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rhizomes/full: Both Prover and Verifier use polynomials in the Lagrange basis#2

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rhizomes/full: Both Prover and Verifier use polynomials in the Lagrange basis#2
armfazh wants to merge 2 commits intobaselinefrom
rhizomes/full

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@armfazh armfazh commented Sep 22, 2025

Both Prover and Verifier use polynomials in the Lagrange basis.

Prover sends the gadget polynomial in Lagrange basis, so gagdets have to be adapted to work in this representation.

Changes Test Vectors: Yes.

Notes:
This is a verbose version of a pull request to libprio-rs.
Changes are behind a feature flag to ease making comparisons.

Faster polynomial evaluation on flp.Query.
Polynomials are directly evaluated in the Lagrange basis.
Uses the batched algorithm from the rhizomes paper.
Both Prover and Verifier use polynomials in the Lagrange basis.
Prover sends the gadget polynomial in Lagrange basis,
so gagdets have to be adapted to work in this representation.

Changes test vectors.
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