Towards Wave Digital Memcomputing With Physical Memristor Models

In a more and more digital world, the protection of sensitive data is an essential challenge. Current cryptographic methods rely on one-way functions based on computationally challenging problems. However, there are several candidates for runtime efficient computing that might require new methods for data security. Among them are Universal Memcomputing Machines (UMM) for which a memristive circuit realization exists, where the eponymous element is a resistor with memory called memristor. While the original concept of UMMs is purely theoretical, we extend the state of the art by providing a thorough circuit theoretical analysis, utilizing models of real memristors and derive a highly flexible software emulator. The deployed memristor is an RRAM-cell which is known to have a rapid transition behavior, making it a suitable choice for runtime critical applications like UMMs. To obtain the emulator, we exploit the wave digital concept which is known to preserve passivity in a signal processing sense. The proper functioning is verified by solving an NP-complete subset sum problem.