Jamieson-Lane, Alastair David2015-03-012015-03-012009http://hdl.handle.net/10092/10203http://dx.doi.org/10.26021/3345The study of elliptic curves is an important part of modern cryptography. In this report we consider the properties of singular elliptic curves over the field Zp, showing that they can always be factorized, that their equations always take a given form and that there are always p + 1 ± 1 points satisfying this equation over the field Zp.enCopyright Alastair David Jamieson-LaneTheses / Dissertations