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Semantic Security with Unreliable Entanglement Assistance: Interception and Loss

Meir Lederman, Uzi Pereg

Abstract

Semantic security is considered with unreliable entanglement assistance, due to one of two reasons: Interception or loss. We consider two corresponding models. In the first model, Eve may intercept the entanglement resource. In the second model, Eve is passive, and the resource may dissipate to the environment beyond her reach. We derive achievable rates for both models, subject to a maximal error criterion and semantic security. As an example, we consider the amplitude damping channel. Under interception, time division is not necessarily possible, and the boundary of our achievable region is disconnected. In the passive model, our rate region outperforms time division.

Semantic Security with Unreliable Entanglement Assistance: Interception and Loss

Abstract

Semantic security is considered with unreliable entanglement assistance, due to one of two reasons: Interception or loss. We consider two corresponding models. In the first model, Eve may intercept the entanglement resource. In the second model, Eve is passive, and the resource may dissipate to the environment beyond her reach. We derive achievable rates for both models, subject to a maximal error criterion and semantic security. As an example, we consider the amplitude damping channel. Under interception, time division is not necessarily possible, and the boundary of our achievable region is disconnected. In the passive model, our rate region outperforms time division.
Paper Structure (16 sections, 2 theorems, 22 equations, 3 figures)

This paper contains 16 sections, 2 theorems, 22 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Coding Definitions
  3. Semantic Security
  4. Security Under Interception
  5. Passive Eavesdropper
  6. Main Results
  7. Security Under Interception
  8. Passive Eavesdropper
  9. Example - Amplitude Damping Channel
  10. Proof of Theorem \ref{['Theorem:Inner_Bound_Interception_Model']}
  11. Random Code Analysis (Previous Work Lederman2024Secure)
  12. De-randomization
  13. Semantic Security
  14. Guaranteed information (expurgation)
  15. Excess information (message permutation)
  16. ...and 1 more sections

Key Result

Theorem 1

The region $\mathcal{R}_\text{SI}(\mathcal{N})$ is achievable with unreliable entanglement assistance and semantic security under interception. That is, the capacity region is bounded by

Figures (3)

  • Figure 1: Interception. As Eve may steal the resource, there are two scenarios: (a) "Left": Bob decodes both $m$ and $m'$. (b) "Right": Bob decodes $m$ alone.
  • Figure 2: Passive eavesdropper. The resource may get lost to the environment.
  • Figure 3: Achievable rate regions for the amplitude damping channel with unreliable entanglement assistance and semantic security, for $\gamma = 0.3$

Theorems & Definitions (5)

  • Definition 1
  • Definition 2
  • Remark 1
  • Theorem 1
  • Theorem 2