I'm not entirely sure I understand my self but I believe it's because they 
generally use different representations of the curve. While it's possible 
to convert between representations apparently that has some implications on 
how point addition works? Generally it just seems to be a thing that people 
don't do. Instead of ECDSA you use the Ed25519 construct for signatures.


On 7 April 2014 18:46:05 Matt Iversen <notifications@github.com> wrote:

> > +    A named `ECDSA`_ curve.
> > +
> > +    .. attribute:: name
> > +
> > +        :type: string
> > +
> > +        The name of the curve. Usually the name defined by SECG. e.g. 
> secp256k1
> > +
> > +    .. attribute:: key_size
> > +
> > +        :type: int
> > +
> > +        The bit length of the curves base point.
> > +
> > +
> > +.. class:: ECDSAPrivateKey
>
> Why can't you use Curve25519 under ECDSA?
>
> ---
> Reply to this email directly or view it on GitHub:
> https://github.com/pyca/cryptography/pull/878/files#r11355645