One-to-one mapping matrix

摘要

The one-to-one mapping matrix is presented. This paper defines a new matrix “one-to-one mapping matrix”. The new matrix can execute a “path change”. When we input a column vector and define the matrix elements by 1 (change) or 0 (not change), the output column vector will be determined easily by some simple rules. Moreover, the inversion of this matrix is so easy. What we have to do is to rewrite the row vector in this matrix by inversion. In other words, we just have to substitute row 1 by row n, row 2 by row n − 1, … ,  row n by row 1, and so on. Therefore, the one-to-one mapping matrix can be used to encode and decode our secret data.