Image encryption based on chaotic maps

In this paper, it is shown how to adapt certain invertible chaotic two-dimensional maps on a torus or on a square to create new symmetric block encryption schemes. The schemes are especially useful for encryption of large amounts of data, such as digital images or electronic databases. 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 sensitivity and mixing properties with its continuous counterpart as long as the number of iterations remains small. It is shown that for the two-dimensional baker map the permutations behave as typical random permutations. The discretized map is further extended to three dimensions and composed with a simple diffusion mechanism. As a result, a block product encryption scheme is obtained. To encrypt an N x N image, the ciphering map is iteratively applied to the image. This paper is an extension of the work of Pichler and Scharinger [1, 2] who first introduced encryption schemes based on two-dimensional baker map.