feat: publish transaction_fee (AztecProtocol#6126)

This includes the transaction_fee in the TxEffects which are published to L1. The transaction_fee is verified in the base rollup.

l1-contracts/src/core/libraries/decoders/TxsDecoder.sol

@@ -21,18 +21,19 @@ import {Hash} from "../Hash.sol";
  *  | 0x0                                                                                       | 0x4        | len(numTxs) (denoted t)
  *  |                                                                                           |            | TxEffect 0 {
  *  | 0x4                                                                                       | 0x1        |   revertCode
- *  | 0x5                                                                                       | 0x1        |   len(newNoteHashes) (denoted b)
- *  | 0x5 + 0x1                                                                                 | b * 0x20   |   newNoteHashes
- *  | 0x5 + 0x1 + b * 0x20                                                                      | 0x1        |   len(newNullifiers) (denoted c)
- *  | 0x5 + 0x1 + b * 0x20 + 0x1                                                                | c * 0x20   |   newNullifiers
- *  | 0x5 + 0x1 + b * 0x20 + 0x1 + c * 0x20                                                     | 0x1        |   len(newL2ToL1Msgs) (denoted d)
- *  | 0x5 + 0x1 + b * 0x20 + 0x1 + c * 0x20 + 0x1                                               | d * 0x20   |   newL2ToL1Msgs
- *  | 0x5 + 0x1 + b * 0x20 + 0x1 + c * 0x20 + 0x1 + d * 0x20                                    | 0x1        |   len(newPublicDataWrites) (denoted e)
- *  | 0x5 + 0x1 + b * 0x20 + 0x1 + c * 0x20 + 0x1 + d * 0x20 + 0x01                             | e * 0x40   |   newPublicDataWrites
- *  | 0x5 + 0x1 + b * 0x20 + 0x1 + c * 0x20 + 0x1 + d * 0x20 + 0x01 + e * 0x40                  | 0x04       |   byteLen(newEncryptedLogs) (denoted f)
- *  | 0x5 + 0x1 + b * 0x20 + 0x1 + c * 0x20 + 0x1 + d * 0x20 + 0x01 + e * 0x40 + 0x4            | f          |   newEncryptedLogs
- *  | 0x5 + 0x1 + b * 0x20 + 0x1 + c * 0x20 + 0x1 + d * 0x20 + 0x01 + e * 0x40 + 0x4 + f        | 0x04       |   byteLen(newUnencryptedLogs) (denoted g)
- *  | 0x5 + 0x1 + b * 0x20 + 0x1 + c * 0x20 + 0x1 + d * 0x20 + 0x01 + e * 0x40 + 0x4 + f + 0x4  | g          |   newUnencryptedLogs
+ *  | 0x5                                                                                       | 0x20       |   transactionFee
+ *  | 0x25                                                                                      | 0x1        |   len(newNoteHashes) (denoted b)
+ *  | 0x25 + 0x1                                                                                | b * 0x20   |   newNoteHashes
+ *  | 0x25 + 0x1 + b * 0x20                                                                     | 0x1        |   len(newNullifiers) (denoted c)
+ *  | 0x25 + 0x1 + b * 0x20 + 0x1                                                               | c * 0x20   |   newNullifiers
+ *  | 0x25 + 0x1 + b * 0x20 + 0x1 + c * 0x20                                                    | 0x1        |   len(newL2ToL1Msgs) (denoted d)
+ *  | 0x25 + 0x1 + b * 0x20 + 0x1 + c * 0x20 + 0x1                                              | d * 0x20   |   newL2ToL1Msgs
+ *  | 0x25 + 0x1 + b * 0x20 + 0x1 + c * 0x20 + 0x1 + d * 0x20                                   | 0x1        |   len(newPublicDataWrites) (denoted e)
+ *  | 0x25 + 0x1 + b * 0x20 + 0x1 + c * 0x20 + 0x1 + d * 0x20 + 0x01                            | e * 0x40   |   newPublicDataWrites
+ *  | 0x25 + 0x1 + b * 0x20 + 0x1 + c * 0x20 + 0x1 + d * 0x20 + 0x01 + e * 0x40                 | 0x04       |   byteLen(newEncryptedLogs) (denoted f)
+ *  | 0x25 + 0x1 + b * 0x20 + 0x1 + c * 0x20 + 0x1 + d * 0x20 + 0x01 + e * 0x40 + 0x4           | f          |   newEncryptedLogs
+ *  | 0x25 + 0x1 + b * 0x20 + 0x1 + c * 0x20 + 0x1 + d * 0x20 + 0x01 + e * 0x40 + 0x4 + f       | 0x04       |   byteLen(newUnencryptedLogs) (denoted g)
+ *  | 0x25 + 0x1 + b * 0x20 + 0x1 + c * 0x20 + 0x1 + d * 0x20 + 0x01 + e * 0x40 + 0x4 + f + 0x4 | g          |   newUnencryptedLogs
  *  |                                                                                           |            | },
  *  |                                                                                           |            | TxEffect 1 {
  *  |                                                                                           |            |   ...
@@ -45,6 +46,7 @@ import {Hash} from "../Hash.sol";
 library TxsDecoder {
   struct ArrayOffsets {
     uint256 revertCode;
+    uint256 transactionFee;
     uint256 noteHash;
     uint256 nullifier;
     uint256 l2ToL1Msgs;
@@ -90,6 +92,7 @@ library TxsDecoder {
          * Compute the leaf to insert.
          * Leaf_i = (
          *    revertCode,
+         *    transactionFee,
          *    newNoteHashesKernel,
          *    newNullifiersKernel,
          *    newL2ToL1MsgsKernel,
@@ -105,6 +108,10 @@ library TxsDecoder {
         offsets.revertCode = offset;
         offset += 0x1;
 
