Counting Keys in Parallel After a Side Channel Attack

Side channels provide additional information to skilled adversaries that reduce the effort to determine an unknown key. If sufficient side channel information is available, identification of the secret key can even become trivial. However, if not enough side information is available, some effort is still required to find the key in the key space (which now has reduced entropy). To understand the security implications of side channel attacks it is then crucial to evaluate this remaining effort in a meaningful manner. Quantifying this effort can be done by looking at two key questions: first, how `deep' (at most) is the unknown key in the remaining key space, and second, how `expensive' is it to enumerate keys up to a certain depth?

We provide results for these two challenges. Firstly, we show how to construct an extremely efficient algorithm that accurately computes the rank of a (known) key in the list of all keys, when ordered according to some side channel attack scores. Secondly, we show how our approach can be tweaked such that it can be also utilised to enumerate the most likely keys in a parallel fashion. We are hence the first to demonstrate that a smart and parallel key enumeration algorithm exists.