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Cryptography based on chaotic random maps with position dependent weighting probabilities

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  • Behnia, S.
  • Akhshani, A.
  • Ahadpour, S.
  • Akhavan, A.
  • Mahmodi, H.

Abstract

Chaotic cryptology has been widely investigated recently. A common feature in the most recent developments of chaotic cryptosystems is the use of a single dynamical rule in the encoding–decoding process. The main objective of this paper is to provide a set of chaotic systems instead of a single one for cryptography. In this paper, we introduce a chaotic cryptosystem based on the symbolic dynamics of random maps with position dependent weighting probabilities. The random maps model is a deterministic dynamical system in a finite phase space with n points. The maps that establish the dynamics of the system are chosen randomly for every point. The essential idea of this paper is that, given two dynamical systems that behave in a certain way, it is possible to combine them (by composing) into a new dynamical system. This dynamically composed system behaves in a completely different way compared to the constituent systems. The proposed scheme exploits the symbolic dynamics of a set of chaotic maps in order to encode the binary information. The performance of the new cryptosystem based on chaotic dynamical systems properties is examined. Both theoretical and experimental results demonstrate that the proposed algorithm using symbolic dynamics achieves the optimal security criteria.

Suggested Citation

  • Behnia, S. & Akhshani, A. & Ahadpour, S. & Akhavan, A. & Mahmodi, H., 2009. "Cryptography based on chaotic random maps with position dependent weighting probabilities," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 362-369.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:1:p:362-369
    DOI: 10.1016/j.chaos.2007.07.070
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    References listed on IDEAS

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    1. Lian, Shiguo & Sun, Jinsheng & Wang, Zhiquan, 2005. "A block cipher based on a suitable use of the chaotic standard map," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 117-129.
    2. Behnia, S. & Akhshani, A. & Mahmodi, H. & Akhavan, A., 2008. "A novel algorithm for image encryption based on mixture of chaotic maps," Chaos, Solitons & Fractals, Elsevier, vol. 35(2), pages 408-419.
    3. Mi, Bo & Liao, Xiaofeng & Chen, Yong, 2008. "A novel chaotic encryption scheme based on arithmetic coding," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1523-1531.
    4. Lian, Shiguo & Sun, Jinsheng & Wang, Jinwei & Wang, Zhiquan, 2007. "A chaotic stream cipher and the usage in video protection," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 851-859.
    5. Wei, Jun & Liao, Xiaofeng & Wong, Kwok-wo & Xiang, Tao, 2006. "A new chaotic cryptosystem," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1143-1152.
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