Public Channel Cryptography: Chaos Synchronization and Hilbert's Tenth Problem

TL;DR

This paper explores secure communication using chaos synchronization with private filters, linking the problem of eavesdropping to NP-Complete problems, and proposes a novel approach for public-channel cryptography.

Contribution

It introduces a method for secure chaos-based communication that conceals signals with private filters and connects the security challenge to Hilbert's tenth problem.

Findings

Synchronization maintained with private filters and convoluted signals

Passive attacker problem mapped to NP-Complete Diophantine equations

Potential for new secure public-channel cryptographic protocols

Abstract

The synchronization process of two mutually delayed coupled deterministic chaotic maps is demonstrated both analytically and numerically. The synchronization is preserved when the mutually transmitted signal is concealed by two commutative private filters that are placed on each end of the communication channel. We demonstrate that when the transmitted signal is a convolution of the truncated time delayed output signals or some powers of the delayed output signals synchronization is still maintained. The task of a passive attacker is mapped onto Hilbert's tenth problem, solving a set of nonlinear Diophantine equations, which was proven to be in the class of NP-Complete problems. This bridge between two different disciplines, synchronization in nonlinear dynamical processes and the realm of the NPC problems, opens a horizon for a new type of secure public-channel protocols.