# Applying Infinite Petri Nets to the Cybersecurity of Intelligent Networks, Grids and Clouds
## 1 Introduction  
Petri Nets have been applied to simulations of Networking and Communications Protocols for many years [1, 2], and more recently to an understanding of Cybersecurity Threats and Defence [3, 4, 5]. For years, Petri nets have been used extensively in Cybersecurity domain [6, 7, 8, 9, 10, 11]. In this paper we explore the growing need to extend the range of Cybersecurity simulation models to include the emerging field of Infinite Petri Nets [12, 13]. During the last 25 years, computer network security has evolved from basic virus attacks to sophisticated custom Trojan attacks such as Stuxnet. More recent attacks have become global with recent cases such as the massive Distributed Denial of Service (DDoS) attack (2.3 TeraBits/Sec) targeting Amazon Web Service (AWS). We have also seen \"BotNet\" attacks using the Internet of Things (IoT) such as the \"Mirai BotNet\" which infiltrated millions of insecure CCTV devices as well as frequent Ransomware attacks such as the malware family of WannaCry and Petya. Ambitious \"Bad Guys\" now strategically target global enterprise and government networks with a new arsenal of custom intelligent malware. Increasingly these malicious tools are being based upon machine learning algorithms and advanced concepts from artificial intelligence. Cybersecurity against suchmassive malware attacks requires new approaches to the design of effective cyber defence tools [14]. During the coming 5 to 10 years, we suggest that the concept of infinite Petri Nets will play a useful role in understanding innovative ways to mitigate such massive, practically infinite, attacks which propagate globally at light speed across trans-continental optical-fibre networks and ultra high-speed switches, routers and servers. We now consider specific aspects of Cybersecurity Networks that may be more effectively secured through Petri Net Models. Many towns, cities and regional government authorities are now implementing large-scale 24/7 surveillance networks using intelligent CCTV together linked with secure access control and other forms of mobile network surveillance [15]. Such security networks pose ethical issues relating to \"human rights\" and \"privacy\" but such discussion lies beyond the scope of this paper. However, the current global COVID-19 pandemic has demonstrated the strong practical applications of such intelligent urban networks to track and trace citizens that require self-isolation or quarantine. Once again, Infinite Petri Nets may be applied to modelling the architecture, connectivity and intelligent adaptive algorithms in the design and operation of these city-wide surveillance networks which are growing ever more complex during recent years. During the last 10 years, International Agencies, such as the UN, have supported the development of National Cybersecurity Strategies with a strong focus upon CNI in major sectors including Energy, Transportation, Defence, Education, Healthcare, Defence and Government. These are all designed and implemented to International Standards, Rules, and Protocols from Organisations such as the ISO/IEC, IEEE, NIST, and UN/ITU. Both Finite and Infinite Petri Nets will provide excellent systems support in the efficient design of emerging cybersecurity standards particularly those involving machine and deep learning algorithms [4]. Traditional ICS and SCADA (Supervisory Control and Data Acquisition) systems have been at the heart of industrial processes for decades. However, these legacy devices together with the PLCs (Programmable Logic Controllers) are now highly vulnerable to Cyber Malware including RansomWare, Custom \"Bots\" and Cyber Sabotage. The massive scale of Chemical, Oil/Gas and Manufacturing Enterprises makes it essential that Cyber Risks and Threats are thoroughly analysed through simulations with practical tools such as Large-Scale Petri Nets [3]. Such modelling of potential malware threats will help Cybersecurity specialists to mitigate the significant cost of possible operational and business disruption.