TY - JOUR

T1 - Public channel cryptography: Chaos synchronization and Hilbert's tenth problem

T2 - Chaos synchronization and Hilbert's tenth problem

AU - Kanter, Ido

AU - Kopelowitz, Evi

AU - Kinzel, Wolfgang

N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.

PY - 2008/8/22

Y1 - 2008/8/22

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=50249124821&partnerID=8YFLogxK

UR - https://scholar.google.co.il/scholar?q=Public+Channel+Cryptography%3A+Chaos+Synchronization+and+Hilbert%27s+Tenth+Problem&btnG=&hl=en&as_sdt=0%2C5

U2 - 10.1103/PhysRevLett.101.084102

DO - 10.1103/PhysRevLett.101.084102

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C2 - 18764616

SN - 0031-9007

VL - 101

JO - Physical Review Letters

JF - Physical Review Letters

IS - 8

M1 - 084102

ER -