A Secret Key Cryptosystem by Iterating a Chaotic Map

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 547)


Chaos is introduced to cryptology. As an example of the applications, a secret key cryptosystem by iterating a one dimensional chaotic map is proposed. This system is based on the characteristics of chaos, which are sensitivity of parameters, sensitivity of initial points, and randomness of sequences obtained by iterating a chaotic map. A ciphertext is obtained by the iteration of a inverse chaotic map from an initial point, which denotes a plaintext. If the times of the iteration is large enough, the randomness of the encryption and the decryption function is so large that attackers cannot break this cryptosystem by statistic characteristics. In addition to the security of the statistical point, even if the cryptosystem is composed by a tent map, which is one of the simplest chaotic maps, setting a finite computation size avoids a ciphertext only attack. The most attractive point of the cryptosystem is that the cryptosystem is composed by only iterating a simple calculations though the information rate of the cryptosystem is about 0.5.


  1. [1]
    J. M. T. Thompson and H. B. Stewart: “Nonlinear Dynamics and Chaos”, John Wiley and Sons, Chichester, 1986.zbMATHGoogle Scholar
  2. [2]
    P. Collet and J. P. Eckmann: “Iterated Maps on the Interval as Dynamical Systems”, Birkhäuser, Boston, 1980.zbMATHGoogle Scholar
  3. [3]
    S. Oishi and H. Inoue: “Pseudo-Random Number Generators and Chaos”, Trans. IECE Japan, E65,9, pp.534–541 (Sept. 1982)Google Scholar
  4. [4]
    G. K. Bhattacharyya and R. A. Johnson: “Statistical Concepts and Methods”, John Wiley and Sons, Tronto, 1977.Google Scholar
  5. [5]
    T. Habutsu, Y. Nishio, I. Sasase, and S. Mori: “A Secret Key Cryptosystem Using a Chaotic Map”, Trans. IEICE Japan, E73,7, pp.1041–1044 (July 1990)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  1. 1.Department of Electrical EngineeringKeio UniversityYokohamaJapan

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