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Optics Letters

Optical image encryption by random shifting in fractional Fourier domains

Bryan M. Hennelly, John T. Sheridan

Published Feb 15, 2003• 426 citations
Publisher

Abstract

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.

DOI
10.1364/ol.28.000269

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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 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.
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.
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.
We present a new method to secure information based on digital optics in this paper. The input image to be encrypted is recorded as interferograms by use of two-step phase-shifting interferometry. Before transmitting through communication channels, the interferograms are encrypted as phase codes in fractional Fourier domain by using a computer generated random phase mask. The set of fractional orders and the computer generated random phase mask form the keys to the encrypted data. With the phase shifts generated in the recording process, the original image can be retrieved from the correct decrypted interferograms successfully. Computer simulations are presented to prove its validity.
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.
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. The Diffie-Hellman protocol allows two users to exchange a secret key over an insecure channel without any prior secrets. 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.