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

[github-actions]

📦 github.com/consensys/gnark-crypto/ecc/bls12-381/fflonk
❌ TestGetIthRootOne 0s

    fflonk_test.go:140: 
        	Error Trace:	/home/runner/work/gnark-crypto/gnark-crypto/ecc/bls12-381/fflonk/fflonk_test.go:140
        	Error:      	An error is expected but got nil.
        	Test:       	TestGetIthRootOne

📦 github.com/consensys/gnark-crypto/ecc/bls24-315/fflonk
❌ TestGetIthRootOne 0s

    fflonk_test.go:140: 
        	Error Trace:	/home/runner/work/gnark-crypto/gnark-crypto/ecc/bls24-315/fflonk/fflonk_test.go:140
        	Error:      	An error is expected but got nil.
        	Test:       	TestGetIthRootOne

📦 github.com/consensys/gnark-crypto/ecc/bw6-761/fflonk
❌ TestGetIthRootOne 0s

    fflonk_test.go:140: 
        	Error Trace:	/home/runner/work/gnark-crypto/gnark-crypto/ecc/bw6-761/fflonk/fflonk_test.go:140
        	Error:      	An error is expected but got nil.
        	Test:       	TestGetIthRootOne

[ivokub]

I think in general looks good. It was quite straightforward to follow shplonk part, but I'm not sure about fflonk. I think lets go through the paper and implementation together to make sense. The utility methods all look good though, it is only the BatchOpen and BatchVerify methods.

Some notes:

• I think it would be better to use the polynomial package. It already has some methods implemented what we need and makes it imo relevant. Otherwise we copy-paste methods all over. And I think it also makes it nicer if we have []polynomial.Polynomial instead of [][]fr.Element etc.
• I think we can also add Points struct as we disccussed in case in the future we want to have some information about the strcture of the points. This would allow to have some optimizations when doing poly-poly multiplication

A few todos on my side what I would like to add:

• add package examples so that the users have an example to copy-paste the correct usage. The example tests are also in CI, which make it a good documentation source.
• I'll also want to revisit package documentation a bit to make it better in the doc site (pkg.go.dev), e.g. inline links etc.

[ivokub]

@ThomasPiellard - I don't touch the branch currently - I'll add the documentation and examples after you have finished.

[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.