FourQ ecc_mul_double implementation

[LINCKODE]

Implemented ecc_mul_double as DoubleScalarMult in curve.go .
Please advise me if the code does not adhere to project standards, I'm somewhat new to Go. 😅

[armfazh]

Hi @LINCKODE what is the use case for this function? and usually, the operation kG+lP is performed using a better algorithm than performing kG, lP, and then add these points.

[LINCKODE]

Thanks for the reply!
This function is required for verifying Schnorr signatures over FourQ.
You can see how it is being used in FourQLib's SchnorrQ_Verify function.
I see that FourQLib defines another way of performing this calculation, but that requires the use of endomorphisms, which I am not familiar with.
If you know of another way of doing this, I'd be happy to give it a go.

[armfazh]

See the implementation of CombinedMult for the P384 curve.
https://github.com/cloudflare/circl/blob/main/ecc/p384/p384opt.go#L135

This method is generic and agnostic to the use of endomorphisms.

[LINCKODE]

That looks interesting, doing both multiplications in one loop.
Ill have to look at this a bit closer to fully understand how it works, then I'll try to replicate it for FourQ.
Thanks for the hint!

[armfazh]

I'm gonna close this PR to keep our list short, happy to review when you push a new PR with the other algorithm.