Ed, RIP

Harold Edwards [here] passed away on 10 November 2020 but left an amazing legacy in computer security. One of his classic papers led to the creation of the Edwards Curve:

The basic form is y² = x² + ax +b, but we can also have a Montgomery curve which is y²=x³+ax²+x. In 2008, Dan Bernstein et all then named a new curve after him — the twisted Edwards curve [here]:

These are the curves used in Ed2215 and EdDSA. Overall, twisted Edwards curve takes the form of:

A plot of 10x²+y² = 1 + 6x²y² is [here]:

For Ed25519 — based on Curve 25519 — it has a finite field defined by a prime number of p=²²⁵⁵−19, a=-1, d=37095705934669439343138083508754565189542113879843219016388785533085940283555 and the base point is at x=5866666666666666666666666666666666666666666666666666666666666666.