docs: Add transaction section to yellow paper

[spalladino]

Fixes #3089

Adds TODOs for #3417

[AztecBot]

Benchmark results

Metrics with a significant change:

• note_trial_decrypting_time_in_ms (32): 69.3 (+126%)

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 d356bac7 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	222,900	868,100	3,447,980
l1_rollup_execution_gas	841,987	3,595,208	22,203,349
l2_block_processing_time_in_ms	2,055 (+1%)	7,807 (+1%)	31,923 (+1%)
note_successful_decrypting_time_in_ms	318	941 (+4%)	3,572 (+7%)
note_trial_decrypting_time_in_ms	30.1 (+9%)	⚠️ 69.3 (+126%)	199
l2_block_building_time_in_ms	18,915	74,506 (-2%)	299,304 (+1%)
l2_block_rollup_simulation_time_in_ms	15,336	60,441 (-2%)	242,786 (+1%)
l2_block_public_tx_process_time_in_ms	3,525	13,915 (+1%)	55,948 (+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	22,843	44,510
note_history_successful_decrypting_time_in_ms	2,136 (-6%)	4,259 (-3%)
note_history_trial_decrypting_time_in_ms	162 (+1%)	351 (-2%)
node_database_size_in_bytes	3,306,154	3,648,191
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	199	43,077	20,441
private-kernel-ordering	115	25,833	9,689
base-rollup	2,539	659,500	873
root-rollup	88.7 (-4%)	4,072	1,097
private-kernel-inner	260	64,484	20,441
public-kernel-private-input	172	25,203	20,441
public-kernel-non-first-iteration	168 (-1%)	25,245	20,441
merge-rollup	12.9 (+17%)	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	10,323	25,938