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Imaging and Applied Optics

Single arm opto-digital JTC cryptosystem based on a phase retrieval algorithm

Carlos Vargas-Castrillón, Alejandro Velez-Zea, John Fredy Barrera

Published Jan 1, 2023• 0 citations
Publisher

Abstract

We present an opto-digital JTC cryptosystem with no interferometric record of the encryption key. It is based on a modified Gerchberg-Saxton algorithm that use two outputs to recover the encryption key digitally.
DOI
10.1364/dh.2023.htu3c.4

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This chapter discusses some of the applications of algorithmic phase retrieval in the field of optical security. There are various iterative phase retrievals algorithms with different rates of convergence and with different requirement of constraints. The chapter describes three major phase retrieval algorithms that have been widely used in optical cryptography. There are: Gerchberg-Saxton algorithm, Error Reduction Algorithm and Hybrid Input-Output Algorithm. Various optical cryptosystems have been proposed in which the decryption or the choice of the random phase masks rely on the method of phase retrieval. Phase functions are obtained in similar fashion for all images. For wavelength multiplexing, different wavelength values for each image are used while implementing the Fresnel transform. As majority of optical cryptosystems are constructed using optical transforms, phase retrieval becomes relevant in these cases to formulate attack algorithms. The chapter shows that the phase retrieval techniques play an important role in the cryptanalysis of optical cryptosystems.
We propose a novel nonlinear image-encryption scheme based on a Gerchberg-Saxton (G-S) phase-retrieval algorithm in the Fresnel transform domain. The decryption process can be performed using conventional double random phase encoding (DRPE) architecture. The encryption is realized by applying G-S phase-retrieval algorithm twice, which generates two asymmetric keys from intermediate phases. The asymmetric keys are generated in such a way that decryption is possible optically with a conventional DRPE method. Due to the asymmetric nature of the keys, the proposed encryption process is nonlinear and offers enhanced security. The cryptanalysis has been carried out, which proves the robustness of proposed scheme against known-plaintext, chosen-plaintext, and special attacks. A simple optical setup for decryption has also been suggested. Results of computer simulation support the idea of the proposed cryptosystem.
A ciphertext-only attack (COA) on a joint transform correlator (JTC) encryption system is proposed. From the perspective view of optical cryptanalysis, we find out that the issue to be solved in the COA scheme could be transferred into a phase retrieval problem with single intensity measurement. And in this paper, the hybrid input-output (HIO) algorithm is employed to handle this issue with the help of an inartificial signal domain support and a given frequency domain constraint. Meanwhile, we provide a set of numerical simulations to demonstrate the validity and feasibility of the presented method.