Image encryption based on Kronecker product over finite fields and DNA operation

Abstract

This paper reports an image encryption algorithm based on a matrix of Kronecker products and a deoxyribonucleic acid (DNA) operation over finite fields. First, a plaintext image is mapped from pixel gray-levels to the finite field. Subsequently, the image pixels are scrambled and diffused simultaneously by the Kronecker-product matrix based on a permutation polynomial over finite fields. Finally, a DNA operation is carried out to obtain greater confusion and scrambling. A widespread of security analyses and experimental results show that the proposed algorithm is safe against several common attacks. Moreover, there were no rounding errors in computation over finite fields, thereby ensuring a strict lossless image encryption and decryption. Due to the intrinsic nonlinearity of the permutation polynomials in the finite field, the proposed image encryption system is nonlinear and can resist known-plaintext and chosen-plaintext attacks.