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Fluctuation and Noise Letters

Error-Rate Controlled Thresholding Method for Bit Acceptance for KLJN Communication Scheme

Andor Tönköly, Róbert Mingesz

Published Sep 5, 2025• 0 citations
Publisher

Abstract

This work introduces a novel thresholding method to control the error rate in the Kirchhoff-Law–Johnson-Noise (KLJN) secure key exchange system, offering precise trade-off tuning between bit acceptance and security. We provide an analytical approach to calculate the probability density functions (PDFs) of voltage and current noise for each KLJN state and propose a thresholding mechanism that leverages the inverse cumulative distribution function to guarantee a desired error probability ([Formula: see text]). Additionally, the rate of dropped bits ([Formula: see text]) is evaluated to quantify performance losses due to thresholding. This integrated analytical approach enhances the practical applicability of KLJN systems, offering error-tunable key exchange mechanisms.

DOI
10.1142/s0219477526500070

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This work introduces a novel thresholding method to control the error rate in the Kirchhoff-Law–Johnson-Noise (KLJN) secure key exchange system, offering precise trade-off tuning between bit acceptance and security. We provide an analytical approach to calculate the probability density functions (PDFs) of voltage and current noise for each KLJN state and propose a thresholding mechanism that leverages the inverse cumulative distribution function to guarantee a desired error probability ([Formula: see text]). Additionally, the rate of dropped bits ([Formula: see text]) is evaluated to quantify performance losses due to thresholding. This integrated analytical approach enhances the practical applicability of KLJN systems, offering error-tunable key exchange mechanisms.
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.
The Kirchhoff’s-Law-Johnson-Noise (KLJN) secure key exchanger is a simple, low-cost scheme that provides symmetric encryption with unconditional security in electronic communication. The key bits are generated based on measurements of the mean-square value of the noise voltage and/or current of the channel between the two communicating parties. In this work, a combined current–voltage measurement mode scenario and an error removal method for the ideal, symmetric KLJN secure key exchanger that uses an identical pair of resistors at both ends of the communication line were considered, which improves the fidelity and reduces the bit error probability compared to the schemes when either voltage or current measurement are being used. It has been shown in previous works that the error probability of the original, symmetric KLJN secure key exchanger decays exponentially with parameters such as the time window for performing the key exchange and other relevant criteria used in the interpretation of the key bits. The objective of this work is to develop optimization strategies for the ideal, symmetric KLJN secure key exchanger in order to obtain optimal values of these parameters while ensuring that errors are kept within acceptable values. For those strategies, closed-form solutions to the optimal values were derived by solving the Karush–Kuhn–Tucker (KKT) conditions. Numerical results show that the proposed optimization techniques not only ensure that the bit probability error remains within the desired limit, but also provide more flexibility to define the thresholds values, reduce the bit exchange period needed to guarantee an acceptable bit error probability, weaken Eve’s statistics, and improve the system resource managing.
A method to quantify the error probability at the Kirchhoff-law-Johnson-noise (KLJN) secure key exchange is introduced. The types of errors due to statistical inaccuracies in noise voltage measurements are classified and the error probability is calculated. The most interesting finding is that the error probability decays exponentially with the duration of the time window of single bit exchange. The results indicate that it is feasible to have so small error probabilities of the exchanged bits that error correction algorithms are not required. The results are demonstrated with practical considerations.
The Kirchhoff-law–Johnson-noise (KLJN) secure key distribution system provides a way of exchanging theoretically secure keys by measuring random voltage and current through the wire connecting two different resistors at Alice's and Bob's ends. Recently new advanced protocols for the KLJN method have been proposed with enhanced performance. In this paper, we analyze the KLJN system and compare with the "intelligent" KLJN (iKLJN) scheme. That task requires determination of the applied resistors and identification of various superpositions of known and unknown noise components. Some statistical tools will be explored to determine how the duration of the bit exchange window (averaging time) influences the performance of the secure bit exchange.
The Kirchhoff-law-Johnson-noise (KLJN) system is a classical physical secure key exchange scheme based on the Kirchhoff?s circuit loop law and the fluctuation-dissipation theorem of statistical physics. This dissertation contains two main studies related to this scheme: bit error analysis and removal, and applications in vehicular communication systems.\n\nThe thesis starts with a presentation of some of the challenges faced by modern communications. It also includes a description of the working principle of the KLJN system and the motivation upon which this dissertation is built. Then, a study of the errors in this scheme is carried out. In the first part, the types of errors due to statistical inaccuracies in the voltage-based and current-based measurement modes are classified and analyzed. In both measurement modes and for all types of errors, at fixed bandwidth, the error probabilities decay exponentially versus the duration of the bit sharing period. In the second part, an error removal method is proposed to improve the fidelity of the system. This method is based on the combination of the voltage-based and current-based schemes and it drastically reduces the error probabilities.\n\nThe second topic of study in the thesis explores a potential practical application for the KLJN key exchange scheme. First, we present a vehicular communication network architecture with unconditionally secure KLJN keys. Secondly, a new solution for secure KLJN key donation to vehicles is proposed and an upper limit for the lifetime of this key is given. \n\nA summary of the work is given in the last section and the main results of the research are discussed. These contributions include: closed-form expressions for the error probabilities in the KLJN system, error removal methods without the need of implementing any error correcting technique, and a new potential vehicular application for the KLJN scheme. Some of the future research initiatives related to these topics are discussed.
The Kirchhoff-Law-Johnson-Noise (KLJN) secure key distribution system provides a way of exchanging information theoretic secure keys by measuring the random voltage and current through the wire connecting two different resistors at Alice's and Bob's ends. Recently new advanced protocols for the KLJN method have been proposed with enhanced performance. In this paper we analyze the KLJN system and compare with “intelligent” KLJN (iKLJN) scheme. This task requires the determination of the applied resistors and the identification of the various superpositions of known and unknown noise components. Some statistical tools to determine how the duration of the bit exchange window (averaging time) influences the performance of secure bit exchange will be explored.