Convergence Analysis of Iterated Best Response for a Trusted Computation Game

TL;DR

This paper analyzes a game-theoretic approach to trusted computation where a sensor and attacker interact, characterizing Nash equilibria and convergence of an iterative best response scheme to ensure reliable function evaluation under attack.

Contribution

It formulates a new trusted computation game model, characterizes all Nash equilibria, and provides conditions for convergence of an iterative best response algorithm.

Findings

Nash equilibria depend on known parameters.

Convergence conditions for the IBR scheme are derived.

Numerical results demonstrate tightness of the convergence conditions.

Abstract

We introduce a game of trusted computation in which a sensor equipped with limited computing power leverages a central node to evaluate a specified function over a large dataset, collected over time. We assume that the central computer can be under attack and we propose a strategy where the sensor retains a limited amount of the data to counteract the effect of attack. We formulate the problem as a two player game in which the sensor (defender) chooses an optimal fusion strategy using both the non-trusted output from the central computer and locally stored trusted data. The attacker seeks to compromise the computation by influencing the fused value through malicious manipulation of the data stored on the central node. We first characterize all Nash equilibria of this game, which turn out to be dependent on parameters known to both players. Next we adopt an Iterated Best Response (IBR) scheme in which, at each iteration, the central computer reveals its output to the sensor, who then computes its best response based on a linear combination of its private local estimate and the untrusted third-party output. We characterize necessary and sufficient conditions for convergence of the IBR along with numerical results which show that the convergence conditions are relatively tight.