Asymmetric Image Encryption Based on Cipher Matrices

In order to make robust encryption, a sparse matrix is defined whose inverse can be obtained easily. The self-invertible matrix and sparse matrix are used as private keys in the asymmetric key cryptosystem. Several methods of generating orthonormal matrices are proposed and used in combination with the sparse matrix for encryption of images. Exponentiation operation on matrices is introduced and used for image encryption. Finally, a two-stage encryption technique based on chaotic sequence followed by any one of the cipher matrix techniques is used to make encryption more robust. All the methods of encryption are validated using simulation technique. The methods highlighted in this book are samples of generalised Hill cipher cryptosystem. In these methods, encryption is simpler in comparison to the decryption process because in decryption, one has to obtain the inverse of a large matrix in GF(p) and GF(p**n). The exponentiation operation makes the cryptosystem more secured but the computational complexity increases.