Simulation Framework, Chi-Distribution Validation, and Reconstruction Methods for KLJN Secure Key Exchange

The Kirchhoff-Law–Johnson-Noise (KLJN) key exchange protocol offers a classical, physics-based alternative to quantum key distribution for achieving informationtheoretic security. It offers a classical and cost-effective solution to secure communications. In this paper we present a simulation framework that models the entire KLJN loop, enabling detailed exploration of the scheme, and propose workflows to generate KLJN key-exchange probability density functions, and to validate their accuracy against analytically calculated ones. We also use our simulation to empirically verify that voltage and current standard deviations of a KLJN scheme follow chi-distributions, a result that crucially impacts threshold optimization and bit-classification algorithms. We also introduce correction techniques that reconstruct the original statistical behavior after signal-processing operations such as windowing and low-pass filtering, which are essential for reducing transients between bit transfers and enhancing security. This work integrates statistical signal analysis, and simulation-driven validation to strengthen the theoretical and practical foundations of KLJN-based secure communication.