaries
  8. Symmetric QPIR protocol for pure real qubit states
  9. Symmetric QPIR protocol for pure real qudit states
  10. TQOT protocol for pure states described by commutative unitaries
  11. Deterministic TQOT protocol for pure qudit states
  12. Secrecy Problems in Protocol \ref{['PR4']}
  13. Probabilistic TQOT protocol for pure qubit states
  14. Probabilistic TQOT protocol for pure qudit states
  15. Two-Server Symmetric QPIR Protocols with Mixed States in Visible Setting
  16. ...and 4 more sections

Key Result

Lemma 1

Protocol PR1 is a correct TQOT protocol that satisfies the user secrecy and the server secrecy. Its upload complexity and its download complexity are $2\mathsf{f}$ bits and $2$ qubits, respectively. The required prior entanglement is one copy of $|I_2\rrangle$, i.e., one ebit.

Figures (2)

  • Figure 1: TQOT protocol with quantum messages.
  • Figure 2: Flow of protocol construction. Proposed protocols are constructed by using other protocol as subprotocols. The arrow, Protocol 1 $\to$ Protocol 2, means that Protocol 2 is constructed by using Protocol 1 as a subprotocol.

Theorems & Definitions (14)

  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Lemma 4
  • proof
  • Lemma 5
  • proof
  • ...and 4 more