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Journal of the Optical Society of America A

Fully phase encrypted image processor

Nasser Towghi, Bahram Javidi, Z. Luo

Published Aug 1, 1999• 229 citations
Publisher

Abstract

A fully phase image encryption technique that uses the double random-phase encoding method is presented. The performance of this fully phase encryption is compared with that of amplitude-based encryption in the presence of noise. Analytic bounds on the mean squared error for the decrypted images are obtained. The accuracy of the theoretical error bounds is confirmed by comparing them with the mean squared errors obtained by using numerical and statistical methods for actual images. Fully phase-based encryption shows better performance than amplitude-based encryption with respect to the mean-squared-error metric.

DOI
10.1364/josaa.16.001915

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A fully phase image encryption technique that uses the double random-phase encoding method is presented. The performance of this fully phase encryption is compared with that of amplitude-based encryption in the presence of noise. Analytic bounds on the mean squared error for the decrypted images are obtained. The accuracy of the theoretical error bounds is confirmed by comparing them with the mean squared errors obtained by using numerical and statistical methods for actual images. Fully phase-based encryption shows better performance than amplitude-based encryption with respect to the mean-squared-error metric.
A fully phase image encryption technique which uses double random phase encoding method is presented. The encryption method can be implemented optically. Robustness of the fully phase encryption and amplitude based encryption in the presence of noise is investigated. Using computer simulations, mean squared error for the decrypted images are obtained. The fully phase based encryption is shown to be robust with respect to the additive noise added to the encrypted image in terms of the mean squared metric. Based on the tests conducted in this paper, the fully phase based encryption method shows better performance than the amplitude based encryption in terms of mean square error metric.
The performance of fully phase- and amplitude-based encryption processors is analyzed. The effects of noise perturbations on the encrypted information are considered. A thresholding method of decryption that further reduces the mean-squared error (MSE) for the fully phase- and amplitude-based encryption processes is provided. The proposed thresholding scheme significantly improves the performance of fully phase- and amplitude-based encryption, as measured by the MSE metric. We obtain analytical MSE bounds when thresholding is used for both decryption methods, and we also present computer-simulation results. These results show that the fully phase-based method is more robust. We also give a formal proof of a conjecture about the decrypted distribution of distorted encrypted information. This allows the analytical bounds of the MSE to be extended to more general non-Gaussian, nonadditive, nonstationary distortions. Computer simulations support this extension.
We investigate a full-phase-based photon-counting double-random-phase encryption (PC-DRPE) method. A PC technique is applied during the encryption process, creating sparse images. The statistical distribution of the PC decrypted data for full-phase encoding and amplitude-phase encoding are derived, and their statistical parameters are used for authentication. The performance of the full-phase PC-DRPE is compared with the amplitude-based PC-DRPE method. The PC decrypted images make it difficult to visually authenticate the input image; however, advanced correlation filters can be used to authenticate the decrypted images given the correct keys. Initial computational simulations show that the full-phase PC-DRPE has the potential to require fewer photons for authentication than the amplitude-based PC-DRPE.
We present a photon-counting double-random-phase encryption technique that only requires the photon-limited amplitude of the encrypted image for decryption. The double-random-phase encryption is used to encrypt an image, generating a complex image. Photon counting is applied to the amplitude of the encrypted image, generating a sparse noise-like image; however, the phase information is not retained. By not using the phase information, the encryption process is simplified, allowing for intensity detection and also less information to be recorded. Using a phase numerically generated from the correct encryption keys together with the photon-limited amplitude of the encrypted image, we are able to decrypt the image. Moreover, nonlinear correlation algorithms can be used to authenticate the decrypted image. Both amplitude-based and full-phase encryption using the proposed method are investigated. Preliminary computational results and performance evaluation are presented.
The amplitude-encoding case of the double random phase encoding technique is examined by defining a cost function as a metric to compare an attempted decryption against the corresponding original input image. For the case when a cipher-text pair has been obtained and the correct decryption key is unknown, an iterative attack technique can be employed to ascertain the key. During such an attack the noise in the output field for an attempted decryption can be used as a measure of a possible decryption key's correctness. For relatively small systems, i.e., systems involving fewer than 5x5 pixels, the output decryption of every possible key can be examined to evaluate the distribution of the keys in key space in relation to their relative performance when carrying out decryption. However, in order to do this for large systems, checking every single key is currently impractical. One metric used to quantify the correctness of a decryption key is the normalized root mean squared (NRMS) error. The NRMS is a measure of the cumulative intensity difference between the input and decrypted images. We identify a core term in the NRMS, which we refer to as the difference parameter, d. Expressions for the expected value (or mean) and variance of d are derived in terms of the mean and variance of the output field noise, which is shown to be circular Gaussian. These expressions assume a large sample set (number of pixels and keys). We show that as we increase the number of samples used, the decryption error obeys the statistically predicted characteristic values. Finally, we corroborate previously reported simulations in the literature by using the statistically derived expressions.
We propose a method to simultaneously transmit double random-phase encryption key and an encrypted image by making use of the fact that an acceptable decryption result can be obtained when only partial data of the encrypted image have been taken in the decryption process. First, the original image data are encoded as an encrypted image by a double random-phase encryption technique. Second, a double random-phase encryption key is encoded as an encoded key by the Rivest-Shamir-Adelman (RSA) public-key encryption algorithm. Then the amplitude of the encrypted image is modulated by the encoded key to form what we call an encoded image. Finally, the encoded image that carries both the encrypted image and the encoded key is delivered to the receiver. Based on such a method, the receiver can have an acceptable result and secure transmission can be guaranteed by the RSA cipher system.