Binary Edwards curves

An elliptic curve in binary Edwards form [database entry; Sage verification script; Sage output] has parameters d1 d2 and coordinates x y satisfying the following equations:

  d1*(x+y)+d2*(x^2+y^2)=(x+x^2)*(y+y^2)

Representations for fast computations

W coordinates with d1=d2 [more information] make the additional assumptions

  d1=d2

and represent x y as w satisfying the following equations:

  x+y=w

W coordinates [more information] represent x y as w satisfying the following equations:

  x+y=w

WZ coordinates with d1=d2 [more information] make the additional assumptions

  d1=d2

and represent x y as W Z satisfying the following equations:

  x+y=W/Z

WZ coordinates [more information] represent x y as W Z satisfying the following equations:

  x+y=W/Z

Affine coordinates with d1=d2 [more information] make the additional assumptions

  d1=d2

and represent x y as X Y satisfying the following equations:

  x=X
  y=Y

Affine coordinates [more information] represent x y as X Y satisfying the following equations:

  x=X
  y=Y

Projective coordinates with d1=d2 [more information] make the additional assumptions

  d1=d2

and represent x y as X Y Z satisfying the following equations:

  x=X/Z
  y=Y/Z

Projective coordinates [more information] represent x y as X Y Z satisfying the following equations:

  x=X/Z
  y=Y/Z