Explicit-Formulas Database
Doubling-oriented Doche–Icart–Kohel curves: y^2=x^3+a*x^2+16*a*x
Tripling-oriented Doche–Icart–Kohel curves: y^2=x^3+3*a*(x+1)^2
Edwards curves: x^2+y^2=c^2*(1+d*x^2*y^2)
Hessian curves: x^3+y^3+1=3*d*x*y
Jacobi intersections: s^2+c^2=1, a*s^2+d^2=1
Jacobi quartics: y^2=x^4+2*a*x^2+1
Montgomery curves: b*y^2=x^3+a*x^2+x
Short Weierstrass curves: y^2=x^3+a*x+b
Twisted Edwards curves: a*x^2+y^2=1+d*x^2*y^2
Twisted Hessian curves: a*x^3+y^3+1=d*x*y
Binary Edwards curves: d1*(x+y)+d2*(x^2+y^2)=(x+x^2)*(y+y^2)
Hessian curves: x^3+y^3+1=3*d*x*y
Short Weierstrass curves: y^2+x*y=x^3+a2*x^2+a6
The Explicit-Formulas Database is joint work by
Daniel J. Bernstein
and
Tanja Lange,
building on work by many authors.
We've completely revamped the EFD
to include
more coordinate systems,
more formulas,
fully automated formula verification,
and fully automated operation counts.
Latest news:
The EFD also covers characteristic 2!
New
paper on the EFD:
"Analysis and optimization of elliptic-curve single-scalar multiplication",
to appear in the proceedings of Fq8.
See also the
zoo pictures.
The
old Explicit-Formulas Database
is still available if you want to look at it.