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Optical Engineering

Random phase and jigsaw encryption in the Fresnel domain

Bryan M. Hennelly, John T. Sheridan

Published Oct 1, 2004• 63 citations
Publisher

Abstract

A number of methods have been recently proposed in the literature for the encryption of 2-D information using optical systems based on linear transforms, i.e., the Fourier (FT), the fractional Fourier (FRT), the Fresnel (FST), and the linear canonical transform (LCT). We propose and examine two encryption schemes using the Fresnel transform (FST) based on the use of random phase screens and random jigsaw transforms (JT). The strength and robustness of the level of encryption of the various techniques are examined with respect to blind decryption. These systems are compared with similar FRT- and LCT-based methods. Optical implementations are also discussed and sampling conditions are investigated in the context of the space-bandwidth product.

DOI
10.1117/1.1790502

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A number of methods have been recently proposed in the literature for the encryption of 2-D information using optical systems based on linear transforms, i.e., the Fourier (FT), the fractional Fourier (FRT), the Fresnel (FST), and the linear canonical transform (LCT). We propose and examine two encryption schemes using the Fresnel transform (FST) based on the use of random phase screens and random jigsaw transforms (JT). The strength and robustness of the level of encryption of the various techniques are examined with respect to blind decryption. These systems are compared with similar FRT- and LCT-based methods. Optical implementations are also discussed and sampling conditions are investigated in the context of the space-bandwidth product.
A number of method have been recently proposed in the literature for the encryption of 2-D information using optical systems based on the fractional Fourier fransform, FRT.In this paper a brief review of the methods proposed to date is presented.A measure of the strength/robustness of the level of encryption of the various techniques is proposed and a comparison is carried out between the methods.Optical implementations are discussed.Robustness of system with respect to misalignment and blind decryption are also discussed.
There has been considerable attention paid in recent literature to the use of optical signal processing in the field of image encryption and security. In most cases this involves the use of optical transforms based on quadratic phase systems (to implement the optical Fourier Transform (FT), the optical fractional Fourier Transform (FRT), the Fresnel transform (FST) and the most general Linear Canonical Transform (LCT). Random phase screens or random shifting.stages are applied after optically transforming to a new domain. The process may be repeated for deeper encryption. Each stage of the encryption process may change the position and spatial extension of the complex distribution on the plane normal to the propagation axis. Each stage may also change the frequency distribution of the signal. Therefore, the space bandwidth product (SBP), which is equal to the number of discrete samples that are required to fully represent our signal, will also change. In general the encrypted image is complex and recording must be carried out using a holographic material or using digital holographic methods. In each case it is desirable to know the spatial extension of the signal to be recorded, its position, and its spatial frequency extension. In this way we can determine which holographic materials will meet the criteria or which cameras will have a suitable number of pixels, greater than or equal to the space bandwidth product, if digital holography is used. We show how the matrices associated with the effect of a LCT on the Wigner Distribution Function (WDF) provide us with an efficient method for finding the position, spatial extent, spatial frequency extent and space bandwidth product of the encrypted signal. We review a number of methods, which have recently been proposed in the literature for the encryption of two-dimensional information using optical systems based on the FT, FRT, FST and LCT. We apply the new matrix technique to some of them.
A number of methods have recently been proposed in the literature for the encryption of two-dimensional information by use of optical systems based on the fractional Fourier transform. Typically, these methods require random phase screen keys for decrypting the data, which must be stored at the receiver and must be carefully aligned with the received encrypted data. A new technique based on a random shifting, or jigsaw, algorithm is proposed. This method does not require the use of phase keys. The image is encrypted by juxtaposition of sections of the image in fractional Fourier domains. The new method has been compared with existing methods and shows comparable or superior robustness to blind decryption. Optical implementation is discussed, and the sensitivity of the various encryption keys to blind decryption is examined.
Recently several optical encryption techniques have been proposed for two-dimensional data. These techniques use random phase masks, jigsaw transforms, digital signatures, and linear transforms like the Fourier transforms, the fractional Fourier transform and the Fresnel transform. The strength of these encryption techniques is dependent on the size of the key but is strongly limited by the security linked with the exchange of the secret key. We propose a new technique, based on the Diffie-Hellman protocol, in which the key can be exchanged with high security. Fractional Fourier transforms have been used for the secure key transfer. Results of computer simulation are presented to verify the proposed idea and analyse the robustness of the proposed technique.
We propose a new optical encryption technique using the fractional Fourier transform. In this method, the data are encrypted to a stationary white noise by two statistically independent random phase masks in fractional Fourier domains. To decrypt the data correctly, one needs to specify the fractional domains in which the input plane, encryption plane, and output planes exist, in addition to the key used for encryption. The use of an anamorphic fractional Fourier transform for the encryption of two-dimensional data is also discussed. We suggest an optical implementation of the proposed idea. Results of a numerical simulation to analyze the performance of the proposed method are presented.
Abstract We present an optical encryption approach based on the combination of fractal Fresnel lens (FFL) and fractional Fourier transform (FrFT). Our encryption approach is in fact a four-fold encryption scheme, including the random phase encoding produced by the Gerchberg–Saxton algorithm, a FFL, and two FrFTs. A FFL is composed of a Sierpinski carpet fractal plate and a Fresnel zone plate. In our encryption approach, the security is enhanced due to the more expandable key spaces and the use of FFL overcomes the alignment problem of the optical axis in optical system. Only using the perfectly matched parameters of the FFL and the FrFT, the plaintext can be recovered well. We present an image encryption algorithm that from the ciphertext we can get two original images by the FrFT with two different phase distribution keys, obtained by performing 100 iterations between the two plaintext and ciphertext, respectively. We test the sensitivity of our approach to various parameters such as the wavelength of light, the focal length of FFL, and the fractional orders of FrFT. Our approach can resist various attacks.