Nazarkevych M. Methods and means for improving security of printed documents based on Ateb-functions

Dissertation is dedicated to increasing security level of public paper medium as based on development of theoretical foundation of graphic protection and development of models and methods, as well as establishing, on their basis, effective specialized protection means and identification of printed documents to prevent violation of integrity and fraud. The first chapter analyses literary resources pertaining to methods and means of security of printed documents. It analyses also the drawbacks of existing approaches to graphic means of printed documents protection. The second chapter describes mathematic models and develops the system of solutions for nonlinear differential equation by means of Ateb-functions. It is suggested to use the specialized Ateb-functions apparatus to establish information protection methods in order to prevent paper medium damaging. The third chapter establishes models and means to calculate Ateb-functions. The mathematical model, using Taylor and Fourier Series, is suggested to elaborate method of numerical representation of Ateb-functions. Ateb-functions properties are deduced as well as it sets periods, definition domains and set of values to incorporate security elements. Based on analysis of the properties of Ateb-functions it indicates that their primary characteristic is the dependency on real argument and two rational parameters which provide a large number of security features. The possibility to combine these features creates a strong basis for the formation of security features standards bank. The fourth chapter considers applied basis of printing data protection. To form protective nets, which are the elements of protection, graphics primitives were copied as based on their affine transformations: zooming, compression and rotation. When combining graphics primitives, mathematical apparatus of Bezier curves were used. Formed bank of standards increases the accuracy of the construction of security grids and significantly enhances the capabilities of the publishing system. Mesh curves can be controlled at each point in the coordinate plane allowing for the proper document identification. In addition, the calculated values in Ateb-functions database allow to create documents with personalization features aimed to improve the security features of each document. The fifth chapter realizes construction of protected images. The methods developed provided for the possibility of modifying the image by introducing different distances between the grid lines, grid lines of different thickness and different size perturbations in formation of pseudo-relief. The lines were thickened in the part of image overlapping areas. The formed protective images are of new defensive shape and can be programmatically imposed on any text or graphic information, while maintaining high quality of printed documents and protecting it against counterfeiting. The sixth chapter develops method of identification of printed documents protected by printing method using Ateb-functions. The considered identification method is used for personifying documents' data and for identification of the Ateb-functions curves. To determine the authenticity of the document, the method of full pixel by pixel comparison of standard and controlled image is suggested. The seventh chapter implements the means to receive, store, use and disseminate textual information, where the input of textual information, processing for errors and formatting to improve informational provision in publishing and printing systems is being realized. Key words: security of printed documents, graphic protection, Ateb-functions, identification, guilloche and micro-graphics.