Our current reference string is in monomial form, having one in lagrange-base form would singificantly improve prover times.
In Barretenberg, our current reference string is interacted with via the io class.
The SRS is contained in srs_db/transcript.dat. It is stored in a raw binary format, with group elements packed into adjacent 64 byte chunks.
The transcript.dat file contains a 'manifest' object at the start of the file, which contains basic details like the SRS size.
The first task would be to use this SRS to produce one in Lagrange-base form, using our polynomial arithmetic and elliptic curve arithmetic libraries.
The first milestone would be to generate a small in-memory Lagrange-base SRS from a monomial SRS, and to validate this via a unit test.
Once the core algorithm is working, the second task would be to create a function that will take a transcript.dat file, produce a lagrange-base form,
and write it out as transcript_lagrange_base.dat or similar.
The second milsestone would be to write passing tests that validate the correctness of this new file.
Once we have transcript_lagrange_base.dat, we can integrate it into our prover algorithm. We have a helper class, ReferenceString, in waffle/reference_string.hpp,
that we use to pre-fetch our SRS and perform some precomputations on it for our Pippenger algorithm.
It currently has a container, monomials, that stores our monomial-form SRS. We would need a second container,
lagrange_base, that contains the lagrange-base variant.
Note that, until we also have produced a variant of the SRS in coset lagrange base form, we cannot remove the monomial basis SRS.
In the constructor of ReferenceString, we need a method that loads up the lagrange-base SRS and writes it into the newly created lagrange_base container.
The third milestone would be to validate the correctness of this via passing unit tests.
The final task would be to use the lagrange-base SRS in prover.tcc, when computing all of our commitments except the quotient polynomial.
TODO. This seems non-trivial due to the fact that we split T(X) up into 4 sub-commitments. This is easy to do in monomial form,
but seems harder to do if our SRS is in coset-lagrange-base form.