Integrate the compression functionality into the prover and network crates

[dorebell]

Building from PR #28, we need to add features to the nexus-zkvm prover and network crates to use the compression features in the supernova repo.

PR #28 adds a compressible option to the parameter generation methods which changes the way Nova's public parameters are set up: instead of sampling them, they are processed using a polynomial commitment scheme SRS which is loaded from file. This is required if we want to use compression later for the proof (we might want to make this behavior the default at some point, but it's optional for now to allow flexibility with testing and benchmarking).

Here's a rough outline of what needs to be done to complete this issue:

• Add a compress command to the top-level CLI (/the network API). This should do two tasks:
  • Handle the parameter setup and r1cs matrix preprocessing for Spartan, using the SNARK::setup() function from supernova. This takes both the Nova public parameters and the PCS's SRS as input, and both of these should be read from file, and creates a SNARKKey object, which should be saved to file.
  • read a proof from file, along with the Spartan parameters generated in the above step, then compress it using the SNARK::compress() function from supernova. Save the result to file: e.g. as an enum which is either a PCDNode or a CompressedPCDProof.
• Add logic to the prover's verify command to detect whether the proof is compressed or not, and if so, verify it using SNARK::verify(). This uses the SNARKKey object created in the first step above.

Note that only the parallel (PCD) version of Nova supports compression right now.

Note: (as of 1.4.24) we're in the process of merging together the supernova, spartan, and nexus-zkvm repos, and this will be cleaner to work on once that is completed. At the moment, the integration with spartan is done inside of supernova's PR #33, so this is the version of supernova that we need to use here. The integration is behind the spartan feature-flag. Working with the various private repos at the same time causes some headaches. In particular, the version of the committed-relaxed-spartan repo used here needs to match the version used in supernova. We don't yet have the ssh keys for the spartan repo saved in the secret store here, which means that for this to build, we need to point the Cargo.toml here to rev 92e884c of supernova rather than the head of the dorebell-spartan-integration branch. Once the repos (and the integration pr) are merged, we won't need to worry about this anymore. However, it should be safe to work on this issue locally before we finish merging if you can get it to build.

[linear]

NEX-54 Integrate the compression functionality into the prover and network crates

Upgrade the CLI tools to support compression with appropriate flags