Orthonormal Matrices and Image Encryption

Standard matrix inversion algorithms take substantial amount of time to find the inverse of a large matrix. Therefore, large matrices can be used as public keys in asymmetric key cryptosystems. But the decryption algorithm of such a cryptosystem has a large time complexity as one or more matrix inversions has to be carried out. Orthonormal matrices are easily invertible and hence can be used as a part of a public key during encryption. In this paper, a new method of generating orthonormal matrices and an asymmetric image encryption technique based on these matrices is presented. In this technique, the public key is a product of an orthonormal matrix and another sparse matrix whose inverse can be found out easily. The inverse of the public key can be calculated in reduced number of operations with the help of private keys. The presented technique is analytically proved to be robust and has been tested with various images.