Automated Formal Analysis of Side-Channel Attacks on Probabilistic Systems

Abstract

The security guarantees of even theoretically-secure systems can be undermined by the presence of side channels in their implementations. We present Sch-imp, a probabilistic imperative language for side channel analysis containing primitives for identifying secret and publicly-observable data, and in which resource consumption is modelled at the function level. We provide a semantics for Sch-imp programs in terms of discrete-time Markov chains. Building on this, we propose automated techniques to detect worst-case attack strategies for correctly deducing a program’s secret information from its outputs and resource consumption, based on verification of partially-observable Markov decision processes. We implement this in a tool and show how it can be used to quantify the severity of worst-case side-channel attacks against a selection of systems, including anonymity networks, covert communication channels and modular arithmetic implementations used for public-key cryptography.