Twisted Edwards curve

In algebraic geometry, the twisted Edwards curves are plane models of elliptic curves, a generalisation of Edwards curves introduced by Daniel J. Bernstein et al. in 2008. The curve set is named after mathematician Harold M. Edwards. Elliptic curves are important in public key cryptography and twisted Edwards curves are at the heart of an electronic signature scheme called EdDSA that offers high performance while avoiding security problems that have surfaced in other digital signature schemes.

As the name suggests, each twisted Edwards curve, is a twist of an Edwards curve. A twisted Edwards curve ${\displaystyle E_{E_{a,d}}}$ over a field ${\displaystyle \mathbb {K} }$ which have ${\displaystyle \mathrm {char} (\mathbb {K} )\neq 2}$ is an plane curve defined by the equation:

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