+        // Transaction Fee
+        offsets.transactionFee = offset;
+        offset += 0x20;
+
         // Note hashes
         uint256 count = read1(_body, offset);
         offset += 0x1;
@@ -143,7 +150,10 @@ library TxsDecoder {
         // Insertions are split into multiple `bytes.concat` to work around stack too deep.
         vars.baseLeaf = bytes.concat(
           // pad the revert code to 32 bytes to match the hash preimage
-          sliceAndPadLeft(_body, offsets.revertCode, 0x1, 0x20),
+          bytes.concat(
+            sliceAndPadLeft(_body, offsets.revertCode, 0x1, 0x20),
+            slice(_body, offsets.transactionFee, 0x20)
+          ),
           bytes.concat(
             sliceAndPadRight(
               _body,
@@ -179,7 +189,7 @@ library TxsDecoder {
       // We pad base leaves with hashes of empty tx effect.
       for (uint256 i = numTxEffects; i < vars.baseLeaves.length; i++) {
         // Value taken from tx_effect.test.ts "hash of empty tx effect matches snapshot" test case
-        vars.baseLeaves[i] = hex"0071f7630d28ce02cc1ca8b15c44953f84a39e1478445395247ae04dfa213c0e";
+        vars.baseLeaves[i] = hex"00822c2cdfbc7a6e5f4dd355251f4dfc9af1b1a64152464b9b83c5007eeed0f3";
       }
     }
 

