Two sides of the same coin: Counting and enumerating keys post side-channel attacks revisited

Motivated by the need to assess the concrete security of a device after a side channel attack, there has been a flurry of recent work designing both key rank and key enumeration algorithms. Two main competitors for key ranking can be found in the literature: a convolution based algorithm put forward by Glowacz et al. (FSE 2015), and a path counting based algorithm proposed by Martin et al. (Asiacrypt 2015). Both key ranking algorithms can be extended to key enumeration algorithms (Poussier et al. (CHES 2016) and Martin et al. (Asiacrypt 2015)). The two approaches were proposed independently, and have so far been treated as uniquely different techniques, with different levels of accuracy. However, we show that both approaches (for ranking) are mathematically equivalent for a suitable choice of their respective discretisation parameter. This settles questions about which one returns more accurate rankings. We then turn our attention to their related enumeration algorithms and determine why and how these algorithms differ in their practical performance.