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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Space bandwidth considerations for optical encryption systems

Bryan M. Hennelly, John T. Sheridan

Published Oct 22, 2004• 1 citation
Publisher

Abstract

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.

DOI
10.1117/12.560486

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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 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.
Optical systems as information processing systems have become quite impressive recently in optical image encryption and watermarking. Benefits of optical systems over the electronic counterparts are that optical processing provides the maximum number of degrees of freedom, and that optical encryption is ideal for information stored in holographic media. Various schemes have been proposed in the last decade. In this article, we review the recent progress and patents in this field, and point out some challenges that might lead to practical optical information security systems Keywords: Double random phase encoding, holography, information security, Optical encryption, phase retrieval, Optical systems, multidimensional information s, spatial coherence, polarization, Optical image encryption, cryptosystem, discrete fractional fourier transform, encoding technique, micro-optics system, decryption method
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.
A new optical security system for image encryption based on a fractional joint transform correlator and nonlinear filtering is proposed.The position of the lens in the proposed optical encryption setup can be chosen, so that an additional key is introduced in the security system.The distributions at the input and output planes of the encryption system are related by a fractional Fourier transform (FrFT) at a given fractional order that is defined, among other parameters, by the focal length and the position of the lens in the setup; this fractional order acts as an additional key of the security system.The optical intensity of the complex distribution in the fractional Fourier domain (output plane) is captured by a CCD camera.The nonlinearity introduced in the last step of the encryption process, maintains the encrypted function as a real-valued function.The security system proposed in this work is an generalization of the encryption system based on a conventional joint transform correlator (JTC), from the Fourier domain to the fractional Fourier domain.Additional advantages of the proposed system are: new degrees of freedom for the optical setup, alleviated alignment requirement, and the introduction of an additional key (the fractional order of the FrFT) that improves security.Numerical simulations verify the validity of this new optical security system.
A technique that combines the high speed and the high security of optical encryption with the advantages of electronic transmission, storage, and decryption is introduced. Digital phase-shifting interferometry is used for efficient recording of phase and amplitude information with an intensity recording device. The encryption is performed by use of two random phase codes, one in the object plane and another in the Fresnel domain, providing high security in the encrypted image and a key with many degrees of freedom. We describe how our technique can be adapted to encrypt either the Fraunhofer or the Fresnel diffraction pattern of the input. Electronic decryption can be performed with a one-step fast Fourier transform reconstruction procedure. Experimental results for both systems including a lensless setup are shown.