ABSTRACT
The study of elliptic curves is often called arithmetic algebraic geometry. Recent mathematical developments in this area has been motivated to a large extent by attempts to prove Fermat’s last theorem which states that the equa-
tion xn+yn = zn does not have non-trivial solutions in integer values of x, y, z for (integers) n > 3. (The trivial solutions correspond to xyz = 0.)1
Purely mathematical objects like elliptic curves are used in a variety of engineering applications, most notably in the area of public-key cryptography. Elliptic curves are often preferred to finite fields, because the curves offer a wide range of groups upon which cryptographic protocols can be built, and also because keys pertaining to elliptic curves are shorter (than those pertaining to finite fields), resulting in easier key management. It is, therefore, expedient to look at the arithmetic of elliptic curves from a computational angle. Moreover, we require elliptic curves for an integer-factoring algorithm.
