Formalising fault injection and countermeasures

Fault injection is widely used as a method to evaluate the robustness and security of a system against many kinds of faults and attacks. Recent works have considered many ways to demonstrate security risks and viable attacks using fault injection, and some have also proposed countermeasures. However, no general and formal definition of fault injection or countermeasure has been provided that can be used to reason about such attacks. This leaves significant results in this area to be ad-hoc and without broad applicability. This paper presents formal definitions of both fault injection on an arbitrary system and what an effective countermeasure is. These definitions are used to prove that fault injection attacks cannot in general be prevented (by any countermeasure). An example is presented that demonstrates how to construct an effective countermeasure for a specific fault injection that parallels some well known approaches. Further extensions to account for probabilistic behaviour and systems with time are also presented. These definitions and results demonstrate formal proofs about the security and defences of systems in ways that can be used, thus yielding a broadly applicable approach that can formalise fault injections and countermeasures in the future.