Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Disruptive RIS for Enhancing Key Generation and Secret Transmission in Low-Entropy Environments

Hibatallah Alwazani, Anas Chaaban

TL;DR

This work proposes an RIS assisted key generation protocol, proposes a scaling law as a function of the rate of change of RIS phase switching for the average secret information rate under this protocol, and describes a scaling law as a function of the rate of change of RIS phase switching for the average secret information rate under this protocol.

Abstract

Key generation, a pillar in physical-layer security (PLS), is the process of the exchanging signals from two legitimate users (Alice and Bob) to extract a common key from the random, common channels. The drawback of extracting keys from wireless channels is the ample dependence on the dynamicity and fluctuations of the radio channel, rendering the key vulnerable to estimation by Eve (an illegitimate user) in low-entropy environments because of insufficient randomness. Added to that, the lack of channel fluctuations lower the secret key rate (SKR) defined as the number of bits of key generated per channel use. In this work, we aim to address this challenge by using a reconfigurable intelligent surface (RIS) to produce random phases at certain, carefully curated intervals such that it disrupts the channel in low-entropy environments. We propose an RIS assisted key generation protocol, study its performance, and compare with benchmarks to observe the benefit of using an RIS while considering various important metrics such as key mismatch rate and secret key throughput. Furthermore, we characterize a scaling law as a function of the rate of change of RIS phase switching for the average secret information rate under this protocol. Then, we use both the key throughput and information rate to optimize the overall secrecy rate. Simulations are made to validate our theoretical findings and effectiveness of the proposed scheme showing an improvement in performance when an RIS is deployed.

Disruptive RIS for Enhancing Key Generation and Secret Transmission in Low-Entropy Environments

TL;DR

This work proposes an RIS assisted key generation protocol, proposes a scaling law as a function of the rate of change of RIS phase switching for the average secret information rate under this protocol, and describes a scaling law as a function of the rate of change of RIS phase switching for the average secret information rate under this protocol.

Abstract

Key generation, a pillar in physical-layer security (PLS), is the process of the exchanging signals from two legitimate users (Alice and Bob) to extract a common key from the random, common channels. The drawback of extracting keys from wireless channels is the ample dependence on the dynamicity and fluctuations of the radio channel, rendering the key vulnerable to estimation by Eve (an illegitimate user) in low-entropy environments because of insufficient randomness. Added to that, the lack of channel fluctuations lower the secret key rate (SKR) defined as the number of bits of key generated per channel use. In this work, we aim to address this challenge by using a reconfigurable intelligent surface (RIS) to produce random phases at certain, carefully curated intervals such that it disrupts the channel in low-entropy environments. We propose an RIS assisted key generation protocol, study its performance, and compare with benchmarks to observe the benefit of using an RIS while considering various important metrics such as key mismatch rate and secret key throughput. Furthermore, we characterize a scaling law as a function of the rate of change of RIS phase switching for the average secret information rate under this protocol. Then, we use both the key throughput and information rate to optimize the overall secrecy rate. Simulations are made to validate our theoretical findings and effectiveness of the proposed scheme showing an improvement in performance when an RIS is deployed.
Paper Structure (21 sections, 16 theorems, 59 equations, 10 figures, 1 table)

This paper contains 21 sections, 16 theorems, 59 equations, 10 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Model
  3. Key Generation and Secret Key Rate
  4. Channel Estimation
  5. Channel Correlation
  6. Secret Key Rate
  7. Key Leakage
  8. Practical Implementation for Secret Key Generation
  9. Quantization of Channel Estimates
  10. Key Mismatch Rate
  11. Effective Secret Key Rate
  12. Eve Intercept Probability
  13. Secrecy Rate
  14. Secure Information Rate
  15. Benchmarks
  16. ...and 6 more sections

Key Result

Lemma 1

Given circularly symmetric complex Gaussian channels, the aggregate channel $g_{{ij},\ell}=h_{ij}+\boldsymbol{h}_{i{\rm r}}^H\boldsymbol{\Phi}_{\ell}\boldsymbol{h}_{{\rm r}j}$, $i\in\{{\rm a,b}\}$, $j\in\{{\rm a,b,e}\}$, $j\neq i$, can be modeled as a circularly symmetric complex Gaussian when $N$ i

Figures (10)

  • Figure 1: System model with an access point Alice, receiver Bob, RIS Rose, and eavesdropper Eve.
  • Figure 2: Key generation time $T_{\rm k}$ split into multiple RIS switching periods with duration $T_{\rm s}$ from each of which a channel estimate is obtained at Alice (A) denoted $\bar{g}_{{\rm ba}, \ell}$ and Bob (B) denoted $\bar{g}_{{\rm ab}, \ell}$. The estimates are then put through a process to generate a common key.
  • Figure 3: Theoretical SKR against $N$ with no RIS as a benchmark. The effects of the correlation coefficient $\rho$ between Bob and Eve and the RIS correlation matrix $\mathbf{R}$ are highlighted.
  • Figure 4: Effect of SNR and $Q$ on the match probability. Parameters taken from Table \ref{['tabsims']}.
  • Figure 5: Schematic of achievable secret transmission using dual-stage encoding and OTP encryption.
  • ...and 5 more figures

Theorems & Definitions (17)

  • Lemma 1
  • Theorem 1
  • Corollary 1
  • Corollary 2
  • Corollary 3
  • Remark 1
  • Corollary 4
  • Corollary 5
  • Corollary 6
  • Theorem 2
  • ...and 7 more