Investigations on Application of Probabilistic and Mathematical Computing in Design and Statistical Analysis of Lightweight Cryptography

Abstract

This research provides in-depth investigation into the application and role of probability and mathematics in lightweight cryptography featuring IoT software. The IoT device fleet growth is continuously accompanied by its resources, often poor. It creates a critical need for cryptographic solutions that will be effective and a heavy burden. The research article underlines the use of latest probabilistic models and mathematical concepts to create cryptographic algorithms that are cryptographically powerful and IoT-embedded devices can process them. The study commences with its deep mathematics investigation and focuses on consequently essential permutations, combinations, modular arithmetic and prime number theory, all of which represents the cornerstone of strong cryptographic algorithms development. The article then proceeds to demonstrate the use of probabilistic tools for scrutinizing the security and the effectiveness of these algorithms. A novel approach to grasping the vulnerabilities that may occur in the course of cryptographic implementations is also brought to light. A remarkable part of the investigation is toward designing small-sized cryptographic algorithms by using methods of mathematics computations to decrease the size of key, complexity and implementations of increased safety margin. The research process involves a thorough statistical demonstration of the algorithmic performance in several agendas of IoT exposing the resistance of the algorithms against cryptographic issues and the intensity of their resource consumption on ordinary IoT devices. By conducting these investigations, the paper contributes a lot of useful information on the harmonious relationship between probability methods, mathematical computing, and cryptographic development as well as providing the solid foundation for creating a lightweight cryptography which can be used in the Internet of Things (IoT) and other similar environments that have their unique needs and constraints. However, it not only advances the field of cryptography itself, but also outlines a practical roadmap on how to design secure, efficient cryptosystems, that can be used in its subsequent applications in the small but fast growing IoT technology landscape.