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Applied Optics

Optical encryption based on double random-phase encoding: secure versus unsecure variants

Ana Hiza Ramirez-Andrade, Rosario Porras-Aguilar, Konstantinos Falaggis

Published Feb 3, 2020• 6 citations
Publisher

Abstract

A smart brute-force double random-phase encoding attack is presented that takes advantage of an unreported vulnerability: the smoothness of mean squared error (MSE) and correlation coefficient (CC) curves in a key-sensitivity analysis. The vulnerability reported here is made visible in a key-sensitivity analysis. It is shown that a modular arithmetic pre-coding provides significant robustness against this form of attack because the pre-coding creates a highly nonlinear, highly oscillatory MSE and CC curve in the key space. Knowledge of this new vulnerability and how to prevent this in the first place provides a better understanding of the robustness of various double random-phase encoding designs.

DOI
10.1364/ao.383506

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A smart brute-force double random-phase encoding attack is presented that takes advantage of an unreported vulnerability: the smoothness of mean squared error (MSE) and correlation coefficient (CC) curves in a key-sensitivity analysis. The vulnerability reported here is made visible in a key-sensitivity analysis. It is shown that a modular arithmetic pre-coding provides significant robustness against this form of attack because the pre-coding creates a highly nonlinear, highly oscillatory MSE and CC curve in the key space. Knowledge of this new vulnerability and how to prevent this in the first place provides a better understanding of the robustness of various double random-phase encoding designs.
This paper analysis the security of the optical encryption scheme based on the classical double random phase encoding. We describe a known-plaintext attack which can be used to successfully access the encryption key with the pre-knowledge of only one arbiturary pair of known plaintext-ciphertext. A phase retrieval algorithm is employed in this attack. Computer simulations are made to demonstrate the effectiveness. The results show that even implementing only one round of iteration in the phase retrieval, an attacker can obtain a clear decoded plaintext (a gray-scale image) from an intercept ciphertext.
A fully phase image encryption technique which uses double random phase encoding method is presented. The encryption method can be implemented optically. Robustness of the fully phase encryption and amplitude based encryption in the presence of noise is investigated. Using computer simulations, mean squared error for the decrypted images are obtained. The fully phase based encryption is shown to be robust with respect to the additive noise added to the encrypted image in terms of the mean squared metric. Based on the tests conducted in this paper, the fully phase based encryption method shows better performance than the amplitude based encryption in terms of mean square error metric.
This Letter proposes an optical encryption technique that disguises the information with modular arithmetic concepts and time-varying noise components that are unknown to the receiver. Optical encryption systems that use these techniques produce a nondeterministic system response, as well as noise like image data that can easily be generated with ordinary spatial light modulators. The principle of this technique is demonstrated for the double random phase encoding (DRPE) method. The conventional DRPE method has major vulnerabilities for Dirac signal and plain signal attacks, making them impractical for secure encryption. It is shown that the proposed encryption technique provides a robustness against these types of attacks, allowing optical DRPE to be employed in secure encryptions. Moreover, applications of this Letter are not limited to DRPE alone but can also be adopted by other optical encryption techniques such as fractional Fourier transform and Fresnel-transform-based techniques.
Double random phase encoding (DRPE) is a classical optical symmetric-key encryption method. DRPE prevents the key length from being determined because of its redundancy between encryption and decryption, unlike digital symmetric-key cryptographies. In our study, we numerically analyzed the key length of DRPE based on key-space analysis. We estimated the key length of DRPE by calculating the inverse value of the cumulative probability of the normal distribution that was estimated from samples of DRPE and then discuss security against brute-force attacks.