Normalize NistP256 signature

[x87-va]

I'm trying to convert signature to low S, but got compilation error.

Dependencies used:

ecdsa           = "0.12"
elliptic-curve  = "0.10"
p256            = "0.9"

Error:

let signature = Signature::<p256::NistP256>::from_der(&data)?;
signature.normalize_s()?;
^^^^^^^^^^^ the trait `NormalizeLow` is not implemented for `Scalar`

How to fix it? What exact type need to implement trait NormalizeLow?

[tarcieri]

It's not currently supported, although wouldn't be terribly hard to add.

We'd need to add a constant similar to k256 that is the modulus divided by two (or right shifted by one, take your pick) and an impl of NormalizeLow.

[x87-va]

Ok, I've implemented it with some amount copying from k256/src/arithmetic/scalar/scalar_4x64.rs and k256/src/arithmetic/util.rs. Seems like we need separate crate for such arithmetics.

[tarcieri]

The crypto-bigint crate is designed to do that, however it's not yet fully integrated into either k256 or p256. That is to say it's used for modeling the Curve::ORDER, but the scalar arithmetic is still implemented on a crate-by-crate basis.

We'd also need to add const fn support for shr to support dividing by two (we presently don't have any other division functionality)

[tarcieri]

FYI, I just updated k256 to use a crypto_bigint::UInt to represent the curve order.

It's now using const fn to calculate FRAC_MODULUS_2 at compile time:

https://github.com/RustCrypto/elliptic-curves/blob/ed9b745/k256/src/arithmetic/scalar/scalar_4x64.rs#L22

[x87-va]

I fixed FRAC_MODULUS_2 using. Please review RustCrypto/elliptic-curves#433

[tarcieri]

ecdsa::Signature<NistP256>>::normalize_s should now work (or at least, will after the next release) as the method is now generically implemented for all curves with ScalarArithmetic: #393