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Optics Letters

Optical encryption with protection against Dirac delta and plain signal attacks

Konstantinos Falaggis, Ana Hiza Ramirez-Andrade, José Gabriel Gaxiola Luna, C. Ojeda, Rosario Porras-Aguilar

Published Oct 7, 2016• 17 citations
Publisher

Abstract

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.

DOI
10.1364/ol.41.004787

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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) systems are prone to plain signal and Dirac delta attacks. A recently proposed modular arithmetic based DRPE system has been shown to mitigate this significant weakness, by introducing a time-varying impulse response that is unknown to the receiver. This prevents the attacker characterizing the DRPE system, even if the attacker has access to the encryption unit. In this work, we show that when using specific decryption techniques that are borrowed from the area of Multi-wavelength interferometry, the amount of time-varying noise can be arbitrarily high, provided there is a correlation in the fractional ratios. Simulations shows that the generated noise-like encrypted images have an entropy is near the theoretical limit.
In this paper, we analyze the security of the classical double random phase encoding (DRPE) technique in Fourier domain, as well as its extended schemes in Fresnel and fractional Fourier domains. These schemes are resistant to bruteforce attacks, for their large key spaces. However, due to the linearity property of their encryption transformations, they are vulnerable to other attacks, such as chosen-plaintext attack and known-plaintext attack. We successfully break each of the three encryption schemes with the help of a certain quantity of plaintext-ciphertext pairs. Each attack is validated by computer simulations. The cryptanalysis indicates that, to minimize the risks, it is recommendable to introduce nonlinear operations to optical encryption systems.
The double random phase encoding (DRPE) image encryption method has garnered significant attention in color image processing and optical encryption thanks to its R, G, and B parallel encryption. However, DRPE-based color image encryption faces two challenges. Firstly, it disregards the correlation of R, G, and B, compromising the encrypted image’s robustness. Secondly, DRPE schemes relying on Discrete Fourier Transform (DFT) and Discrete Fractional Fourier Transform (DFRFT) are vulnerable to linear attacks, such as Known Plaintext Attack (KPA) and Chosen Plaintext Attack (CPA). Quantum walk is a powerful tool for modern cryptography, offering robust resistance to classical and quantum attacks. Therefore, this study presents an optical color image encryption algorithm that combines two-dimensional quantum walking (TDQW) with 24-bit plane permutation, dubbed OCT. This approach employs pseudo-random numbers generated by TDQW for phase modulation in DRPE and scrambles the encrypted image’s real and imaginary parts using the generalized Arnold transform. The 24-bit plane permutation helps reduce the R, G, and B correlation, while the generalized Arnold transform bolsters DRPE’s resistance to linear attacks. By incorporating TDQW, the key space is significantly expanded. The experimental results validate the effectiveness and security of the proposed method.
In this Letter, we propose an information encryption technique based on the theory of phase-space optics. We show that encoding the plaintext in phase space provides a higher level of security: first, the key-space is significantly enlarged. Second, it is immune to various known-plaintext (cyphertext) attacks to which the double-random phase encryption (DRPE) is vulnerable. Third, the bilinearity of phase-space distributions offers additional security. Theoretical analysis and numerical calculation results show that the proposed technique has significantly different responses to errors added to the cypheretext and the two phase keys in comparison to the classical DRPE.
Double random phase encryption (DRPE) is one of the well-known optical encryption techniques, and many techniques with DRPE have been developed for information security. However, most of these techniques may not solve the fundamental security problem caused by using fixed phase masks for DRPE. Therefore, in this paper, we propose a key phase mask updating scheme for DRPE to improve its security, where a spatial light modulator (SLM) is used to implement key phase mask updating. In the proposed scheme, updated key data are obtained by using previous image data and the first phase mask used in encryption. The SLM with the updated key is used as the second phase mask for encryption. We provide a detailed description of the method of encryption and decryption for a DRPE system using the proposed key updating scheme, and simulation results are also shown to verify that the proposed key updating scheme can enhance the security of the original DRPE.