| Jiri Fridrich.
Symmetric Ciphers Based on Two-Dimensional Chaotic Maps, International Journal of Bifurcation and Chaos (IJBC) in Applied Sciences and Engineering.
Vol. 8 No. 6 1998.
[ZIP]
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ABSTRACT: In this paper, methods are shown how to adapt invertible twodimensional chaotic maps on a torus or on a square to create new symmetric block encryption schemes. A chaotic map is first generalized by introducing parameters and then discretized to a finite square lattice of points which represent pixels or some other data items. Although the discretized map is a permutation and thus cannot be chaotic, it shares certain properties with its continuous counterpart as long as the number of iterations remains small. The discretized map is further extended to threedimensions and composed with a simple diffusion mechanism. As a result, a symmetric block product encryption scheme is obtained. To encrypt an N × N image, the ciphering map is iteratively applied to the image. The construction of the cipher and its security is explained with the twodimensional baker map. It is shown that the permutations induced by the baker map behave as typical random permutations. Computer simulations indicate that the cipher has good diffusion properties with respect to the plaintext and the key. A nontraditional pseudorandom number generator based on the encryption scheme is described and studied. Examples of some other twodimensional chaotic maps are given and their suitability for secure encryption is discussed. The paper closes with a brief discussion of a possible relationship between discretized chaos and cryptosystems. Also available as MS Word 7.0 | ||||||||
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