Cryptography Systems using Ellíptic Curves

Abstract

In this work we will discuss and compare some Cryptosystems based on Elliptic Curves. And why use Elliptic Curves in Cryptography? The main reason is that they provide equivalent security to classical systems using fewer bits. For example, in [1] it was estimated that a key size of 4096 bits for the RSA system provides the same level of security as 313 bits in a system using Elliptic Curves. This means that the implementation for systems with Elliptic Curves requires smaller chips, lower power consumption, among other factors. In [4], the authors did an experiment on a small portable device (3Com’s Palm Pilot) larger than a smart card but smaller than a laptop. They found that generating a 512-bit RSA key takes 3.4 minutes, while generating a 163-bit key in the ECC-DSA system takes 0.597 seconds. Although certain procedures, such as signature verification, were slightly faster for RSA, Elliptic Curve methods, such as ECC-DSA, offer greater speed in several situations.