Fast unitary heap transforms: theory and application in cryptography

Artyom M. Grigoryan; Khalil Naghdali

doi:10.1117/12.818946

4 May 2009 Fast unitary heap transforms: theory and application in cryptography

Artyom M. Grigoryan, Khalil Naghdali

Proceedings Volume 7351, Mobile Multimedia/Image Processing, Security, and Applications 2009; 73510H (2009) https://doi.org/10.1117/12.818946
Event: SPIE Defense, Security, and Sensing, 2009, Orlando, Florida, United States

Abstract

This paper presents a novel approach to compose discrete unitary transforms that are induced by input signals which are considered to be generators of the transforms. Properties and examples of such transforms, which we call the discrete heap transforms are given. The transforms are fast, because of a simple form of decomposition of their matrices, and they can be applied for signals of any length. Fast algorithms of calculation of the direct and inverse heap transforms do not depend on the length of the processed signals. In this paper, we demonstrate the applications of the heap transforms for transformation and reconstruction of one-dimensional signals and two-dimensional images. The heap transforms can be used in cryptography, since the generators can be selected in different ways to make the information invisible; these generators are keys for recovering information. Different examples of generating and applying heap transformations over signals and images are considered.

Citation Download Citation

Artyom M. Grigoryan and Khalil Naghdali "Fast unitary heap transforms: theory and application in cryptography", Proc. SPIE 7351, Mobile Multimedia/Image Processing, Security, and Applications 2009, 73510H (4 May 2009); https://doi.org/10.1117/12.818946

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