New image encryption combining fractional DCT via polynomial interpolation with dependent scrambling and diffusion

Based on the fractional discrete cosine transform(DCT) via polynomial interpolation(PI-Fr DCT) and the dependent scrambling and diffusion(DSD), an image encryption algorithm is proposed. Under certain conditions, the introduction of PI-Fr DCT reduces computational complexity compared with fractional DCT(Fr DCT). By using a sigmoid function, the encrypted results are limited within a range from 0 to 255. The real-valued output of PI-Fr DCT is beneficial to the storage, display and transmission of the cipher-text. During the stage of confusion and diffusion, the values of all PI-Fr DCT coefficients change simultaneously as their locations are replaced. DSD enhances the scrambling and diffusion level of encrypted images and provides nonlinearity to the encryption system. Simulation results demonstrate that the proposed encryption algorithm is feasible, effective and secure.