Formal Framework for the Evaluation of Waveform Resynchronization Algorithms

In side-channel analysis, the waveforms can be acquired misaligned. Several algorithms have been put forward to resynchronize signals, as a pretreatment before the attack proper. In this article, we examine two of them, namely amplitude-only and phase-only correlation (abridged AOC and POC), and introduce a third one, called thresholdPOC (T-POC) that corrects a flaw of the phase-only correlation. Those three resynchronization algorithms are computationally efficient insofar as they find the correct displacement in O(n log n) steps per waveform made up of n samples. Former studies on resynchronization algorithms quantified their quality by their indirect effect on side-channel attacks. We introduce in this article a formal framework for the evaluation of the resynchronization algorithms per se. A benchmarking on representative waveforms shows that there is an adequation between the waveforms and the most suitable resynchronization algorithm. On unprotected circuits, the intrawaveform similarity in amplitude or in phase determines the choice for either the AOC or the POC algorithm. Circuits protected by hiding countermeasures have their amplitude made as constant as possible. Therefore, the intra-waveform similarity in amplitude is lowered and the POC is better. Circuits protected by masking countermeasures have their amplitude made as random as possible. Therefore, even if the intrawaveform similarity in amplitude is high, the inter-waveform similarity is reduced; hence a trade-off between AOC and POC, namely T-POC, is the most adequate resynchronization algorithm.