Duality on the Thermodynamics of the Kirchhoff-Law-Johnson-Noise (KLJN) Secure Key Exchange Scheme

This study investigates a duality approach to information extraction in the generalized Kirchhoff-Law-Johnson-Noise secure key exchange scheme proposed by Vadai, Mingesz and Gingl (VMG-KLJN). While previous work by Chamon and Kish sampled voltages at zero-current instances, this research explores sampling currents at zero-voltage crossings. The objective is to determine if this dual approach can extract information in non-equilibrium KLJN systems. Results indicate that the duality method successfully provides knowledge about the exchanged bit value, further supporting the necessity of thermal equilibrium for unconditional security in KLJN systems. Our findings confirm that the duality method successfully provides knowledge about the exchanged bit value, with results closely mirroring those of Chamon and Kish, showing comparable vulnerabilities in non-equilibrium conditions. These results further support the necessity of thermal equilibrium for unconditional security in the KLJN scheme.