Public channel cryptography: Chaos synchronization and Hilbert's tenth problem: Chaos synchronization and Hilbert's tenth problem

Ido Kanter, Evi Kopelowitz, Wolfgang Kinzel

Research output: Contribution to journalArticlepeer-review

60 Scopus citations

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 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. © 2008 The American Physical Society.
Original languageEnglish
Article number084102
JournalPhysical Review Letters
Volume101
Issue number8
DOIs
StatePublished - 22 Aug 2008

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