In this talk we will go over one an algorithm of Kohel-Lauter-Petit-Tignol that, given a left ideal for a maximal order in a quaternion algebra, returns an equivalent left ideal with $\ell$-power reduced norm (The preprint can be found here: https://arxiv.org/pdf/1406.0981.pdf). This algorithm was mentioned in the previous talk as a supplementary algorithm to the reductions between certain computational problems. If there is time, we will also discuss a recent signatue scheme proposed by Galbraith-Petit-Silva based on this algorithm.