Tag: curves

Another week, another point operation on elliptic curves. This time we are about to explore a simple point addition of two different points on elliptic curve in simple Weierstrass form. Although there are still some possibilities of enhancing the visualizations, our focus is now on finishing this series to a point where we can show at least Diffie-Hellman key exchange[1].

Venturing closer to our goal of using elliptic curves for digital signatures and encryption, we describe the simplest point operation on elliptic curve in Weierstrass form. This operation is called negation and it somehow resembles the negation of numbers you learned about in elementary school. We have (sort of) finalized the software stack for visualizing elliptic curves both in 2D or 3D so I would like to hear some feedback if the pictures - and especially the video - are clear and easy to understand. And now for something completely negating...

After a quick introduction to simple elliptic curves used in cryptography and finally for securing our online communication, we cannot move forward without solving one major problem. How to represent these curves, and all of their points thereof, in computer memory. Why this is a major problem? There is an infinite number of real numbers, but computers can store only a finitely-sized things - including numbers. I'd like to explain how we can overcome this inherent trouble and show you that anyone can understand these modern cryptographic fundamentals.

We are about to start a journey to the realm of elliptic curve cryptography. It may seem strange at this point as why we should bother with that, but rest assured that we will eventually find out how to use this knowledge to secure our email communication. In this introduction, you can expect to see what an elliptic curve looks like, how it is defined and how it can be simplified if we want to make some practical use of it.

As I have had to give a talk about elliptic curve cryptography for the testing community in Czech Republic at the regular pro[test] event held in Prague two weeks ago, I wondered what could be actually tested about ECC in real-world scenarios. As I was digging through my notes, I realized there is something everybody really hates - waiting for web page to load. And with HTTPs everywhere now the crucial part slowing the whole browsing experience down is how fast the connection can be established. That is because encrypted connection requires exchanging quite a lot of information at the beginning and can go on without much overhead afterwards.