ABSTRACT
In the 1980s, about the same time that elliptic curves were being introduced into cryptography, two related applications of elliptic curves were found, one to factoring and one to primality testing. These are generalizations of classical methods that worked with multiplicative groups Z×n . The main advantage of elliptic curves stems from the fact that there are many elliptic curves mod a number n, so if one elliptic curve doesn’t work, another can be tried.
