Musleh, Yossef2018-09-212018-09-212018-09-212018-09-19http://hdl.handle.net/10012/13889This thesis introduces a new Monte Carlo randomized algorithm for computing the characteristic polynomial of a rank-2 Drinfeld module. We also introduce a deterministic algorithm that uses some ideas seen in Schoof's algorithm for counting points on elliptic curves over finite fields. Both approaches are a significant improvement over the current literature.enDrinfeldModuleEllipticCurveCryptographyAlgorithmRandomizedMaster Thesis