ANALYSIS OF IN-PLACE MATRIX ROTATION OF SQUARE MATRIX FOR INFORMATION SECURITY APPLICATIONS

Abstract

The concept of matrices was developed to represent complex data into understandable and formattable data. There is a huge number of applications in which matrices are used like classification and data size reduction used to store it. Matrices are widely used in most cryptographic algorithms. Every image can be represented as a matrix where each pixel value is stored as an element of a matrix. The rotation of the matrix defines that a matrix is rotated in the XY-plane to a certain angle concerning the x-axis about the origin. A rotation matrix is a transformation matrix in linear algebra that is used to make a rotation in Euclidean space. The rotation of the matrix includes transformation such that it requires additional memory for a new transformed value. This paper describes the in-place matrix rotation of square matrix using 45° rotation of information. In-place algorithm alters the input without requiring additional memory. A little amount of additional memory could be needed for the implementation of an in-place algorithm. However, the amount of memory required should be consistent and not dependent on the size of the input. With the help of In-place Matrix Rotation (IMR) of the complementary angle, the IMR of 45° is proved. In IMR, the elements change their positions, but the elements remain the same in the matrix. Using IMR is the matrix dimensions are changed with the center fixed to a particular position just by rotating the matrix not transforming the position.