Edwards normal form

An elliptic curve is in Edwards normal form if it can be described by the equation

$x^{2}+y^{2}=1+dx^{2}y^{2}$

The more general original Edwards form has another parameter c

$x^{2}+y^{2}=c^{2}(1+dx^{2}y^{2})$

but it is very simple to eliminate the scale parameter c and reduce this equation to its normal form for ease of performing algebraic group operations on rational points or finite fields.

The twist

There is also a “twisted” Edwards form

$ax^{2}+y^{2}=1+dx^{2}y^{2}$

And this brings us back to the ancient Greek word στραγγός with the idea of using something “twisted” for strong cryptography.