Stochastic Models for Cyber Attack Detection and Response: A Mathematical Approach to Intrusion Detection Systems

Abstract

Cyberattacks are a big problem in today's world because everything is linked online. They can damage the security, privacy, and access of private information. Intrusion Detection Systems (IDS) are very important for keeping networks safe because they quickly find and stop harmful activity. To successfully find and stop attacks, however, we need more advanced methods because online risks are always changing. This paper suggests a new mathematical approach for improving IDS that is based on random models. Traditional ways of finding intrusions often use signature- or anomaly-based methods, which might not be able to keep up with how attackers' strategies change all the time. By using random processes, our method provides a more flexible and adaptable way to find online threats. IDS can tell the difference between normal network traffic and hostile activities because stochastic models use a statistical framework to capture the uncertainty that comes with cyberattack behaviors. We use methods from probability theory, Markov chains, and queue theory to make models of how network traffic and possible cyberattacks might behave. Our random models can find differences that could mean someone is doing something bad by looking at the statistical features of different network factors, like the rate at which packets arrive, the length of a link, and the size of the payloads. Using Markov models, the IDS can also guess how likely it is that an attack will happen in the future based on past data, which helps with strategic strategies for reducing threats. Along with monitoring, our system includes ways to respond to cyberattacks and lessen their effects. By using stochastic optimization methods, we can change how resources are used and how reactions are prioritized based on how likely and how bad the threats are to be. This flexible method makes the network infrastructure more resistant to complex attack routes, which lowers the damage and downtime that can happen during cyber events. We show that our stochastic models can improve the performance of IDS in real-world situations by analyzing them theoretically and running simulations. Adopting a scientific approach to cyber security makes it possible for stronger and smarter defenses against cyber risks that are always changing.