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arXiv:2509.11373

Resistor Hopping KLJN Noise Communication Using Small Bias Voltages Supported by ML and Optimum Threshold-Based Detectors

Hadi Zayyani, Felipe A. P. de Figueiredo, Mohammad Salman, Rausley A. A. de Souza

Published Sep 14, 2025• 0 citations
arXivHTMLPDF

Abstract

In this paper, a Resistor Hopping (RH) scheme with the addition of biases is proposed for secure Kirchhoff Law Johnson-Noise (KLJN) communication. The RH approach enables us to increase the bit rate of secure communication between Alice and Bob, while also ensuring that the inherent unconditional security of KLJN is satisfied. The biases are added to the proposed scheme to better distinguish between Gaussian distributed noises in terms of their means, rather than just using variances. Throughout the paper, we strive to minimize biases to achieve a power-efficient scheme. For the detection part of the proposed algorithm, a Maximum-Likelihood (ML) detector is derived. The separability condition of Gaussian distributions is investigated, along with the provision of a threshold-based detector that offers both simple and optimal thresholds in terms of minimizing the error probability. Some analysis of the proposed RH-KLJN communication scheme is provided, including Physical Layer Security (PLS) equations. Simulation results demonstrate the advantages of the proposed scheme over the classical KLJN scheme, offering a higher data rate and lower bit error probability at the expense of increased complexity.

DOI
10.48550/arxiv.2509.11373

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In this paper, a Resistor Hopping (RH) scheme with the addition of biases is proposed for secure Kirchhoff Law Johnson-Noise (KLJN) communication. The RH approach enables us to increase the bit rate of secure communication between Alice and Bob, while also ensuring that the inherent unconditional security of KLJN is satisfied. The biases are added to the proposed scheme to better distinguish between Gaussian distributed noises in terms of their means, rather than just using variances. Throughout the paper, we strive to minimize biases to achieve a power-efficient scheme. For the detection part of the proposed algorithm, a Maximum-Likelihood (ML) detector is derived. The separability condition of Gaussian distributions is investigated, along with the provision of a threshold-based detector that offers both simple and optimal thresholds in terms of minimizing the error probability. Some analysis of the proposed RH-KLJN communication scheme is provided, including Physical Layer Security (PLS) equations. Simulation results demonstrate the advantages of the proposed scheme over the classical KLJN scheme, offering a higher data rate and lower bit error probability at the expense of increased complexity.
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.
The information-theoretically (unconditionally) secure Kirchhoff-law-Johnson-noise (KLJN) bit exchange protocol uses two identical resistor pairs with high (H) and low (L) resistance values, driven by Gaussian noise generators emulating Johnson noise with a high common temperature. The resulting mean-square noise voltage on the wire connecting Alice and Bob has three levels: low (L/L), intermediate (H/LorL/H), and high (H/H), and secure key sharing is achieved at the intermediate level (L/HorH/L). This paper introduces the Flip-KLJN scheme, where a pre-agreed intermediate level, such asH/L, triggers a flip of the bit map value during the bit exchange period. For Eve, the bit map flips appear random. Thus, the formerly discardedH/HandL/Lsituations can also have a pre-agreed bit value mapping, which flips together with the original bit mapping. Thus, Flip-KLJN doubles the key rate and ensures that all three levels on the wire are indistinguishable for Eve. Bit error probabilities are addressed through analytic calculations and computer simulations.
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.
Abstract We introduce two new Kirchhoff-law-Johnson-noise (KLJN) secure key distribution schemes which are generalizations of the original KLJN scheme. The first of these, the Random-Resistor (RR-) KLJN scheme, uses random resistors with values chosen from a quasi-continuum set. It is well-known since the creation of the KLJN concept that such a system could work in cryptography, because Alice and Bob can calculate the unknown resistance value from measurements, but the RR-KLJN system has not been addressed in prior publications since it was considered impractical. The reason for discussing it now is the second scheme, the Random Resistor Random Temperature (RRRT-) KLJN key exchange, inspired by a recent paper of Vadai, Mingesz and Gingl, wherein security was shown to be maintained at non-zero power flow. In the RRRT-KLJN secure key exchange scheme, both the resistances and their temperatures are continuum random variables. We prove that the security of the RRRT-KLJN scheme can prevail at a non-zero power flow, and thus the physical law guaranteeing security is not the Second Law of Thermodynamics but the Fluctuation-Dissipation Theorem. Alice and Bob know their own resistances and temperatures and can calculate the resistance and temperature values at the other end of the communication channel from measured voltage, current and power-flow data in the wire. However, Eve cannot determine these values because, for her, there are four unknown quantities while she can set up only three equations. The RRRT-KLJN scheme has several advantages and makes all former attacks on the KLJN scheme invalid or incomplete.
The Kirchhoff-Law-Johnson-Noise (KLJN) secure key exchange system has been introduced as a simple, very low cost and efficient classical physical alternative to quantum key distribution systems. The ideal system uses only a few electronic components-identical resistor pairs, switches and interconnecting wires-in order to guarantee perfectly protected data transmission. We show that a generalized KLJN system can provide unconditional security even if it is used with significantly less limitations. The more universal conditions ease practical realizations considerably and support more robust protection against attacks. Our theoretical results are confirmed by numerical simulations.
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.