Reconstructing AES Key Schedule Images with SAT and MaxSAT

Cold boot attack is a side channel attack that recovers data from memory, which persists for a short period after power is lost. In the course of this attack, the memory gradually degrades over time and only a corrupted version of the data may be available to the attacker. Recently, great efforts have been made to reconstruct the original data from a corrupted version of AES key schedules, based on the assumption that all bits in the charged states tend to decay to the ground states while no bit in the ground state ever inverts. However, in practice, there is a small number of bits flipping in the opposite direction, called reverse flipping errors. In this paper, motivated by the latest work that formulates the relations of AES key bits as a Boolean Satisfiability problem, we move one step further by taking the reverse flipping errors into consideration and employing off-the-shelf SAT and MaxSAT solvers to accomplish the recovery of AES-128 key schedules from decayed memory images. Experimental results show that, in the presence of reverse flipping errors, the MaxSAT approach enables reliable recovery of key schedules with significantly less time, compared with the SAT approach that relies on brute force search to find out the target errors. Moreover, in order to further enhance the efficiency of key recovery, we simplify the original problem by removing variables and formulas that have relatively weak relations to the whole key schedule. Experimental results demonstrate that the improved MaxSAT approach reduces the scale of the problem and recover AES key schedules more efficiently when the decay factor is relatively large.