hypnosec writes: Sudoku puzzles, solved the world over by millions of users every day, have managed to grab attention of mathematicians allowing them to use the underlying mathematics as a means for scrambling or encrypting images. Yue Wu at Tufts University in Medford along with a couple of friends has used Sudoku’s 9x9 grid to formulate a completely new type of matrix mathematics. For readers who are not so mathematics savvy, a matrix is a rectangular array of numbers wherein each element can uniquely identified by its row and column number – in other words, its grid reference. As Sudoku is the reference for new technique, according to Wu and co it is possible to identify elements in an array such that each of the elements contains a digit from 1 to 9 and that it satisfies the rules of Sudoku. This means that each element can now be identified by a row reference, a column reference and a digit. According to the team there are a total of six different ways of representing each element according to Wu. Through the use of simple mathematical functions [PDF], the co-ordinates in one system can be converted to that of the other. When we consider encryption, these simple conversion functions are the key to scrambling images. So, how to go about it? One can start with an image made up of 9x9 pixels. Next, superimpose a Sudoku solution onto this grid such that each of the pixels can now be represented by the new coordinate systems. Now using any one of the conversion functions swap the position of pixels. This will effectively scramble the image.
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