Enforce that Fr of Engine is the scalar for curve points
In bellman, I want to write:
```rust
pub struct Point<C: CurveProjective>(pub C);
impl<C: CurveProjective> Copy for Point<C> { }
impl<C: CurveProjective> Clone for Point<C> {
fn clone(&self) -> Point<C> {
*self
}
}
impl<C: CurveProjective> Group<C::Engine> for Point<C> {
fn group_zero() -> Self {
Point(C::zero())
}
fn group_mul_assign(&mut self, by: &C::Scalar) {
self.0.mul_assign(by.into_repr());
}
fn group_add_assign(&mut self, other: &Self) {
self.0.add_assign(&other.0);
}
fn group_sub_assign(&mut self, other: &Self) {
self.0.sub_assign(&other.0);
}
}
```
However, this doesn't typecheck because the compiler cannot know that the `Engine`'s `Fr` type (as dictated by the `Group` trait) is the same as the `Scalar` type of the `CurveProjective` point. This can be solved with a where bound over the trait (for now), but it is generally a good idea for this to be constrained in `pairing`.
Add "scale_by_cofactor".
Add a function for Affine types that multiplies point by the cofactor of the
group. If the points are in the group, they'll thus end up in the
correct subgroup.
note: this patch is already being tested with previous unittests.
note: this patch raises warning for unused functions and consts.
RELIC interop
Closes#2
RELIC has changed the G2 generator to match ours: 25aafecbec
RELIC will not have the same serialization as us.
One last difference is that RELIC conjugates the pairing result to account for the negative curve parameter. It doesn't matter for BLS curves but it's strictly more correct.
Sean Bowe
bmerge
Michele Orrù