Binary Classifier Wire-Resistance Attack on KLJN: Impact of Narrowing the Resistor Gap

Abstract

It is shown that narrowing the difference between the high and low resistor values in the Kirchhoff Law-Johnson Noise (KLJN) key exchange strongly affects security against a recently introduced binary classifier-based wire resistance attack. Using time domain simulations of a non-ideal KLJN loop with finite cable resistance, we generate large ensembles of secure (HL/LH) bits and evaluate the mean-square noise voltages at Alice's and Bob's ends. For each bit, these mean-square values form a point in a two-dimensional classifier plane, where the separation between the HL and LH point clouds characterizes the information available to an eavesdropper (Eve). We quantify Eve's success probability p by a simple decision rule based on the sign of the difference between the measured mean-square voltages. For strongly asymmetric resistors (for example RL = 4 kOhm and RH = 10 kOhm) and realistic wire resistances, the HL and LH clouds are fully separable and Eve's p approaches 1, which confirms that the classifier attack can practically recover all secure bits. As the low resistor value approaches the high one (for example RL = 9 kOhm and RH = 10 kOhm) at the same cable resistance, the HL and LH clouds increasingly overlap, and the measured p drops close to 0.7, approaching the ideal limit p = 0.5 as RL approaches RH. A surprising phenomenon is that, in this classifier-based scenario, increasing the wire resistance can decrease the information leak. This counterintuitive effect is strikingly the opposite of the behavior in the classical Bergou-Scheuer-Yariv wire resistance attack, where the mean-square voltages at the two ends of the wire are simply compared.