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" IAENG International Journal of Applied Mathematics, vol. 49, no. 2, pp212-228, 2019.


Abstract—We study then-dimensional deconvolution prob-lem associated with an impulse response function and an(additive) noise function that are both characterised by thesame phase-only stochastic spectrum. In this case, it is shownthat the deconvolution problem becomes well-posed and has ageneral solution that is both exact and unique, subject to are-normalisation condition relating to the scale of the solution.While the phase-only spectral model considered is of limitedvalue in general (in particular, problems arising in the fieldsof digital signal processing and communications engineering,specifically with regard to the retrieval of information fromnoise), its application to digital cryptography has potential.One of the reasons for this (as discussed in this paper),is that it provides a method of encrypting data where thediffused plaintext can be effectively embedded in a (phase-only)cipher (subject to the floating point precision used for dataprocessing), thereby fully dissipating the statistical signatureof the plaintext in the distribution of the cipher. Further,a decrypt can be generated that is computationally efficientsubject to the usual cases of sender and receiver havingaccess to identical algorithm(s) and key(s), deconvolution beingequivalent to decryption in the context of the (phase-only)encryption model that is considered. For the two-dimensionalcase, this approach has a potential weakness in terms of a‘correlation attack’ using phase retrieval algorithms and asolution to this problem is provided by introducing a (stochastic)amplitude weighting function. Prototype MATLAB functionsare provided in the Appendices that accompany this paper togive readers the opportunity to repeat the computational resultspresented and extend them further. The functions constitute asymmetric algorithm for encrypting and decrypting full colourimages in which the key(s) have been exchangeda priori. In thiscontext, the final part of the paper considers the applicationof phase-only encryption for key exchange using a Three-way Pass Protocol for which a further prototype MATLABfunction is provided for validation and further development ofthe approach by interested readers.


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