feat: fold batching challenge (alpha)

[maramihali]

This PR provides an initial version of folding the subrelation batching challenge alpha. The future plan is to have one alpha per subrelation to ensure the degree of the combiner stays reasonable, to be handled in a future PR . and so, for now, we use one alpha per Instance, fold them and use the same folded alpha to batch each subrelation in the combiner.

I separated some code between sumcheck and protogalaxy because supporting both was starting to make it too complicated. Also alpha is now passed to the sumcheck protocol rather than produced inside the protocol to facilitate extracting and including as part of the instances.

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

Metrics with a significant change:

• note_trial_decrypting_time_in_ms (8): 4.02 (-96%)

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 0dc2d586 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	222,984	868,160	3,449,456
l1_rollup_execution_gas	842,071	3,595,268	22,204,825
l2_block_processing_time_in_ms	2,039 (+2%)	7,741 (+2%)	30,245 (+1%)
note_successful_decrypting_time_in_ms	302 (+2%)	885 (+1%)	3,229 (+1%)
note_trial_decrypting_time_in_ms	⚠️ 4.02 (-96%)	95.7 (+10%)	141 (-1%)
l2_block_building_time_in_ms	20,727	82,241 (+1%)	328,155 (+1%)
l2_block_rollup_simulation_time_in_ms	12,033	47,707 (+1%)	189,745 (+1%)
l2_block_public_tx_process_time_in_ms	8,649	34,393	137,885

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	22,355 (+2%)	43,209 (+1%)
note_history_successful_decrypting_time_in_ms	2,140 (+5%)	4,227 (+6%)
note_history_trial_decrypting_time_in_ms	126	158 (+1%)
node_database_size_in_bytes	1,632,027	1,097,114 (-1%)
pxe_database_size_in_bytes	29,748	59,307

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	778 (+1%)	61,697	18,905
private-kernel-ordering	129 (+2%)	24,297	8,153
base-rollup	1,753	656,428	873
root-rollup	177 (+3%)	4,072	1,097
private-kernel-inner	804 (+1%)	81,568	18,905
public-kernel-private-input	578 (+1%)	41,519	18,905
public-kernel-non-first-iteration	415 (+2%)	41,561	18,905
merge-rollup	15.7 (+2%)	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	8,787	27,547

[codygunton]

Looks fine to continue onward, only added small comments in the review, please address and merge.

[codygunton]

Will you leave a comment explaining this formula for the length? Why this sum?