Feat/fflonk

[ThomasPiellard]

Description

Implementation of shplonk
Implementation of fflonk (only the commitment)

Type of change

Please delete options that are not relevant.

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to not work as expected)
• This change requires a documentation update

How has this been tested?

Please describe the tests that you ran or implemented to verify your changes. Provide instructions so we can reproduce.

• see fflonk_test.go
• see shplonk_test_go

Checklist:

• I have performed a self-review of my code
• I have commented my code, particularly in hard-to-understand areas
• I have made corresponding changes to the documentation
• I have added tests that prove my fix is effective or that my feature works
• I did not modify files generated from templates
• golangci-lint does not output errors locally
• New and existing unit tests pass locally with my changes
• Any dependent changes have been merged and published in downstream modules

[ivokub]

As a note - we discussed with @ThomasPiellard about how to compute the n-ths roots of the input points. But in the field implementations we have, n is usually a power of two and we can do successive square roots.

[ivokub]

A few TODOs for another PR to improve the packages:

• instead of using []fr.Element for points in shplonk, we could define a structure a la struct Points { Pts []fr.Element, Shape shplonk.PointShape}. Depending on the shape of the points (they are roots of unity, or some known powers etc.) we can have different approaches for polynomial multiplication etc.

[ivokub]

Looks good now. There are still a few issues unresolved, but can currently leave as is as the package is experimental anyway. I'll create a new issue to gather the open issues (see #550)