feat: public kernel in noir

[dan-aztec]

starting rewrite based off of #2740

literal cpp -> noir translation for first conversion

Checklist:

• 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:

• circuit_simulation_time_in_ms (public-kernel-private-input): 566 (+1278%)
• circuit_simulation_time_in_ms (public-kernel-non-first-iteration): 405 (+1472%)
• l2_block_building_time_in_ms (8): 20,706 (+56%)
• l2_block_building_time_in_ms (32): 82,201 (+57%)
• l2_block_building_time_in_ms (128): 327,182 (+56%)
• l2_block_public_tx_process_time_in_ms (8): 8,611 (+556%)
• l2_block_public_tx_process_time_in_ms (32): 34,182 (+564%)
• l2_block_public_tx_process_time_in_ms (128): 137,072 (+570%)
• note_trial_decrypting_time_in_ms (8): 7.89 (-92%)
• note_trial_decrypting_time_in_ms (32): 26.2 (-65%)

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 4623d916 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	868,124	3,449,492
l1_rollup_execution_gas	842,071	3,595,232	22,204,861
l2_block_processing_time_in_ms	2,025 (+2%)	7,751 (+2%)	30,147 (+1%)
note_successful_decrypting_time_in_ms	305 (+4%)	917 (+6%)	3,306 (+5%)
note_trial_decrypting_time_in_ms	⚠️ 7.89 (-92%)	⚠️ 26.2 (-65%)	132 (-1%)
l2_block_building_time_in_ms	⚠️ 20,706 (+56%)	⚠️ 82,201 (+57%)	⚠️ 327,182 (+56%)
l2_block_rollup_simulation_time_in_ms	12,051 (+1%)	47,884 (+2%)	189,607 (+1%)
l2_block_public_tx_process_time_in_ms	⚠️ 8,611 (+556%)	⚠️ 34,182 (+564%)	⚠️ 137,072 (+570%)

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	21,985 (+2%)	42,066 (-1%)
note_history_successful_decrypting_time_in_ms	2,052 (+1%)	3,924 (-2%)
note_history_trial_decrypting_time_in_ms	121	145 (-18%)
node_database_size_in_bytes	1,630,749	1,098,589
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	761	61,697	18,905
private-kernel-ordering	125 (-1%)	24,297	8,153
base-rollup	1,765	656,428	873 (+7%)
root-rollup	169	4,072	1,097
private-kernel-inner	786	81,568	18,905
public-kernel-private-input	⚠️ 566 (+1278%)	41,519	18,905
public-kernel-non-first-iteration	⚠️ 405 (+1472%)	41,561	18,905
merge-rollup	15.3 (+1%)	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

[kevaundray]

for reference: can you add a comment here to say why this has changed?

[kevaundray]

Left some comments