Jeffery, Stacey2011-08-312011-08-312011-08-312011http://hdl.handle.net/10012/6200In this thesis, we investigate the cost of finding collisions in a black-box function, a problem that is of fundamental importance in cryptanalysis. Inspired by the excellent performance of the heuristic rho method of collision finding, we define several new models of complexity that take into account the cost of moving information across a large space, and lay the groundwork for studying the performance of classical and quantum algorithms in these models.enMaster ThesisCombinatorics and Optimization