الفهرس 
AbstractOnly 14 pages are availabe for public view
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Abstract
In this thesis, we provide a detailed study to secure biomedical images using a modified ECC algorithm with different cases of algebraic equation forms to choose the best form that verify security issue. These objectives can be programmed using software or be implemented using hardware such as FPGA which is a quicker solution than software. In the beginning, a complete survey of Elliptic Curve encryption is discussed with the method of encoding images according to the generated finite field. A new technique is surveyed to perform point operations multiplication, addition and doubling using MATLAB. The New technique depends on calculating the mathematical expression of point addition and doubling in a faster way. According to results, modifications success to achieve a faster manner to execute point operations in different data types like gray images, color images and text. In addition to that, the thesis discusses a simple implementation for elliptic curve equation on Field Programmable Gate Array (FPGA). As Elliptic Curve Cryptography (ECC) offers a smaller key size without sacrificing security level. A brief survey on applying the main equation of Elliptic Curve (EC) with different values of the coefficients a and b. A comparison between results depended on the correlation coefficient of each value. Value of a and b implemented on FPGA (Xilinx - Spartan3E:3S500EFG320) according to correlation results between plaintext image and ciphertext image on MATLAB. The EC equation will be applied to an ultra-wide band (UWB) system to secure transmission of data in a wireless channel. A brief survey on UWB technology has been implemented with software simulation for a secured system based on ECC algorithm.