Random-resistor-random-temperature KLJN key exchange

We introduce two new Kirchhoff-law–Johnson-noise (KLJN) secure key distribution schemes, which are the generalization of the original KLJN version. The first system, the Random-Resistor (RR-) KLJN scheme is using random resistors chosen from a quasi-continuum set of resistance values. It is well known since the creation of the KLJN concept that such system could work because Alice and Bob can calculate the unknown resistance value from measurements; however, it has not been addressed in publications as it was considered impractical. The reason for discussing it is the second scheme, the RandomResistor-Random-Temperature (RRRT-) KLJN key exchanger inspired by a recent paper of Vadai-Mingesz-Gingl where security was maintained at non-zero power flow. In the RRRT-KLJN secure key exchanger scheme, both the resistances and their temperatures are continuum random variables. We prove that the security of the RRRT-KLJN system can be maintained at non-zero power flow thus the physical law guaranteeing the security is not the Second Law of Thermodynamics but the Fluctuation-Dissipation Theorem. Knowing their own resistance and temperature values, Alice and Bob can calculate the resistance and temperature values at the other end from the measured voltage, current and power-flow data in the wire. Eve cannot determine these values because, for her, there are 4 unknown quantities, while she can set up only 3 equations. The RRRT-KLJN scheme has several advantages and makes all the existing former attacks invalid or incomplete.