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CRC Press eBooks

Phase Retrieval in Optical Cryptography

Naveen Kumar Nishchal, Areeba Fatima

Published Dec 7, 2018• 0 citations
Publisher

Abstract

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.

DOI
10.1201/9780429435461-5

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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.
The security of the encryption and verification techniques with significant output images is examined by a known-plaintext attack. We introduce an iterative phase-retrieval algorithm based on multiple intensity measurements to heuristically estimate the phase key in the Fourier domain by several plaintext-cyphertext pairs. We obtain correlation output images with very low error by correlating the estimated key with corresponding random phase masks. Our studies show that the convergence behavior of this algorithm sensitively depends on the starting point. We also demonstrate that this algorithm can be used to attack the double random phase encoding technique.
In this paper, the security of the cryptosystem based on phase-truncation Fourier transform (PTFT) and Gerchberg-Saxton (G-S) algorithm is analyzed. In this cryptosystem, the phase key generated using phase-truncated (PT) operation is bonded with the phase key generated in G-S algorithm to form the first private key, which improves the complexity of the first private key. In addition, since the second private key is generated using the G-S algorithm, the number of known constraints decreases compared to the traditional PTFT-based cryptosystem, which will lead the non-convergence of special attacks. However, it has been found that two private keys generated in the cryptosystem based on PTFT and G-S algorithm are related to one phase key generated in the G-S algorithm, which provides an additional constraint to retrieve the other private key when one private key is disclosed. Based on this analysis, two iterative processes with different constraints are proposed to crack the cryptosystem based on PTFT and G-S algorithm. This is the first time to report the silhouette problem existing in the cryptosystem based on PTFT and G-S algorithm. Numerical simulations are carried out to validate the feasibility and effectiveness of our analysis and proposed iterative processes.
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.
As a typical technology for optical encryption, phase retrieval algorithms have been widely used in optical information encryption and authentication systems. This paper presents three applications of two-dimensional (2D) phase retrieval for optical encryption and authentication: first, a hierarchical image encryption system, by which multiple images can be hidden into cascaded multiple phase masks; second, a multilevel image authentication system, which combines (t, n) threshold secret sharing (both t and n are positive integers, and t ≤ n ) and phase retrieval, and provides both high-level and low-level authentication; and finally, a hierarchical multilevel authentication system that combines the secret sharing scheme based on basic vector operations and the phase retrieval, by which more certification images can be encoded into multiple cascaded phase masks of different hierarchical levels. These three phase retrieval algorithms can effectively illustrate phase-retrieval-based optical information security. The principles and features of each phase-retrieval-based optical security method are analyzed and discussed. It is hoped that this review will illustrate the current development of phase retrieval algorithms for optical information security and will also shed light on the future development of phase retrieval algorithms for optical information security.
We report a simultaneous image compression and encryption scheme based on solving a typical optical inverse problem. The secret images to be processed are multiplexed as the input intensities of a cascaded diffractive optical system. At the output plane, a compressed complex-valued data with a lot fewer measurements can be obtained by utilizing error-reduction phase retrieval algorithm. The magnitude of the output image can serve as the final ciphertext while its phase serves as the decryption key. Therefore the compression and encryption are simultaneously completed without additional encoding and filtering operations. The proposed strategy can be straightforwardly applied to the existing optical security systems that involve diffraction and interference. Numerical simulations are performed to demonstrate the validity and security of the proposal.