4.3.2. Histogram

The histogram of an image reflects the distribution of pixel levels. A natural image often has a histogram with certain irregular shapes, such as mountain peaks and valleys. A well-designed encryption scheme should break the original distribution of gray-levels and make the new distribution as even as possible. The histograms obtained by the MBPD are shown in Figure 6, where the test images' orders are the same as in Table 4.

**Figure 6.** Histograms of plain images and their corresponding cipher images. Each plain image is followed by its histogram, the corresponding cipher image, and its histogram.

From this figure, we can find that all the natural images (those except for Gray512 Bw512) appear irregular histograms. Since plain Gray512 and Bw512 have evenly 21 and 2 gray-levels, respectively, they only have 21 and 2 bars in the histograms. However, the distributions of the pixel values of the cipher images are so uniform that the tops of the bars in the histograms appear as horizontal lines, even for Gray512 and Bw512. The results reveal that the proposed MBPD can effectively break the distributions of cipher images and produce sufficiently uniform histograms.