l1-contracts/test/fixtures/empty_block_0.json

@@ -8,23 +8,23 @@
     "l2ToL1Messages": []
   },
   "block": {
-    "archive": "0x080ba94e0599e43b20d1d5dd297f12eee1ab3b74fc07c4b6e505d0d54dc4c878",
+    "archive": "0x092e7b5812f430a11de252abb67ba28c237b78aa717cf67a0a7d13ac229cb476",
     "body": "0x00000000",
-    "txsEffectsHash": "0x00df6b1c97b9e01113fa0363d9ff71c85addc74e92b22d433b2fb082d2493896",
+    "txsEffectsHash": "0x0041e05321b3603fcde9458e9c664d50a08187c7fdeeb6a1cf39932849df577c",
     "decodedHeader": {
       "contentCommitment": {
         "inHash": "0x00089a9d421a82c4a25f7acbebe69e638d5b064fa8a60e018793dcb0be53752c",
         "outHash": "0x0007638bb56b6dda2b64b8f76841114ac3a87a1820030e2e16772c4d294879c3",
         "txTreeHeight": 1,
-        "txsEffectsHash": "0x00df6b1c97b9e01113fa0363d9ff71c85addc74e92b22d433b2fb082d2493896"
+        "txsEffectsHash": "0x0041e05321b3603fcde9458e9c664d50a08187c7fdeeb6a1cf39932849df577c"
       },
       "globalVariables": {
         "blockNumber": 1,
         "chainId": 31337,
         "timestamp": 0,
         "version": 1,
-        "coinbase": "0xc1e85ff1bdb95e08537b887b0f371638903460e3",
-        "feeRecipient": "0x0cb7735e3f0a0df7ec2303f5817cec5ad40812a970544fc1fc2c310eeb3988cc",
+        "coinbase": "0xb35cee29ec094ab8b8be05b158e0bf50d2432952",
+        "feeRecipient": "0x2e318034e3a2c52d895e8af8e14f8b95c5e49c461d12b4657ab8c85539013b02",
         "gasFees": {
           "feePerDaGas": 0,
           "feePerL2Gas": 0
@@ -55,8 +55,8 @@
         }
       }
     },
-    "header": "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",
-    "publicInputsHash": "0x000cae072f9ae6a94c6c642594e0985c0df681cfa951939a901291b8e569bc2c",
+    "header": "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",
+    "publicInputsHash": "0x00ae98c27e880d898c1dd0cdb9b2da88de6719f7b3bf0707a4f13381ac22dce8",
     "numTxs": 0
   }
 }

l1-contracts/test/fixtures/empty_block_1.json

@@ -8,31 +8,31 @@
     "l2ToL1Messages": []
   },
   "block": {
-    "archive": "0x12b17b38f46254c7143bd35e6348dc09cc8833d6b34e192cd00e243a3bbe562f",
+    "archive": "0x0a195ab304da7c6cf916ff7a40cb570f728481aac14b2d5df776c5306d0671f5",
     "body": "0x00000000",
-    "txsEffectsHash": "0x00df6b1c97b9e01113fa0363d9ff71c85addc74e92b22d433b2fb082d2493896",
+    "txsEffectsHash": "0x0041e05321b3603fcde9458e9c664d50a08187c7fdeeb6a1cf39932849df577c",
     "decodedHeader": {
       "contentCommitment": {
         "inHash": "0x00089a9d421a82c4a25f7acbebe69e638d5b064fa8a60e018793dcb0be53752c",
         "outHash": "0x0007638bb56b6dda2b64b8f76841114ac3a87a1820030e2e16772c4d294879c3",
         "txTreeHeight": 1,
-        "txsEffectsHash": "0x00df6b1c97b9e01113fa0363d9ff71c85addc74e92b22d433b2fb082d2493896"
+        "txsEffectsHash": "0x0041e05321b3603fcde9458e9c664d50a08187c7fdeeb6a1cf39932849df577c"
       },
       "globalVariables": {
         "blockNumber": 2,
         "chainId": 31337,
-        "timestamp": 1714163483,
+        "timestamp": 1714575319,
         "version": 1,
-        "coinbase": "0xc1e85ff1bdb95e08537b887b0f371638903460e3",
-        "feeRecipient": "0x0cb7735e3f0a0df7ec2303f5817cec5ad40812a970544fc1fc2c310eeb3988cc",
+        "coinbase": "0xb35cee29ec094ab8b8be05b158e0bf50d2432952",
+        "feeRecipient": "0x2e318034e3a2c52d895e8af8e14f8b95c5e49c461d12b4657ab8c85539013b02",
         "gasFees": {
           "feePerDaGas": 0,
           "feePerL2Gas": 0
         }
       },
       "lastArchive": {
         "nextAvailableLeafIndex": 2,
-        "root": "0x080ba94e0599e43b20d1d5dd297f12eee1ab3b74fc07c4b6e505d0d54dc4c878"
+        "root": "0x092e7b5812f430a11de252abb67ba28c237b78aa717cf67a0a7d13ac229cb476"
       },
       "stateReference": {
         "l1ToL2MessageTree": {
@@ -55,8 +55,8 @@
         }
       }
     },
-    "header": "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",
-    "publicInputsHash": "0x00f4dc87aadb7c9e401412f285d770460dcd43d2baba6b7cceecde9b86361663",
+    "header": "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",
+    "publicInputsHash": "0x00dde76c303e0e4d99151f2178e0b6cca10687f5a956084cae2fe6d320e3b9ec",
     "numTxs": 0
   }
 }

