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Toward a Mathematical Understanding of the Malware Problem

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dc.contributor.author Fiske, Michael
dc.date.accessioned 2020-01-04T08:34:42Z
dc.date.available 2020-01-04T08:34:42Z
dc.date.issued 2020-01-07
dc.identifier.isbn 978-0-9981331-3-3
dc.identifier.uri http://hdl.handle.net/10125/64563
dc.description.abstract Malware plays a significant role in breaching computer systems. Previous research has focused on malware detection even though detection is up against theoretical limits in computer science and current methods are inadequate in practice. We explain the susceptibility of computation to malware as a consequence of the instability of Turing and register machine computation. The behavior of a register machine program can be sabotaged, by making a very small change to the original, uninfected program. Stability has been studied extensively in dynamical systems and in engineering fields such as aerospace. Our primary contribution introduces mathematical tools from topology and dynamical systems to explain why register machine computation is susceptible to malware sabotage. A correspondence is constructed such that one computational step of a Turing machine maps to one iteration of a dynamical system in the x-y plane and vice versa. Using this correspondence, another contribution defines and demonstrates a structural instability in a Universal Turing machine encoding. One research direction proposes to better understand instability in conventional computation by studying non-isolated metrics on the space of Turing machines; another suggests searching for stable computation in unconventional machines.
dc.format.extent 10 pages
dc.language.iso eng
dc.relation.ispartof Proceedings of the 53rd Hawaii International Conference on System Sciences
dc.rights Attribution-NonCommercial-NoDerivatives 4.0 International
dc.rights.uri https://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subject The Science and Engineering of Cyber Systems
dc.subject dynamical system
dc.subject instability
dc.subject malware
dc.subject register machine
dc.subject structurally stable
dc.title Toward a Mathematical Understanding of the Malware Problem
dc.type Conference Paper
dc.type.dcmi Text
dc.identifier.doi 10.24251/HICSS.2020.821
Appears in Collections: The Science and Engineering of Cyber Systems


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