Three-dimensional multidepth object authentication using partial fractional Fourier spectrum and phase-retrieval method

•Partial 3D object is recovered from an FrFT sub-block by a phase retrieval method.•A novel field function is devised to increase key space of position keys.•Lateral spatial positions are introduced as additional private keys.•3D Plaintext can be authenticated from a size-adjustable 2D ciphertext. In this paper, a novel scheme for multidepth three dimensional (3D) object authentication is presented based on partial fractional Fourier transform spectrum (FrFT) and phase retrieval technique. An inverse layer-based Fresnel transform (FT) is utilized to covert an original 3D object into a two-dimensional (2D) interim image whose phase and amplitude components are then merged in a random complex-valued field distribution, respectively. The random field distribution is further processed by an optical FrFT, resulting in an intensity spectrum where a sub-block area is randomly selected as ciphertext and recorded by a charged couple device (CCD). Simulation results show that partial information of the 3D object can be retrieved from a size-adjustable 2D FrFT spectrum by using a modified iterative retrieval method in FrFT domain with correct keys. Via this design, lateral position of the ciphertext and the merged location of the 2D interim image are introduced as additional keys. Consequently, the proposal achieve more design freedom and key space against potential attacks. The designed complex-valued random field distribution contains the main keys of the proposed scheme. Moreover, the introduction of this field distribution can further increase the dimension degree of position keys. The simulation results validate the feasibility and effectiveness of the proposed scheme.