What’s the “Ed” in Ed25519?
Curve 25519 is one of the most trusted elliptic curve methods, and there’s a chance you are using it on a daily basis. With this, you may be connecting to a remote service and performing a key exchange using X25519. This is a key exchange method that uses Curve 25519. Basically, we have a Montgomery curve defined by:
And here is a plot:
The curve uses a base point (G) and which is at: (9,1478161944 … 7755586237401). For key exchange, Bob generates a value of b, and computes an elliptic curve point of b.G. Alice generates a and computes, a.G. They exchange these points, and then Bob multiples the a.G value by b to get a.b.G. Alice takes Bob’s public key point, and multiples by a to get a.b.G. They should then have the same shared point, and can derive the same encryption key.
Meet “Ed”
While X25519 implements key exchange, we can also use Curve 25519 for digital signatures: Ed25519. The “Ed” part is named the Edwards Twisted Curve — after Harold Edwards [here]. Unfortunately, he passed away on 10 November 2020 but left an amazing legacy in computer…
