Multi-rate Threshold FlipThem

Abstract

Abstract. A standard method to protect data and secrets 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; and 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 examine two key extensions of the FlipThem game to more realistic scenarios; namely separate costs and strategies on each resource, and a learning approach obtained using so-called fictitious play in which players do not know about opponent costs, or assume rationality.

$\mathtt{FlipIn}$ : A Game-Theoretic Cyber Insurance Framework for Incentive-Compatible Cyber Risk Management of Internet of Things

“…In [26] FlipThem games have been proposed to extend the FlipIt games and study the interactions between one defender and on attacker over multiple resources [59]- [62]. In [59], Laszka et al, have proposed an AND control model where an attacker takes control of all resources to compromise the system and an OR model where an attacker only needs to take control of one resource to achieve that; in [60], Zhang et al, have considered a situation where a defender and an attacker have strict constraints on their actions across all the resources; in [61] and [62], Leslie et al, have investigated a scenario where an attacker compromises a defender's resources with a threshold. However, they have not considered situations where multiple defenders and attackers interact in the same network of resources.…”

Defending Against Stealthy Attacks on Multiple Nodes with Limited Resources: A Game-Theoretic Analysis

“…However, only preliminary analytic results are provided. Leslie et al extend the "FlipThem" model in [19], [20] where the attacker can obtain partial benefits by compromising a certain number (larger than a threshold) of nodes. Further, an extended model with a networked system of multiple resources, called "FlipNet", is condisdered in [27].…”

“…Theorem V.1. Any pair of strategies (m, p) with F (p) = F and D(m, p) = D is an NE iff it is a solution to one of the following sets of constraints in addition to (20) to (25).…”