Recently, Gunn, Allison and Abbott (GAA) [http://arxiv.org/pdf/1402.2709v2.pdf] proposed a new scheme to utilize electromagnetic waves for eavesdropping on the Kirchhoff-law-Johnson-noise (KLJN) secure key distribution. We proved in a former paper [Fluct. Noise Lett. 13 (2014) 1450016] that GAA’s mathematical model is unphysical. Here we analyze GAA’s cracking scheme and show that, in the case of a loss-free cable, it provides less eavesdropping information than in the earlier (Bergou)-Scheuer-Yariv mean-square-based attack [Kish LB, Scheuer J, Phys. Lett. A 374:2140-2142 (2010)], while it offers no information in the case of a lossy cable. We also investigate GAA’s claim to be experimentally capable of distinguishing—using statistics over a few correlation times only—the distributions of two Gaussian noises with a relative variance difference of less than 10-8. Normally such distinctions would require hundreds of millions of correlations times to be observable. We identify several potential experimental artifacts as results of poor KLJN design, which can lead to GAA’s assertions: deterministic currents due to spurious harmonic components caused by ground loops, DC offset, aliasing, non-Gaussian features including non-linearities and other non-idealities in generators, and the timederivative nature of GAA’s scheme which tends to enhance all of these artifacts.

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.