2008/06/05 by Ido Kanter, Evi Kopelowitz, Wolfgang Kinzel
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Channel (broadcasting) #Chaos control and synchronization #Chaos-based Image/Signal Encryption #Computer science #Discrete mathematics #Fractal and DNA sequence analysis #Hilbert space #Mathematical analysis #Mathematics #Nondeterministic algorithm #Nonlinear system #Physics #Polynomial #Pure mathematics #Quantum mechanics #Synchronization (alternating current) #Telecommunications #Time complexity #nlin.CD
paper · pdf · doi:10.1103/physrevlett.101.084102
arxiv created 2008/06/05 · openalex publication_date 2008/08/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 signals are concealed by two commutative private filters, a convolution of the truncated time-delayed output signals or some powers of the delayed output signals. 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 [problems that are both NP (verifiable in nondeterministic polynomial time) and NP-hard (any NP problem can be translated into this problem)]. This bridge between nonlinear dynamics and NP-complete problems opens a horizon for new types of secure public-channel protocols.