feat: Efficient ZM quotient computation

[ledwards2225]

Implements the efficient algorithm detailed in the ZM paper for computing the multilinear quotients $q_k$ that are fundamental to the ZM protocol. This replaces the original naive (and inefficient) implementation. This work does not address parallelism in all possible locations.

Checklist:

Remove the checklist to signal you've completed it. Enable auto-merge if the PR is ready to merge.

• If the pull request requires a cryptography review (e.g. cryptographic algorithm implementations) I have added the 'crypto' tag.
• I have reviewed my diff in github, line by line and removed unexpected formatting changes, testing logs, or commented-out code.
• Every change is related to the PR description.
• I have linked this pull request to relevant issues (if any exist).

[AztecBot]

Benchmark results

No metrics with a significant change found.

Detailed results

All benchmarks are run on txs on the Benchmarking contract on the repository. Each tx consists of a batch call to create_note and increment_balance, which guarantees that each tx has a private call, a nested private call, a public call, and a nested public call, as well as an emitted private note, an unencrypted log, and public storage read and write.

This benchmark source data is available in JSON format on S3 here.

Values are compared against data from master at commit 84f8db20 and shown if the difference exceeds 1%.

L2 block published to L1

Each column represents the number of txs on an L2 block published to L1.

Metric	8 txs	32 txs	128 txs
l1_rollup_calldata_size_in_bytes	45,444	179,588	716,132
l1_rollup_calldata_gas	222,924	867,836	3,449,864
l1_rollup_execution_gas	842,011	3,594,944	22,205,233
l2_block_processing_time_in_ms	1,997 (+2%)	7,574 (-1%)	29,612
note_successful_decrypting_time_in_ms	295	863	3,150 (+1%)
note_trial_decrypting_time_in_ms	97.0 (-2%)	71.0 (-3%)	135 (+1%)
l2_block_building_time_in_ms	13,186	52,375	209,261 (+1%)
l2_block_rollup_simulation_time_in_ms	11,868 (+1%)	47,143 (+1%)	188,191 (+1%)
l2_block_public_tx_process_time_in_ms	1,278 (-1%)	5,100	20,581 (+1%)

L2 chain processing

Each column represents the number of blocks on the L2 chain where each block has 16 txs.

Metric	5 blocks	10 blocks
node_history_sync_time_in_ms	21,512	42,436
note_history_successful_decrypting_time_in_ms	1,999	3,906 (-1%)
note_history_trial_decrypting_time_in_ms	122 (+2%)	143
node_database_size_in_bytes	1,629,983	1,096,689
pxe_database_size_in_bytes	27,188	54,187

Circuits stats

Stats on running time and I/O sizes collected for every circuit run across all benchmarks.

Circuit	circuit_simulation_time_in_ms	circuit_input_size_in_bytes	circuit_output_size_in_bytes
private-kernel-init	72.3	61,697	18,841
private-kernel-ordering	43.5	24,233	8,089
base-rollup	1,772	656,309	811
root-rollup	79.5 (+5%)	4,072	1,097
private-kernel-inner	53.3	81,504	18,841
public-kernel-private-input	41.6	41,455	18,841
public-kernel-non-first-iteration	26.6	41,497	18,841
merge-rollup	0.928 (+3%)	2,592	873

Miscellaneous

Transaction sizes based on how many contracts are deployed in the tx.

Metric	0 deployed contracts	1 deployed contracts
tx_size_in_bytes	8,723	27,240

[ledwards2225]

I think this is basically good to go in as-is but let's go ahead and just fully replace the old algorithm with the new one. We can simply delete the old method (and its test) and remove the _efficient tag from your new method.

[TohruKohrita]

@ledwards2225 I made the change. zeromorph.test.ccp is now identical to the initial file.

There is one issue. Build fails with the error "PCH file built from a different branch."

[TohruKohrita]

Luke and I discussed and reviewed in detail. I approve because I could not add him as a reviewer.