From Smooth to Dot-to-Dot … Meet The Curve That Protects Your Online Security Like No Other

You will find elliptic curves in so many areas of cybersecurity. In fact, the network connection you are using now is probably using them to generate the shared encryption key that your browser uses, and which is the same key that the same server. Everytime your connect, you both generate a new encryption key. We define this method as ECDH (Elliptic Curve Diffie Hellman).

For digital signatures, too, you’ll find them hard at work matching a user’s public key to a signature. In blockchain, Bitcoin and Ethereum use them as a core of their infrastructure, and where you’ll find the mighty secp256k1 curve. Two common elliptic curve signatures are ECDSA (Elliptic Curve Digital Signature Algorithm) and EdDSA (Edwards-curve Digital Signature Algorithm).

So let’s see how elliptic curves actually work. First, we start off with an elliptic curve equation of:

and where a and b are well-defined constants for our curve, and p is a large prime number (typically this has 256 bits, but can be larger). Overall a prime number of around 256 bits gives us around 128-bit security, which is more than enough for current security levels. There are another two parameters that we need. The first is the base point on the curve: G, and the second is the order of the…