Physical Sciences and Mathematics Commons^™

Security Systems Based On Gaussian Integers : Analysis Of Basic Operations And Time Complexity Of Secret Transformations, Aleksey Koval

Dissertations

Many security algorithms currently in use rely heavily on integer arithmetic modulo prime numbers. Gaussian integers can be used with most security algorithms that are formulated for real integers. The aim of this work is to study the benefits of common security protocols with Gaussian integers. Although the main contribution of this work is to analyze and improve the application of Gaussian integers for various public key (PK) algorithms, Gaussian integers were studied in the context of image watermarking as well.

The significant benefits of the application of Gaussian integers become apparent when they are used with Discrete Logarithm Problem …