The Error Analysis of the Secret Key Generation Algorithm Using Analog Function Computation

TL;DR

This paper analyzes the error characteristics of a decentralized secret key generation algorithm using analog function computation, focusing on factors like noise, fading, and parameter tolerance to improve security and reliability.

Contribution

It introduces an error model for a Gaussian prime-based secret key generation system and evaluates its robustness under fading channel conditions and different user scenarios.

Findings

Path loss significantly affects success rate.

Tolerance value impacts factorization success.

Performance varies with number of users.

Abstract

This study introduces a decentralized approach to secure wireless communication using a cryptographic secret key generation algorithm among distributed nodes. The system model employs Gaussian prime numbers, ensuring the collaborative generation of a secret key. Pre-processing and post-processing functions enable to generate a secret key across the network. An error model evaluates aspects like thermal noise power and channel estimation errors, while simulations assess the success rate to factorize the norm of the secret key. It is observed that path loss-induced large scale fading emerges as a critical component impacting information and power loss. The robustness of the proposed model under fading channel conditions is evaluated with a success rate. Additionally, it is also observed that the tolerance value set in the factorization algorithms has a significant impact on the success rate. Furthermore, the success rate is compared in two scenarios, one with 2 users and another with 3 users, to provide a comprehensive evaluation of the system performance.