Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Electronics

Optical Color Image Encryption Algorithm Based on Two-Dimensional Quantum Walking

Guohao Cui, Xiaoyi Zhou, Hao Wang, Wentao Hao, Anshun Zhou, Jianqiang Ma

Published May 22, 2024• 8 citations
Publisher

Abstract

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.

DOI
10.3390/electronics13112026

Related papers

Optical encryption with protection against Dirac delta and plain signal attacks

Konstantinos Falaggis, Ana Hiza Ramirez-Andrade, José Gabriel Gaxiola Luna +2 more

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.

Optics Letters•Oct 7, 2016•17 citations

Quantum image encryption based on hyper-chaotic system and double-random phase encoding

Lei Wu, Meiju Li, Jiyang Jia +1 more

In order to enhance the security of encrypted images, a new quantum image encryption algorithm is proposed. This algorithm combines Chen's hyper-chaotic system with Double-random Phase Encoding (DRPE). The pixel values of the original quantum image are diffused using DRPE, while the pixel positions are scrambled through Cyclic Translation (CT). The hyper-chaotic sequences generated by Chen's hyper-chaotic system control the scrambling and diffusion operations. Numerical simulations and theoretical analyses have shown that this algorithm is highly effective in resisting illegal attacks. The encrypted image generated by this algorithm exhibits lower pixel correlation and more evenly distributed histogram. Overall, the proposed algorithm represents a robust and secure approach for image encryption

International Conference on Advanced Algorithms and Signal Image Processing (AASIP)•Oct 10, 2023•2 citations

Image quality and security through nonlinear joint transform encryption

Juan M. Vilardy, Elisabet Pérez–Cabré, María Sagrario Millán

Joint-transform correlator (JTC) architecture presents some advantages, such as no requirement of interferometric recording of the phase distribution or complex conjugation of the key phase mask, in order to optically implement the well-known double random phase encryption (DRPE) method. In addition, a practical optical realization was proposed in a way that the whole information (primary image and two random phase masks) was easily introduced in the same input plane of the JTC system. However, poor image quality was obtained in the decryption stage. Cryptanalysis of JTC-based encryption systems demonstrated that they were vulnerable to certain intruder attacks, similarly to the original DRPE method. In this work, we review recent modifications of encryption algorithms based on JTC architecture that permit, on the one hand, to significantly increase the quality of the retrieved image after information decryption, and on the other hand, to achieve a high security level against a variety of system attacks. The modifications, which were firstly introduced in the Fourier-based JTC system, have been also adapted to be used in the Fresnel and Fractional Fourier domains as well as in the Gyrator domain. Nonlinear operations have been also introduced in multifactor encryption-authentication.

Workshop on Information Optics•Jul 1, 2016•1 citation

Optical cryptanalysis of DRPE-based encryption systems

Wan Qin, Wenqi He, Xiangfeng Meng +1 more

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.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Nov 4, 2009•6 citations

Vulnerability to known-plaintext attack of optical encryption schemes based on two fractional Fourier transform order keys and double random phase keys

W Qin, Xiang Peng

From the perspective of optical information security, we demonstrate that conventional phase retrieval algorithms, such as the Gerchberg–Saxton algorithm, can be still valid when extended from the Fourier transform domain into the fractional Fourier transform (FRFT) domain. Based on this extension, we propose a method of known-plaintext attack (KPA) on double random phase encoding in the fractional Fourier transform domain (DRPE-FRFT). With this attack, an opponent can access two encryption phase keys with the help of the phase retrieval algorithm in the FRFT domain, and meanwhile obtain the two FRFT order keys by using an exhaustive search. This indicates that the optical encryption scheme based on the DRPE-FRFT scheme is vulnerable to KPA due to the nature of the linearity of FRFT. The validity of this attack is verified by numerical simulations.

Journal of Optics A Pure and Applied Optics•Apr 20, 2009•94 citations

Review of Optical Cryptosystem for Gray Image and Color Image

Hang Chen, Camel Tanougast, Harry K. Ramenah +2 more

Optical information security is one of the most important research directions in information science and technology, especially in the copyright protection, confidential information transmission/storage and military remote sensing. Since double random phase encoding technology (DRPE) was proposed, optical image encryption technology has become the main topic of optical information security and it has been developed and studied deeply. Much significant research and investigation on optical image encryption have been presented based on DRPE or further optical operation, such as digital holography, and Fresnel transform, gyrator transform. In this paper, the optical encryption system for gray image and color image is reviewed.

IEEE International Conference on Information Systems and Computer Aided Education (ICISCAE)•Sep 1, 2019•1 citation
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.
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.
In order to enhance the security of encrypted images, a new quantum image encryption algorithm is proposed. This algorithm combines Chen's hyper-chaotic system with Double-random Phase Encoding (DRPE). The pixel values of the original quantum image are diffused using DRPE, while the pixel positions are scrambled through Cyclic Translation (CT). The hyper-chaotic sequences generated by Chen's hyper-chaotic system control the scrambling and diffusion operations. Numerical simulations and theoretical analyses have shown that this algorithm is highly effective in resisting illegal attacks. The encrypted image generated by this algorithm exhibits lower pixel correlation and more evenly distributed histogram. Overall, the proposed algorithm represents a robust and secure approach for image encryption
Joint-transform correlator (JTC) architecture presents some advantages, such as no requirement of interferometric recording of the phase distribution or complex conjugation of the key phase mask, in order to optically implement the well-known double random phase encryption (DRPE) method. In addition, a practical optical realization was proposed in a way that the whole information (primary image and two random phase masks) was easily introduced in the same input plane of the JTC system. However, poor image quality was obtained in the decryption stage. Cryptanalysis of JTC-based encryption systems demonstrated that they were vulnerable to certain intruder attacks, similarly to the original DRPE method. In this work, we review recent modifications of encryption algorithms based on JTC architecture that permit, on the one hand, to significantly increase the quality of the retrieved image after information decryption, and on the other hand, to achieve a high security level against a variety of system attacks. The modifications, which were firstly introduced in the Fourier-based JTC system, have been also adapted to be used in the Fresnel and Fractional Fourier domains as well as in the Gyrator domain. Nonlinear operations have been also introduced in multifactor encryption-authentication.
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.
From the perspective of optical information security, we demonstrate that conventional phase retrieval algorithms, such as the Gerchberg–Saxton algorithm, can be still valid when extended from the Fourier transform domain into the fractional Fourier transform (FRFT) domain. Based on this extension, we propose a method of known-plaintext attack (KPA) on double random phase encoding in the fractional Fourier transform domain (DRPE-FRFT). With this attack, an opponent can access two encryption phase keys with the help of the phase retrieval algorithm in the FRFT domain, and meanwhile obtain the two FRFT order keys by using an exhaustive search. This indicates that the optical encryption scheme based on the DRPE-FRFT scheme is vulnerable to KPA due to the nature of the linearity of FRFT. The validity of this attack is verified by numerical simulations.
Optical information security is one of the most important research directions in information science and technology, especially in the copyright protection, confidential information transmission/storage and military remote sensing. Since double random phase encoding technology (DRPE) was proposed, optical image encryption technology has become the main topic of optical information security and it has been developed and studied deeply. Much significant research and investigation on optical image encryption have been presented based on DRPE or further optical operation, such as digital holography, and Fresnel transform, gyrator transform. In this paper, the optical encryption system for gray image and color image is reviewed.