Sudoku Associated Two Dimensional Bijections for Image Scrambling

Sudoku puzzles are now popular among people in many countries across the world with simple constraints that no repeated digits in each row, each column, or each block. In this paper, we demonstrate that the Sudoku configuration provides us a new alternative way of matrix element representation by using block-grid pair besides the conventional row-column pair. Moreover, we discover six more matrix element representations by using row-digit pair, digit-row pair, column-digit pair, digit-column pair, block-digit pair, and digit-block pair associated with a Sudoku matrix. These parametric Sudoku associated matrix element representations not only allow us to denote matrix elements in secret ways, but also provide us new parametric two-dimensional bijective mappings. We study these two-dimensional bijections in the problem of image scrambling and propose a simple but effective Sudoku Associated Image Scrambler only using Sudoku associated two dimensional bijections for image scrambling without bandwidth expansion. Our simulation results over a wide collection of image types and contents demonstrate the effectiveness and robustness of the proposed method. Scrambler performance analysis with comparisons to peer algorithms under various investigation methods, including human visual inspections, gray degree of scrambling, autocorrelation coefficient of adjacent pixels, and key space and key sensitivities, suggest that the proposed method outperforms or at least reaches state-of-the-art. Similar scrambling ideas are also applicable to other digital data forms such as audio and video.