Devices, such as in mobile devices or RFID. In brief, ECC based algorithms can be easily comprised into existing protocols to get the same retrograde compatibility and security with lesser resources.: Recent variants of Distributed Denial-of-Service (DDoS) attacks influence the flexibility of application-layer procedures to disguise malicious activities as normal traffic patterns, while concurrently overwhelming the target destination with a large application rate. New countermeasures are necessary, aimed at guaranteeing an early and dependable identification of the compromised network nodes (the botnet). This work familiarizes a formal model for the above-mentioned class of attacks, and we devise an implication algorithm that estimates the botnet hidden in the network, converging to the true solution as time developments. Notably, the analysis is validated over real network traces. An important building block for digital communication is the Public-key cryptography systems. Public-Key cryptography (PKC) systems can be used to provide secure substructures over insecure channels without swapping a secret key. Applying Public-Key cryptography organizations is a challenge for most submission stages when several factors have to be considered in selecting the application platform. The most popular public-key cryptography systems nowadays are RSA and Elliptic Curve Cryptography (ECC). The compensations can be achieved from smaller key sizes including storing, speed and efficient use of power and bandwidth. The use of shorter keys means lower space necessities for key storage and quicker calculation operations. These advantages are essential when public-key cryptography is applied in constrained