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Quantum-inspired secure wireless communication protocol under spatial and local Gaussian noise assumptions

Masahito Hayashi

TL;DR

The paper introduces a quantum-inspired secure wireless protocol that enables Alice and Bob to distill secret keys even when an adversary controls the transmission space, by leveraging backward reconciliation and random sampling under a local Gaussian-noise detector model. It reduces Eve’s knowledge to a single leakage variable $E'$, enabling tractable finite-length security bounds and a computable asymptotic rate expressed as $\big(H[P_{E'},v_{B|E'}]-H(B'|A)[P_{B',A}]\big)_+$. The protocol combines reverse-information reconciliation, universal-hash privacy amplification, and public-channel verification to achieve strong, composable security with practical computation costs, including LDPC-based reconciliation and $O(n\log n)$ privacy amplification. It also extends to multi-antenna, complex-number, and interference scenarios, and provides finite-sample estimation methods (e.g., Kolmogorov-Smirnov) to bound leakage under parameter uncertainty. The work has potential practical impact by offering a QKD-inspired alternative that uses cheaper hardware and can adapt to dynamic Eve strategies within the assumed model, with explicit finite-length guarantees and a clear path to real-world deployment.

Abstract

Inspired from quantum key distribution, we consider wireless communication between Alice and Bob when the intermediate space between Alice and Bob is controlled by Eve. That is, our model divides the channel noise into two parts, the noise generated during the transmission and the noise generated in the detector. Eve is allowed to control the former, but is not allowed to do the latter. While the latter is assumed to be a Gaussian random variable, the former is not assumed to be a Gaussian random variable. In this situation, using backward reconciliation and the random sampling, we propose a protocol to generate secure keys between Alice and Bob under the assumption that Eve's detector has a Gaussian noise and Eve is out of Alice's neighborhood. In our protocol, the security criteria are quantitatively guaranteed even with finite block-length code based on the evaluation of error of the estimation of channel.

Quantum-inspired secure wireless communication protocol under spatial and local Gaussian noise assumptions

TL;DR

The paper introduces a quantum-inspired secure wireless protocol that enables Alice and Bob to distill secret keys even when an adversary controls the transmission space, by leveraging backward reconciliation and random sampling under a local Gaussian-noise detector model. It reduces Eve’s knowledge to a single leakage variable , enabling tractable finite-length security bounds and a computable asymptotic rate expressed as . The protocol combines reverse-information reconciliation, universal-hash privacy amplification, and public-channel verification to achieve strong, composable security with practical computation costs, including LDPC-based reconciliation and privacy amplification. It also extends to multi-antenna, complex-number, and interference scenarios, and provides finite-sample estimation methods (e.g., Kolmogorov-Smirnov) to bound leakage under parameter uncertainty. The work has potential practical impact by offering a QKD-inspired alternative that uses cheaper hardware and can adapt to dynamic Eve strategies within the assumed model, with explicit finite-length guarantees and a clear path to real-world deployment.

Abstract

Inspired from quantum key distribution, we consider wireless communication between Alice and Bob when the intermediate space between Alice and Bob is controlled by Eve. That is, our model divides the channel noise into two parts, the noise generated during the transmission and the noise generated in the detector. Eve is allowed to control the former, but is not allowed to do the latter. While the latter is assumed to be a Gaussian random variable, the former is not assumed to be a Gaussian random variable. In this situation, using backward reconciliation and the random sampling, we propose a protocol to generate secure keys between Alice and Bob under the assumption that Eve's detector has a Gaussian noise and Eve is out of Alice's neighborhood. In our protocol, the security criteria are quantitatively guaranteed even with finite block-length code based on the evaluation of error of the estimation of channel.

Paper Structure

This paper contains 37 sections, 16 theorems, 99 equations, 4 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Purpose and assumptions
  3. Comparison with previous papers
  4. Comparison with other attacks
  5. Comparison with other attacks
  6. Mathematical structure
  7. General case
  8. Gaussian case
  9. Protocol
  10. Description of protocol
  11. Choice of code and its calculation complexity
  12. Privacy amplification, verification, and their calculation complexity
  13. Privacy amplification
  14. Verification of correctness and public channel
  15. Security analysis and sacrifice bit length
  16. ...and 22 more sections

Key Result

Theorem 1

Using the variable we have the following relation where $e'=\frac{a_B a_E}{a_E^2+b_E^2}e+ y$, and $P_{X|E'=e'}$ is the conditional distribution for $X$ when $E'$ is $e'$. Also, $P_{B|E'=e'}$ is the Gaussian distribution with average $e'+e_B$ and variance $v_{B|E'}:=\frac{a_B^2 b_E^2}{a_E^2+b_E^2}+b_B^2$.

Figures (4)

  • Figure 1: Eve injects artificial noise to Bob's observation. $e_B=e_B'+e_B"$.
  • Figure 2: Key generation rate
  • Figure 3: Logarithm of upper bound of leaked information
  • Figure 4: Interference model: This figure shows the case when Eve has the same interference as that in Bob's detection.

Theorems & Definitions (16)

  • Theorem 1
  • Corollary 2
  • Lemma 3
  • Lemma 4
  • Lemma 5
  • Theorem 6
  • Lemma 7
  • Lemma 8
  • Proposition 9: Kolmogorov-Smirnov testMTW
  • Lemma 10
  • ...and 6 more