K-Potent Matrices-Construction and Applications in Digital Image Encryption

A k -potent matrix is any matrix A , the k th power of which is a linear combination of the identity matrix and A , for example, unipotent, idempotent, and involutary matrices are special k -potent matrices. Such matrices have values in applications to digital image encryption. In order to achieve lossless image decryption, all arithmetic operations are restricted over the integer field. Therefore, algorithms are sought to construct integral k -potent matrices. It turns out that the unique eigenstructure of these matrices provides the key for constructing k -potent matrices systematically. In this paper, we explore the spectral properties of k -potent matrices and applications to digital image encryption.