 Hi everyone, Maria here. Today I'll be talking to you about accelerating the Delft-Galbraith algorithm with fast sub-field root detection. This is based on joint work with Craig Costello and GSU. The general super-singular isogenic problem is the foundational problem in isogenic-based cryptography and it's believed to be secure against both classical and quantum computers. Given two super-singular elliptic curves defined over fp squared, it asks us to find an isogenic between them. Note that we do not assume the knowledge of any torsion point or that we know the degree of the isogenic. This makes the problem substantially easier, as shown independently by Castrick and DeCru and Mano and Martindale in their recent papers giving polynomial attacks against the key exchange SIDH or the encryption scheme Psyche. So here we're really just considering the general isogenic problem, where all we know is that we have two elliptic curves defined over fp squared and we want to find an isogenic between them. We can convert the isogenic problem to a path finding problem in the isogenic graph. Here the nodes are elliptic curves which we label with the J invariant which lies in fp squared. The edges are then isogenes. So finding a path between two J invariants in this isogenic graph is equivalent to finding an isogenic between the two elliptic curves labeled by this J invariant. In the isogenic graph there are two types of nodes, those lying in fp squared and those lying in fp. Gelsen-Gelbreit's key idea was that finding paths between the fp nodes is comparatively easy. So the bottleneck set of finding isogenes between these two J invariants is really walking in the graph until you hit a node defined over fp. Because once you find a path from your start and end node to nodes defined over fp, then you can navigate in the fp subgraph which is a lot easier. In Solver we implement an optimized Gelsen-Gelbreit's algorithm and determine its concrete complexity. This is really important for determining concrete parameters for schemes whose best attack is the Gelsen-Gelbreit algorithm such as the soundness of a recent isogenic-based signature scheme, SkiSign. Building on this we present Supersolver with superpower fast subfield root detection. This allows us to scan a larger proportion of the graph at each step, therefore minimizing the number of fp operations per node revealed in the graph. In this way we can cover a larger proportion of the graph while still minimizing the number of fp operations. In doing so we provide the best algorithm for finding paths to the fp subgraph and we decrease the concrete complexity of the Gelsen-Gelbreit's algorithm. This affects schemes such as SkiSign and isogenic-based signature scheme and Beeside and isogenic-based key exchange. For more details please come to the full talk on Wednesday. Thank you.