Data-Driven Debugging for Functional Side Channels

Functional side channels arise when an attacker knows that the secret value of a server stays fixed for a certain time, and can observe the server executes on a sequence of different public inputs, each paired with the same secret input. Thus for each secret, the attackers observe a (partial) function from public values to (for instance) running time, and they can compare these functions for different secrets. First, we define a notion of noninterference for functional side channels. We focus on the case of noisy observations, where we demonstrate on examples that there is a practical functional side channel in programs that would be deemed information-leak-free using the standard definition. Second, we develop a framework and techniques for debugging programs for functional side channels. We adapt existing results and algorithms in functional data analysis (such as functional clustering) to discover the existence of side channels. We use a functional extension of standard decision tree learning to pinpoint the code fragments causing a side channel if there is one. Finally, we empirically evaluate the performance of our tool Fuschia on a series of micro-benchmarks, as well as on realistic Java programs with thousands of methods. Fuschia is able to discover (and locate in the code) functional side channels, including one that was since fixed by the original developers.