Maha Toufig Fadle Elseid2018-10-102018-10-102011http://hdl.handle.net/123456789/13151A thesis submitted in Research For T he Degree of Doctor of philosophy In MathematicsABSTRACT This research deals with different operations of encryption These are illustrated using elliptic curves where a program for this operation is used to embed a message in an elliptic curve and convert it to a point, so as to encrypt/decrypt the message. This is illustrated by finite field of order p(where p is a prime number).The message is embed in an elliptic curve and transformed as a point and then, encrypt/decrypt it. A program is designed to do this operation using Java Programming and in particular Java Biglnteger to make it more difficultenelliptic curvesThesis