As both standalone and networked computing capabilities continue to grow in-line with Moore’s law, key sizes for the most widely used public-key cryptographic systems have to grow disproportionately fast. This trend makes a switch to elliptic-curve cryptography (ECC) more and more attractive.
Unfortunately, ECC has a reputation for being difficult to understand. And this reputation, deserved or not, deters many from exploring the principles on which it is based.
This is particularly unfortunate now, when we are called upon to make informed judgments about the soundness of elliptic curve standards and the processes by which they were developed. We need more people willing to enter into the debate, and, in order for this to happen, more people must have a grasp of the basics.
A full appreciation of all aspects of ECC does demand a thorough grounding in some advanced branches of mathematics. But, few of us need the depth of understanding required to design new elliptic-curve schemes, or implement existing schemes in software or hardware.
The basic principles, on the other hand, are easily understood by anyone who studied mathematics through high-school. And a wider understanding of the basics will result in a wider circle of informed discussion. It’s time to dispel the myth that knowledge of ECC is out of reach to all but the mathematical elite.