Sudoku Associated Two Dimensional Bijections for Image Scrambling
Yue Wu, Student Member, IEEE, Sos Agaian, Senior Member, IEEE, and Joseph P. Noonan, Life Member, IEEE,
arXiv:1207.5856v1 [cs.CR] 25 Jul 2012
Abstract Sudoku puzzles are now popular among people in many countries across the world with simple constraints thatno 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 ImageScrambler 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.
Index Terms Sudoku Matrix, Matrix Element Representation, Two Dimensional Bijection, Image Scrambling
YueWu and Joseph P. Noonan is with the Department of Electrical and Computer Engineering, Tufts University, Medford, MA 02155, United States; e-mail: email@example.com. Sos Agaian is with the Electrical and Computer Engineering, University of Texas at San Antonio, San Antonio, TX 78249, United States.
A PAPER DRAFT SUBMITTED TO IEEE TRANSACTIONS ON MULTIMEDIA
I. I NTRODUCTION In the newcentury, business news about conventional industries and companies keep reminding us how much impact the digital revolution bring to us and to the world. United States Postal Service is struggling hard to survive these days and have already closed hundreds of facilities and sites, because paper letters are not used as often as they were in the last century after email and other electroniccommunications dominates the way that people communicate with each other. Borders, an international book and music retailer once pioneered in the kind of large supermarket style bookstores, failed to survive under the impacts from online and e-books and has already bankrupted in the early of the year. Similar stories also happened to Eastman Kodak company, commonly known as Kodak, an Americanmultinational imaging and photographic equipment, materials and service company that once dominated the photographic ﬁlm industry for many years and invent and built the ﬁrst digital camera as early as in 1975 , but now was bankrupted due to its slowness in transitioning to digital photography. As emails, digital images, digital books and other digital data carriers play an important role in people’slife, the demand on the secure storage and transmission on digital data become a problem must be solved. Digital images, one typical type of two dimensional data, are considered to contain a huge amount of information, for example, a family photo might tell not only who are in this family and how they look like, but rough ages for each member and maybe their healthy conditions; a diagnosis CT image...