  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 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.
