  Haar wavelet is one of the best mathematical tools in image cryptography and
analysis. Because of the specific structure, this wavelet has the ability which
is combined with other mathematical tools such as chaotic maps. The rational
order chaotic maps are one of clusters of chaotic maps which their
deterministic behaviors have high sensitivity. In this paper, we propose a
novel method of gradient Haar wavelet transform for image encryption. This
method use linearity properties of the scaling function of the gradient Haar
wavelet and deterministic behaviors of rational order chaotic maps in order to
generate encrypted images with high security factor. The security of the
encrypted images is evaluated by the key space analysis, the correlation
coefficient analysis, and differential attack. The method could be used in
other fields such as image and signal processing.
