Cryptography with chaos. (English) Zbl 0936.94013

Summary: It is possible to encrypt a message (a text composed by some alphabet) using the ergodic property of the simple low-dimensional and chaotic logistic equation. The basic idea is to encrypt each character of the message as the integer number of iterations performed in the logistic equation, in order to transfer the trajectory from an initial condition towards an \(\varepsilon\)-interval inside the logistic chaotic attractor.


94A60 Cryptography
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37N99 Applications of dynamical systems
Full Text: DOI


[1] Li, T. Y.; Yorke, J. A., Amer. Math. Monthly, 82, 985 (1975) · Zbl 0351.92021
[2] Pecora, L. M.; Carroll, T. L., Phys. Rev. Lett., 64, 821 (1990) · Zbl 0938.37019
[3] Hayes, S.; Grebogi, C.; Ott, E.; Mark, A., Phys. Rev. Lett., 73, 1781 (1994)
[4] Schweizer, J.; Kennedy, M. P., Phys. Rev. E, 52, 4865 (1995)
[5] Gligoroski, D.; Dimovski, D.; Kocarev, L.; Urumov, V.; Chua, L. O., Int. J. Bifurcation Chaos, 6, 2119 (1996) · Zbl 1298.70037
[6] Menezes, A. J.; van Oorschot, P. C.; Vanstone, S. A., (Handbook of Appl. Cryptography (1996), CRC Press: CRC Press New York)
[7] Ott, E., (Chaos in Dynamical Systems (1993), Cambridge University Press: Cambridge University Press New York) · Zbl 0792.58014
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.