Optical image encryption based on phase retrieval combined with three-dimensional particle-like distribution

Abstract

We propose a new phase retrieval algorithm for optical image encryption in three-dimensional (3D) space. The two-dimensional (2D) plaintext is considered as a series of particles distributed in 3D space, and an iterative phase retrieval algorithm is developed to encrypt the series of particles into phase-only masks. The feasibility and effectiveness of the proposed method are demonstrated by a numerical experiment, and the advantages and security of the proposed optical cryptosystems are also analyzed and discussed.

A review of optical image encryption techniques

“…It involves using an iterative phase retrieval algorithm for decrypting the original image from the recorded diffraction patterns [67][68][69][70]. Furthermore, two dimensional optical encryption processing has been extended into a three dimensional spacebased encryption processing, where each pixel of the image is axially considered as one particle and phase-shifting digital holography technique is applied to the diffraction of all pixels in space (particles) [71][72][73][74]. In the context of cryptography and cryptoanalysis, both chosen-plaintext [60] and known-plaintext attack [75][76][77] on DRPE have been examined, as have several other attacking methods [78][79][80][81][82] and the key space of DRPE technique itself [83][84][85][86] has also been analysed.…”

Gyrator transform based double random phase encoding with sparse representation for information authentication

“…In recent years, researchers also developed optical encryption schemes in gyrator transform (GT) domains [6][7][8][9], especially after Liu et al addressed the numerical simulation difficulties of GT [10]. Some other techniques, such as discrete fractional random transform [11][12][13], phase retrieval [14,15], diffractive imaging [16], arbitrarily modulated beam [17] and many enhancements of DRPE [18][19][20], have also been employed to build optical encryption systems. Meanwhile, cryptanalysis of optical cryptosystems has also been achieved.…”

Optical encryption based on 3-D sphere and phase retrieval in gyrator transform domain

“…The constraint applied in the plaintext plane can be described by [11]- [13] ( , ) ( , ) ( , ) ( , )…”

“…where ( , ) O   denotes the plaintext, and  denotes a ratio between the summations of calculated and desired outputs (i.e., the plaintext) within a signal window [11], [13]. The signal window is defined as a specific transverse area which only contains the particle i, and all the particles are sequentially processed by using the phase retrieval algorithm based on Eqs.…”

“…(2). After all the particles are processed within one iterative operation, an iterative error is calculated between the calculated and desired outputs for a specific particle [11]. When iterative error is larger than a preset threshold, the updated phase-only mask ( , ) …”