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

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 R L = 4 kOhm and R H = 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 R L = 9 kOhm and R H = 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 R L approaches R H . 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.