Abstract
Correctness of networking protocols represents the principal requirement of cybersecurity. Correctness of protocols is established via the procedures of their verification. A classical communication system includes a pair of interacting systems. Recent developments of computing and communication grids for radio broadcasting, cellular networks, communication subsystems of supercomputers, specialized grids for numerical methods and networks on chips require verification of protocols for any number of devices. For analysis of computing and communication grid structures, a new class of infinite Petri nets has been introduced and studied for more than 10 years. Infinite Petri nets were also applied for simulating cellular automata. Rectangular, triangular and hexagonal grids on plane, hyper cube and hyper torus in multidimensional space have been considered. Composing and solving in parametric form infinite Diophantine systems of linear equations allowed us to prove the protocol properties for any grid size and any number of dimensions. Software generators of infinite Petri net models have been developed. Special classes of graphs, such as a graph of packet transmission directions and a graph of blockings, have been introduced and studied. Complex deadlocks have been revealed and classified. In the present paper, infinite Petri nets are divided into two following kinds: a single infinite construct and an infinite set of constructs of specified size (and number of dimensions). Finally, the paper discusses possible future work directions.
Highlights
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]
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 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
Summary
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]. Ambitious “Bad Guys” strategically target global enterprise and government networks with a new arsenal of custom intelligent malware These malicious tools are being based upon machine learning algorithms and advanced concepts from artificial intelligence. Cybersecurity against such massive malware attacks requires new approaches to the design of effective cyber defence tools [14]. 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. It is likely that Infinite Petri Nets will become useful in understanding the potential for stochastic machine learning tools to be used to mitigate attacks from intelligent algorithmic “AI-Bot” attacks
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