noir-projects/noir-protocol-circuits/crates/rollup-lib/src/base/base_rollup_inputs.nr

@@ -107,7 +107,8 @@ impl BaseRollupInputs {
         // Calculate the tx effects hash of the transaction
         let tx_effects_hash = compute_tx_effects_hash(
             self.kernel_data.public_inputs.end,
-            self.kernel_data.public_inputs.revert_code
+            self.kernel_data.public_inputs.revert_code,
+            self.kernel_data.public_inputs.compute_transaction_fee()
         );
         let out_hash = compute_kernel_out_hash(self.kernel_data.public_inputs.end);
 

noir-projects/noir-protocol-circuits/crates/rollup-lib/src/components.nr

@@ -124,13 +124,19 @@ pub fn compute_txs_effects_hash(previous_rollup_data: [PreviousRollupData; 2]) -
     )
 }
 
-global TX_EFFECTS_HASH_INPUT_FIELDS = 197;
+global TX_EFFECTS_HASH_INPUT_FIELDS = 198;
 
 // Computes the tx effects hash for a base rollup (a single transaction)
 // TODO(Alvaro): This is too slow for brillig without the array optimization
-pub fn compute_tx_effects_hash(combined: CombinedAccumulatedData, revert_code: u8) -> Field {
+pub fn compute_tx_effects_hash(
+    combined: CombinedAccumulatedData,
+    revert_code: u8,
+    transaction_fee: Field
+) -> Field {
     // Compute tx effect hash
     // Consist of
+    // 1 field for revert code
+    // 1 field for transaction fee
     // MAX_NEW_NOTE_HASHES_PER_TX fields for note hashes
     // MAX_NEW_NULLIFIERS_PER_TX fields for nullifiers
     // 2 l2 -> l1 messages -> 2 fields
@@ -153,6 +159,9 @@ pub fn compute_tx_effects_hash(combined: CombinedAccumulatedData, revert_code: u
     txs_effects_hash_input[offset] = revert_code as Field;
     offset += 1;
 
+    txs_effects_hash_input[offset] = transaction_fee;
+    offset += 1;
+
     for j in 0..MAX_NEW_NOTE_HASHES_PER_TX {
         txs_effects_hash_input[offset + j] = new_note_hashes[j];
     }
@@ -200,7 +209,9 @@ pub fn compute_tx_effects_hash(combined: CombinedAccumulatedData, revert_code: u
 #[test]
 fn consistent_TX_EFFECTS_HASH_INPUT_FIELDS() {
     // 1 for revert_code
+    // 1 for transaction_fee
     let expected_size = 1
+        + 1
         + MAX_NEW_NOTE_HASHES_PER_TX
         + MAX_NEW_NULLIFIERS_PER_TX
         + MAX_PUBLIC_DATA_UPDATE_REQUESTS_PER_TX * 2

noir-projects/noir-protocol-circuits/crates/types/src/abis/kernel_circuit_public_inputs/kernel_circuit_public_inputs.nr

@@ -1,9 +1,9 @@
 use crate::{
     abis::{
     accumulated_data::CombinedAccumulatedData, combined_constant_data::CombinedConstantData,
-    validation_requests::RollupValidationRequests
+    validation_requests::RollupValidationRequests, gas::Gas
 },
-    partial_state_reference::PartialStateReference
+    partial_state_reference::PartialStateReference, traits::Empty
 };
 use crate::mocked::AggregationObject;
 
