Random-resistor-random-temperature Kirchhoff-law-Johnson-noise (RRRT-KLJN) key exchange

TL;DR

This paper introduces two generalized KLJN secure key distribution schemes involving random resistors and temperatures, demonstrating security at non-zero power flow and invalidating previous attack methods.

Contribution

The paper proposes the RRRT-KLJN scheme with continuum random variables for resistances and temperatures, proving security at non-zero power flow based on the Fluctuation-Dissipation Theorem.

Findings

Security maintained at non-zero power flow.

Eve cannot determine resistance and temperature values due to insufficient equations.

All previous attacks on KLJN are invalidated or incomplete.

Abstract

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.