elliptic_curve: add BatchInvert and BatchNormalize traits

[ycscaly]

Addresses RustCrypto/elliptic-curves#943

[ycscaly]

Also, I'd like to write tests but I couldn't as dev::Scalar doesn't implement Invert, and importing k256 doesn't work. What should I do

[ycscaly]

@tarcieri what do you think of this design? this allows for both a const-generic implementation and a dynamically alloced one while reusing the code. If you like it, I'd like to do the same with lincomb

[tarcieri]

I'm reconsidering whether InvertBatch being a trait is a good idea. It seems like it could just be two free functions, e.g.:

pub fn invert_batch_generic<T, const N: usize>(field_elements: &[T; N]) -> CtOption<[T; N]> {
where
    T: Invert<Output = CtOption<Self>>
        + Mul<T, Output = T>
        + Copy
        + Default
        + ConditionallySelectable,

It just seems a little weird that there's invert_batch which is gated on the trait by alloc, but it's really the implementation that requires alloc.

[tarcieri]

As another option: they could potentially be provided methods on the Invert trait

[ycscaly]

As another option: they could potentially be provided methods on the Invert trait

Can't do that, as the output from the Invert trait is a generic type Output, I need to work with CtOption<Self>

[tarcieri]

This looks good now, although I'd like to see RustCrypto/elliptic-curves#971 green before merging

[tarcieri]

What issues did you run into with the AsRef bound? It seems handy for writing generic code

[ycscaly]

What issues did you run into with the AsRef bound? It seems handy for writing generic code

The Rust compiler complained that it didn't provided it. We can try to fight it if its important

[ycscaly]

Thanks!