Mathematicians Encrypt Images Using Mathematics of Sudoku 27-07-2012

The number-placement puzzle, Sudoku, consists of a 9 x 9 grid which must be filled using the digits 1 to 9. 

However, there are several additional constraints. Each digit can only appear once in each column, once in each row and once in each of the nine 3 x 3 blocks that make up the grid. A Soduko solution grid is shown below. Players are given a number of digits from the solution to get the game started. 

Sudoku has thrown up a number of interesting challenges for mathematicians. Earlier this year, for example, we looked at how mathematicians had solved the 'minimum Sudoku problem' to find the smallest number of clues that leads to a unique solution (answer, 17).  

Today, Yue Wu at Tufts University in Medford and a couple of buddies use Sudoku to tackle a different problem--how to encrypt images before sending them. 

These guys say that the special properties of Sudoku grids lead to an entirely new type of matrix mathematics that they've exploited to scramble images. 

First, a little background about matrices. A matrix is simply a rectangular array of numbers. Each element in the array is uniquely identified by a grid reference--its column and row number.

But Wu and co say it is possible to identify elements in an array in other ways if you think of it as a Sudoku grid. In that case, each element contains a digit from 1 to 9 that satisfies the rules of Sudoku. In other words, in addition to the row and column, each element also has a digit.

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