@@ -15,3 +15,68 @@ struct KernelCircuitPublicInputs {
     start_state: PartialStateReference,
     revert_code: u8,
 }
+
+impl KernelCircuitPublicInputs {
+
+    pub fn compute_transaction_fee(self) -> Field {
+        let gas_fees = self.constants.global_variables.gas_fees;
+        let inclusion_fee = self.constants.tx_context.gas_settings.inclusion_fee;
+        inclusion_fee + self.end.gas_used.compute_fee(gas_fees)
+    }
+}
+
+impl Empty for KernelCircuitPublicInputs {
+    fn empty() -> Self {
+        KernelCircuitPublicInputs {
+            aggregation_object: AggregationObject::empty(),
+            rollup_validation_requests: RollupValidationRequests::empty(),
+            end: CombinedAccumulatedData::empty(),
+            constants: CombinedConstantData::empty(),
+            start_state: PartialStateReference::empty(),
+            revert_code: 0,
+        }
+    }
+}
+
+mod tests {
+    use crate::abis::{
+        kernel_circuit_public_inputs::kernel_circuit_public_inputs::KernelCircuitPublicInputs,
+        accumulated_data::CombinedAccumulatedData, combined_constant_data::CombinedConstantData,
+        validation_requests::RollupValidationRequests, gas::Gas, gas_fees::GasFees
+    };
+    use crate::partial_state_reference::PartialStateReference;
+    use crate::mocked::AggregationObject;
+
+    #[test]
+    unconstrained fn empty_has_zero_gas_and_fee() {
+        let empty = KernelCircuitPublicInputs::empty();
+        assert_eq(empty.compute_transaction_fee(), 0);
+    }
+
+    #[test]
+    unconstrained fn non_empty_gas_and_fee() {
+        let mut inputs = KernelCircuitPublicInputs {
+            aggregation_object: AggregationObject::empty(),
+            rollup_validation_requests: RollupValidationRequests::empty(),
+            end: CombinedAccumulatedData::empty(),
+            constants: CombinedConstantData::empty(),
+            start_state: PartialStateReference::empty(),
+            revert_code: 0
+        };
+
+        inputs.end.gas_used = Gas {
+            da_gas: 10,
+            l2_gas: 20
+        };
+
+        inputs.constants.tx_context.gas_settings.inclusion_fee = 42;
+
+        inputs.constants.global_variables.gas_fees = GasFees {
+            fee_per_da_gas: 2,
+            fee_per_l2_gas: 3
+        };
+
+        let transaction_fee = inputs.compute_transaction_fee();
+        assert_eq(transaction_fee, 42 + 2 * 10 + 3 * 20);
+    }
+}

noir-projects/noir-protocol-circuits/crates/types/src/abis/validation_requests/rollup_validation_requests.nr

@@ -1,7 +1,16 @@
-use crate::{abis::max_block_number::MaxBlockNumber};
+use crate::{abis::max_block_number::MaxBlockNumber, traits::Empty};
 
 // These are validation requests that cannot be fulfilled in the current context (private or public), and must be 
 // instead forwarded to the rollup for it to take care of them.
 struct RollupValidationRequests {
     max_block_number: MaxBlockNumber,
 }
+
+impl Empty for RollupValidationRequests {
+    fn empty() -> Self {
+        RollupValidationRequests {
+            max_block_number: MaxBlockNumber::empty(),
+        }
+    }
+}
+

yarn-project/circuit-types/src/tx/processed_tx.ts

@@ -162,6 +162,7 @@ export function makeEmptyProcessedTx(header: Header, chainId: Fr, version: Fr):
 export function toTxEffect(tx: ProcessedTx): TxEffect {
   return new TxEffect(
     tx.data.revertCode,
+    tx.data.transactionFee,
     tx.data.end.newNoteHashes.filter(h => !h.isZero()),
     tx.data.end.newNullifiers.filter(h => !h.isZero()),
     tx.data.end.newL2ToL1Msgs.filter(h => !h.isZero()),