Optimization-Based Strategies for the Error Removal Method in the Ideal, Symmetric KLJN Secure Key Exchanger

Abstract

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.