Simple Illustration and Gentle Description of ECC Process

Abstract

With the advance of cryptography, not only do a large number of devices have to maintain security but they should also minimize the key size, which is a great concern. In turn, Elliptical Curve Cryptography (ECC), introduced by Victor Miller and Neal Koblitz have gained tremendous attention in recent years, which might be referred to as an "improvement" of RSA. While the security of RSA and ECC are both based on discrete logarithm problem, which is also called the hard problem, ECC is based on a more complex one, the elliptic curve discrete logarithm problem (ECDLP). Simultaneously, having equivalent levels of security with the RSA, ECC’s operation depends on the combination of elliptic curves and modular arithmetic, meaning a much smaller key size. On the other hand, even though ECC is of great significance, only a small number of people are familiar with them. Accordingly, this article will illustrate the operation of elliptic curves with some pictures, such as the addition and doubling. Furthermore, some description of them will also be discussed in detail, demonstrating why ECC generates a much smaller key size. To be specific, some math will be included such as the group law and the arithmetic modular, but most of them are only simple ones and sets no barrier to understand, comparing to the long and boring proof.