Feat/plonk update

[ThomasPiellard]

Description

Updating plonk to the latest version https://eprint.iacr.org/archive/2019/953/1660839633.pdf

[wait for linea to redeploy the contract before merging to avoid incompatibility between prover/verifier]

• The folded quotient is appended to the linearisation polynomial
• the opening of the linearisation polynomial corresponds to the constant term of the algebraic relation
• one less opening to do (since the quotient is now opened throughout the opening of the linearisation polynomial)
• no more modular inverse to compute in the algebraic check to verify a plonk proof

Type of change

• [ ] Bug fix (non-breaking change which fixes an issue)
• [x] 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?

Test suite for plonk unchanged

benchmark

• for native chain bls12-377 -> bw6-761 we go from 319k to 312k constraints
• for non native (bw6 -> bn254) the number of constraints is unchanged -> something might be off

Checklist:

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