Statistical investigation of the double random phase encoding technique
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|Title:||Statistical investigation of the double random phase encoding technique||Authors:||Monaghan, David S.
Naughton, Thomas J.
Sheridan, John T.
|Permanent link:||http://hdl.handle.net/10197/3392||Date:||24-Aug-2009||Online since:||2011-12-08T16:55:25Z||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 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.||Funding Details:||Science Foundation Ireland
Irish Research Council for Science, Engineering and Technology
|Type of material:||Journal Article||Publisher:||Optical Society of America||Journal:||Journal of the Optical Society of America A||Volume:||26||Issue:||9||Start page:||2033||End page:||2042||Copyright (published version):||2009 Optical Society of America||Subject LCSH:||Data encryption (Computer science)
Optical data processing
|DOI:||10.1364/JOSAA.26.002033||Other versions:||http://dx.doi.org/10.1364/JOSAA.26.002033||Language:||en||Status of Item:||Not peer reviewed|
|Appears in Collections:||Electrical and Electronic Engineering Research Collection|
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