Application of a Hyperbolic Tangent Chaotic Map to Random Bit Generation and Image Encryption

In this paper, a two-parameter one-dimensional chaotic map with hyperbolic tangent and two nested sinusoidal terms is proposed. The reported map exhibits rich chaotic behavior including such phenomena as the period-doubling route to chaos, crisis, and antimonotonicity appearing. The proposed map is applied for the pseudo-random bit generation and image encryption. To generate bit sequences, a simple rule is used. The generated sequences are verified using NIST statistical tests and cross-correlation analysis. Image encryption is performed using two rounds of shuffling of image pixels and XOR operation. We explicitly show the suitability of the proposed algorithm through histogram, correlation, and entropy analysis for the sample grayscale image.