The paper documents a holistic mathematical modeling
theory to provide a rigorous description of cyber-attacks and cyber-security.
After determining valuations and vulnerabilities of parts of a node
constituent, we recall the definitions of cyber-effect and cyber-interaction.
Based on these concepts, we give the mathematical definitions of cyber
navigation and infected node and we explain what is meant by dangerous cyber
navigation and protection of cyber nodes from unplanned attacks. Our discussion
proceeds to a rigorous description of passive and active cyber-attacks, as well
as the relevant protections.
Keywords: Mathematical modeling (models of systems), internet
topics, measure theory, complex spaces, valuation of a part of node
constituent, vulnerability of a part of node constituent, node supervision,
cyber-effect, cyber-interaction, germ of cyber-attack, cyber defense, proactive