Unmodulated fully-phase and shifted-phase encoded encryption key using Arnold transform and joint fractional Fourier transform correlator

Abstract

We propose a nonlinear image encryption system using Arnold transform (ART) and a fully-phase encoded images as inputs to a nonzero-order joint transform correlator (JTC) in the fractional Fourier transform (FRFT) domain. Unlike other reported works, the fully-phase image along with two random-phase masks (RPMs) are introduced directly without linear phase modulation at the input plane of the JTC where the FRFT modulates this joint input image and produces the joint fractional power distribution (JFPD) at the output plane. It will be demonstrated that using modulating inputs in the optical setup makes the decryption scheme prone to error and leads to retrieving image failure. Further, a shifted-phase encoded key mask is applied in this proposal to achieve the non-zero order JFPD, which is adjusted by a nonlinear operation to guarantee a securely and high-quality retrieved ciphertext image. Furthermore, the proposed encryption scheme has four security keys: (i) two-random-phase masks, (ii) an ART frequency parameter, and (iii) a fractional order of the FRFT. It will be demonstrated that the decryption process is very sensitive to small variations of the ART frequency parameter, the fractional order of the FRFT, and the RPM. The cryptanalysis shows that the proposed encryption system is very invulnerable to Chosen plaintext (CPA), known plaintext (KPA), ciphertext only (COA) and brute force attacks. In addition, the robustness of the proposed scheme against noise and occlusion is presented using computer simulations.