Four-image encryption method based on spectrum truncation, chaos and the MODFrFT

With the help of spectrum truncation, an encryption and decryption method for four images is proposed based on chaos and the multiple-order discrete fractional Fourier transform (MODFrFT). The spectra of four images gotten by the discrete cosine transform (DCT) are truncated and combined into a single array sequentially encrypted by the MODFrFT. The resulting performance is better than other similar algorithms in literature where the spectrum truncation is done in discrete Fourier transform(DFT) domain. Furthermore, the complex mode is introduced to reduce the data loss. The combined spectrum array is encoded with the MODFrFT twice and chaos is introduced to scramble the phases of complex matrix before each MODFrFT. The technology of rate-distortion control is introduced to balance the qualities of the decrypted images. Numerical simulations demonstrate the effectiveness and the security of the proposed four-image encryption algorithm.

► DCT is used to transform the image into DCT domain instead of DFT owing to the better energy concentrating ability.
► Spectrum cutting truncation is used in DCT domain to extract the lower frequency parts which are then combined to form a single array.
► Rate-distortion control is used to balance the qualities of the four decrypted images to enhance the average image quality.
► MODFrFT and chaos are used to disorder and diffuse images to be encrypted.