Game theory applied to cybersecurity threat mitigation - Analysis of Threshold FlipThem

  • Chris Sherfield

Student thesis: Doctoral ThesisDoctor of Philosophy (PhD)


A standard method to protect data is to apply threshold cryptography in the form of secret sharing. This is motivated by the acceptance that adversaries will compromise systems at some point; hence using threshold cryptography provides a defence in depth.
The existence of such powerful adversaries has also motivated the introduction of game theoretic techniques into the analysis of systems, e.g. via the FlipIt game of van Dijk et al. This work further analyses the case of FlipIt when used with multiple resources, dubbed FlipThem in prior papers. We define key extensions of the FlipThem game as a customisable framework where the attacker’s goal is to compromise a threshold of the resources, a game we aptly name Threshold FlipThem.
We introduce the single-rate version of the game which restricts the number of rates to just one per player. Two forms of reset are considered based on how many resources are flipped in one move. Another consideration is separate costs and strategies for each resource. We calculate analytic benefit functions based on the rates and costs of the players. From these, equilibria of the game are found for the benefit functions and conditions calculated to see when these equilibria are valid.
Next, we consider two learning approaches. Fictitious play is introduced in which players do not know opponent costs, or assume rationality. Each player responds to the observed actions of the other player over a continuing sequence of epochs, instead of calculating an equilibrium. In our final form of learning, we remove the assumption that players know analytically their payoff functions and move costs and use genetic algorithms. Populations of strategies are evolved over many iterations to find optimal strategies within multiple strategy populations.
We introduce the FlipThem simulation lab, a python framework designed to create and test strategies within the game of Threshold FlipThem. This is offered as open-source software, allowing researchers to explore their own defined strategy classes.
Date of Award25 Sept 2018
Original languageEnglish
Awarding Institution
  • University of Bristol
SupervisorDavid Leslie (Supervisor) & Nigel Smart (Supervisor)

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