SAT-based Formal Verification of Fault Injection Countermeasures for Cryptographic Circuits

Abstract

Fault injection attacks represent a type of active, physical attack against cryptographic circuits. Various countermeasures have been proposed to thwart such attacks, however, the design and implementation of which are intricate, error-prone, and laborious. The current formal fault-resistance verification approaches are limited in efficiency and scalability. In this paper, we formalize the fault-resistance verification problem and show that it is coNP-complete. We then devise a novel approach for encoding the fault-resistance verification problem as the Boolean satisfiability (SAT) problem so that modern off-the-shelf SAT solvers can be utilized. The approach is implemented in an open-source tool FIRMER which is evaluated extensively on realistic cryptographic circuit benchmarks. The experimental results show that FIRMER is able to verify fault-resistance of almost all (72/76) benchmarks in 3 minutes (the other three are verified in 35 minutes and the hardest one is verified in 4 hours). In contrast, the prior approach fails on 31 fault-resistance verification tasks even after 24 hours (per task).