A novel exponential one-dimensional chaotic map enhancer and its application in an image encryption scheme using modified ZigZag transform

The rapid development of Internet communication technology requires more secure and effective chaotic map to encrypt and protect digital images. The common approach is to combine one-dimensional chaotic map with sines or cosines. However many existing sine or cosine type 1D chaotic map present the safety risk of lacking chaotic performance when the control parameter approaches zero. To address this issue, in this paper, we propose a one-dimensional exponential chaotic map enhancer (called 1D-ECE) by combining the exponential factor eμ. The experimental results suggest that proposed 1D-ECE solves the problem of insufficient chaotic performance when the control parameter is close to zero in cosine type chaotic amplifier, and better improve the randomness of input chaotic maps. Next, we have designed a modified ZigZag transform (called BNIZ-transform), which performs ZigZag transform on the adaptive indexes of the matrix elements after blocking and flipping at the bit-level, and then the columns of the matrix are permutated at the pixel level according to the chaotic sequence. Proposed BNIZ-transform not only transforms non-square matrices, but also enables simultaneous confusion and diffusion. Finally, to demonstrate that the proposed 1D-ECE and BNIZ-transform can be applied for cryptographic purposes, we propose an image encryption scheme including 1D-ECE and BNIZ-transform. The simulation results indicate that our proposed scheme is highly secure and can resist chosen plaintext attacks.