Statistical investigation of the double random phase encoding technique

Abstract

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 5 ϫ 5 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.

A Review of Some Recent Work in the Area of Imaging and Optical Signal Processing

“…There has been significant interest in encryption schemes which can be implemented optically [18][19][20][21][22][23]. Practical optical implementation of such systems is difficult [19,22] and the security and robustness of these systems is still a matter of study and analysis [18,[20][21][22][23].…”

“…Practical optical implementation of such systems is difficult [19,22] and the security and robustness of these systems is still a matter of study and analysis [18,[20][21][22][23]. However not only do such systems pose a very interesting problem for the fast algorithms described above in Section 3, it has been shown that the problems of encryption and multiplexing can be discussed fruitfully using PSO [24].…”

A review of optical image encryption techniques

“…Furthermore, two dimensional optical encryption processing has been extended into a three dimensional spacebased encryption processing, where each pixel of the image is axially considered as one particle and phase-shifting digital holography technique is applied to the diffraction of all pixels in space (particles) [71][72][73][74]. In the context of cryptography and cryptoanalysis, both chosen-plaintext [60] and known-plaintext attack [75][76][77] on DRPE have been examined, as have several other attacking methods [78][79][80][81][82] and the key space of DRPE technique itself [83][84][85][86] has also been analysed.…”

A Multispectral Photon-Counting Double Random Phase Encoding Scheme for Image Authentication

“…The original image can be extracted only when appropriate keys are given. Even though the DRPE algorithm has performed well in the image security field [6,7], it has been reported that DRPE is vulnerable to chosen-cipher text attacks [8,9]. Therefore, the encryption keys used in DRPE could be reproduced by an intruder who has repeatedly accessed the DRPE system.…”