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Applied Optics

Compressive sensing based robust multispectral double-image encryption

Nitin Rawat, Byoung‐Ho Kim, Inbarasan Muniraj, Guohai Situ, Byung‐Geun Lee

Published Feb 26, 2015• 61 citations
Publisher

Abstract

We demonstrate a multispectral double-image-based cryptosystem that exploits only a tiny number of random white noise samples for proper decryption. Primarily, one of the two downsampled images is converted into the phase function after being shuffled by Arnold transform (AT), while the other image is modulated as an amplitude-based image after AT. Consecutively, a full double-image encryption can be achieved by employing classical double random phase encryption (DRPE) technique in the fractional Fourier transform domain with corresponding fractional orders. In this study, the encrypted complex data is randomly sampled via compressive sensing (CS) framework by which only 25% of the sparse white noise samples are being reserved to realize decryption with zero or small errors. As a consequence, together with correct phase keys, fractional orders and proper inverse AT operators, lpminimization must be utilized to decrypt the original information. Thus, in addition to the perfect image reconstruction, the proposed cryptosystem provides an additional layer of security to the conventional DRPE system. Both the mathematical and numerical simulations were carried out to verify the feasibility as well as the robustness of the proposed system. The simulation results are presented in order to demonstrate the effectiveness of the proposed system. To the best of our knowledge, this is the first report on integrating CS with encrypted complex samples for information security.

DOI
10.1364/ao.54.001782

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We demonstrate a multispectral double-image-based cryptosystem that exploits only a tiny number of random white noise samples for proper decryption. Primarily, one of the two downsampled images is converted into the phase function after being shuffled by Arnold transform (AT), while the other image is modulated as an amplitude-based image after AT. Consecutively, a full double-image encryption can be achieved by employing classical double random phase encryption (DRPE) technique in the fractional Fourier transform domain with corresponding fractional orders. In this study, the encrypted complex data is randomly sampled via compressive sensing (CS) framework by which only 25% of the sparse white noise samples are being reserved to realize decryption with zero or small errors. As a consequence, together with correct phase keys, fractional orders and proper inverse AT operators, lpminimization must be utilized to decrypt the original information. Thus, in addition to the perfect image reconstruction, the proposed cryptosystem provides an additional layer of security to the conventional DRPE system. Both the mathematical and numerical simulations were carried out to verify the feasibility as well as the robustness of the proposed system. The simulation results are presented in order to demonstrate the effectiveness of the proposed system. To the best of our knowledge, this is the first report on integrating CS with encrypted complex samples for information security.
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In order to ensure the secure and effective transmission of image information, a new method of optical image encryption using the multimode fiber (MMF) specklegram based compressive sensing combined with the double random phase encoding (DRPE) is proposed in this paper. The specklegrams obtained from the facet of the multimode fiber are used as the measurement matrix of compressive sensing (CS), and the compression and the first-stage encryption of the image are completed by compressive sensing, in which the specklegram also functions as the first secret key. Then, the second-stage encryption is implemented by using the double random phase encoding technology, in which the random phase mask acts as the second secret key. All of the specklegrams used in this paper are obtained from the facet of a 5 m-long and 105-μm-diameter-MMF and offset launching technique. Then the fiber specklegrams are proposed in several steps to provide the measurement matrix in CS. By performing an encryption and decryption test on a standard Lena image of 256 × 256 size, it is found that the decrypted image and the original image are visually consistent, and the encryption is also realized in the process of compression, which indicates the method proposed in this paper is feasible. Furthermore, the comparison studies of the performances of specklegram based measurement matrix and some classic measurement matrices show that the decrypted image quality using the specklegram matrix is better. And at the same time, comparing with the high hardware implementation complexity and high cost of other measurement matrices, specklegram based matrix can be easily realized by simple optical device, and the corresponding secret key can be easily changed by the working wavelength, which is helpful for enlarging the secret key space. It is further proved that the encryption method be able to effectively resist the statistical analysis attacks, cropping attacks and noise interference, and also have high sensitivity to the secret key, which shows good robustness and high security. Therefore, the image encryption method combined with the specklegram matrix based compression sensing with the optical DRPE can obtain good encryption effect and has a great secret key space, which may provide a good candidate scheme for the pure optical realization of image encryption.
An image compression-encryption scheme utilizing the combination of fiber specklegram-based compressive sensing (CS) and double random phase encoding (DRPE) was demonstrated. The original image is compressed and encrypted by CS and then re-encrypted by DRPE. The measurement matrices for CS are constructed from multimode fiber specklegrams resulting from modes excitation and interference, which show better performance compared with those based on Gaussian random variables. Since fiber specklegrams have strong dependence on configuration, such measurement matrix can be constructed either by one specklegram or by specklegrams from different launched wavelengths. The double-encrypted image demonstrated good safety and reliability in several common attacks and presented high key sensitivity, which indicates good performance of the proposed scheme.
An image compression and encryption method integrating compressive sensing (CS) and Detour Cylindrical-diffraction-based double Random-phase Encoding (DCRE) is proposed. The plaintext image is first compressed by CS and then encrypted by the DCRE algorithm. The existing integrated CS and double random phase encoding (DRPE) methods are known to be vulnerable to the plaintext attack and even ciphertext-only attack. The combination of CS and DCRE, however, will be free of the plaintext attack and ciphertext-only attack, free of phase retrieval attack and allows enlarged key space. Numerical simulation results demonstrate the effectiveness and flexibility of the proposed scheme.
A hybrid cryptosystem is proposed, in which one image is encrypted to two interferograms with the aid of double random-phase encoding (DRPE) and two-step phase-shifting interferometry (2-PSI), then three pairs of public–private keys are utilized to encode and decode the session keys (geometrical parameters, the second random-phase mask) and interferograms. In the stage of decryption, the ciphered image can be decrypted by wavefront reconstruction, inverse Fresnel diffraction, and real amplitude normalization. This approach can successfully solve the problem of key management and dispatch, resulting in increased security strength. The feasibility of the proposed cryptosystem and its robustness against some types of attack are verified and analyzed by computer simulations.