chore: Add base rollup

[kevaundray]

Adds the base rollup circuit into Noir

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).

[kevaundray]

Noting this: for the small optimisation gain, the cpp code was almost unreadable. It makes sense to do it the non-optimal way first and then optimize

[kevaundray]

This is the main method that is left to implement, ideally we pull out that logic into a separate module named "indexed_merkle_tree" so it can be tested properly but probably okay to do what the cpp code is doing

[AztecBot]

Benchmark results

Metrics with a significant change:

• note_trial_decrypting_time_in_ms (8): 3.00 (-97%)
• note_trial_decrypting_time_in_ms (128): 211 (+57%)

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 d707d4e3 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	222,828	868,172	3,449,480
l1_rollup_execution_gas	841,915	3,595,280	22,204,849
l2_block_processing_time_in_ms	2,006 (+1%)	7,594	29,764
note_successful_decrypting_time_in_ms	298	882 (-1%)	3,216
note_trial_decrypting_time_in_ms	⚠️ 3.00 (-97%)	90.0 (-7%)	⚠️ 211 (+57%)
l2_block_building_time_in_ms	13,145 (-1%)	52,414 (-1%)	209,631
l2_block_rollup_simulation_time_in_ms	11,812 (-1%)	47,091	188,339
l2_block_public_tx_process_time_in_ms	1,295	5,188 (-1%)	20,794 (-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	21,778	42,554
note_history_successful_decrypting_time_in_ms	2,041 (+1%)	4,013 (+2%)
note_history_trial_decrypting_time_in_ms	120	144 (+1%)
node_database_size_in_bytes	1,632,126	1,097,958
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	773	61,697	18,905
private-kernel-ordering	124 (+1%)	24,297	8,153
base-rollup	1,772	656,311	814
root-rollup	81.1 (+5%)	4,072	1,097
private-kernel-inner	789	81,568	18,905
public-kernel-private-input	41.7	41,519	18,841
public-kernel-non-first-iteration	26.5	41,497	18,841
merge-rollup	0.899 (-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	8,787	27,548

[Maddiaa0]

superceded by #3257