mul_mod does not work on all provided types

[weaversa]

I appreciate the addition of mul_mod in the release candidate 0.6.0. So, thank you!

While exploring this new function I received errors when using certain types. For example:

use crypto_bigint::{U576, NonZero};

pub fn main() {

    let p = NonZero::new(U576::from(3u32)).unwrap();
    let a = U576::from(1u32);
    let b = U576::from(1u32);

    a.mul_mod(&b, &p);
}

gives the following error when building:

the trait bound `Uint<9>: crypto_bigint::Concat` is not satisfied
...
 |     a.mul_mod(&b, &p);
 |       ^^^^^^^ the trait `ConcatMixed` is not implemented for `Uint<9>`, which is required by `Uint<9>: crypto_bigint::Concat`

However, swapping U576 for U256 builds w/out error. I have not tested against other types.

[tarcieri]

cc @andrewwhitehead

I would also expect this to work. The ConcatMixed impls are written by these macros:

https://github.com/RustCrypto/crypto-bigint/blob/78f70ae/src/uint.rs#L425-L445

I'm not sure exactly what would need to change to be able to support this offhand.

[fjarri]

I think that only defines splitting U576 in various proportions, but not joining two U576 which is what you need for multiplication.

Also I wonder if we can get rid of the Concat bound for multiplication by just using two separate Uint of single size for storage.

[andrewwhitehead]

The bound appears to be required because MontyForm::new uses rem of a double-wide UInt in its calculation of R2, since rem_wide is not defined (only rem_wide_vartime).

I think Concat of U576 might be gated on the extra-sizes feature.