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Batch aggregation


This document is a continuation in the series of articles explaining the transaction life cycle inside Polygon zkEVM.

The trusted aggregator should aggregate the sequences of batches previously committed by the trusted sequencer in order to achieve the L2 state final stage, which is the consolidated state.

Aggregating a sequence means successfully adding the resulting L2 state root to the batchNumToStateRoot mapping in the L1 PolygonZkEVM.sol contract. This is a storage structure that contains all of the consolidated L2 state roots, which are keyed by the last batch index of each aggregated sequence of batches.

// BatchNum --> state root
mapping (uint64 => bytes32) public batchNumToStateRoot;

Furthermore, the aggregation implies the successful verification of the zero-knowledge proof of the computational integrity of the transaction batches execution.

A SNARK (succinct non-interactive arguments of knowledge) is the underlying zero-knowledge proof verification schema. One of its key characteristics is the proof’s conciseness and speed of verification.

As a result, the integrity of an exhaustive computation can be verified using a fraction of the computational resources required by the original computation. As a result, by employing a SNARK schema, we can provide on-chain security to exhaustive off-chain computations in a gas-efficient manner.

Off-chain L2 state transition with on-chain security inheritance

As shown in the above diagram, the off-chain execution of the batches will suppose an L2 state transition and consequently, a change to a new L2 state root.

A computation integrity (CI) proof of the execution is generated by the aggregator, and its on-chain verification ensures validity of that resulting L2 state root.

Aggregating a sequence of batches

In order to aggregate a sequence of batches, the trusted aggregator must call the trustedVerifyBatches method:

function trustedVerifyBatches (
  uint64 pendingStateNum,
  uint64 initNumBatch,
  uint64 finalNewBatch,
  bytes32 newLocalExitRoot,
  bytes32 newStateRoot,
  uint256 [2] calldata proofA,
  uint256 [2][2] calldata proofB,
  uint256 [2] calldata proofC
) public onlyTrustedAggregator


  • pendingStateNum is the number of state transitions pending to be consolidated, which is set to 0 for as long as the trusted aggregator is in operation. The pendingState functions as a security measure to be used when L2 state is consolidated by an independent aggregator.
  • initNumBatch is the index of the last batch in the last aggregated sequence.
  • finalNewBatch is the index of the last batch in the sequence being aggregated.
  • newLocalExitRoot is the root of the Bridge’s L2 exit Merkle tree at the end of sequence execution used to compute new global exit root when the sequence is aggregated, and allows bridge claiming transactions to be successfully executed in L1.
  • newStateRoot is the L2 state root resulting from the execution of the sequence of batches over an older L2 state.
  • proof(A,B and C) is the zero-knowledge proof.

For a sequence of batches to be successfully aggregated, the following conditions must be met:

  • Aggregation transaction must be sent from the trusted aggregator account.
  • initNumBatch argument must be the index of an already aggregated batch. That is, it must have an L2 state root in batchNumToStateRoot mapping.
  • initNumBatch argument must be less or equal to the last aggregated batch index.
  • The sequence to be aggregated must have at least one batch.
  • initNumBatch and finalNewBatch arguments have to be sequenced batches, that is, to be present in the sequencedBatches mapping.
  • Zero-knowledge proof of computational integrity must be successfully verified.

The executor and the prover are services of the aggregator node that execute batches and generate zero-knowledge proofs. We will herein treat them as Ethereum Virtual Machine black box interpreters that can:

  • execute a sequence of transaction batches on the current L2 state,
  • calculate the resulting L2 state root, and
  • generate a zero-knowledge proof of computational integrity for the execution.

The proving/verification system is designed in such a way that successful proof verification equates to cryptographically proving that executing the given sequence of batches over a specific L2 state results in an L2 state represented by the newStateRoot argument.

The following code snippet is a part of the PolygonZkEVM.sol contract, which shows the zero-knowledge proof verification:

// Get snark bytes
bytes memory snarkHashBytes = getInputSnarkBytes (

// Calculate the snark input
uint256 inputSnark = uint256(sha256(snarkHashBytes)) % _RFIELD;

// Verify proof
require (
  rollupVerifier.verifyProof(proofA, proofB, proofC, [inputSnark]),
  "PolygonZkEVM :: _verifyBatches : Invalid proof"


rollupVerifier is an external contract that has a function verifyProof that takes a proof (proofA, proofB, proofC) and a value inputSnark and returns a boolean value that will be true if the proof is valid and false if it isn’t.

The successful verification of the proof just confirms the integrity of the computation, but not that the correct inputs were used and that they resulted in the correct output values. Public arguments are used to publicly disclose key points of the computation being proved, in order to prove that it was performed using the correct inputs and reveal the outputs.

This way, during the proof verification, the L1 smart contract will set the public arguments to ensure that the state transition being proved corresponds to the execution of the batches committed by the trusted sequencer.


inputSnark is a 256-bits unique cryptographic representative of a specific L2 state transition, which is used as public argument. It is computed as sha256 mod % _RFIELD hash of a bytes string called snarkHashBytes (modulo operator is needed due to math primitives used in SNARKs).

snarkHashBytes array is computed by a smart contract’s function called getInputSnarkBytes and it is an ABI-encoded packed string of the following values:

  • msg.sender: Address of trusted aggregator.
  • oldStateRoot: L2 state root that represents the L2 state before the state transition that wants to be proven.
  • oldAccInputHash: Accumulated hash of the last batch aggregated.
  • initNumBatch: Index of the last batch aggregated.
  • chainID: Unique chain identifier.
  • newStateRoot: L2 state root that represents the L2 state after the state transition that is being proved.
  • newAccInputHash: Accumulated hash of the last batch in the sequence that is being aggregated.
  • newLocalExitRoot: Root of the bridge’s L2 exit Merkle tree at the end of sequence execution.
  • finalNewBatch: Number of the final batch in the execution range.

inputSnark will represent all the L2 transactions of a specific L2 state transition, executed in a specific order, in a specific L2 (chainID), and proved by a specific trusted aggregator (msg.sender). The trustedVerifyBatches function not only verifies the validity of the zero-knowledge proof, but it also checks that the value of inputSnark corresponds to an L2 State transition that is pending to be aggregated.

If the internal call to _verifyAndRewardBatches returns true, it will mean that the sequence of batches is verified successfully, and then the newStateRoot argument will be added to the batchNumToStateRoot mapping. The index of the last batch in the sequence will be used as the key for the entry.

Finally a TrustedVerifyBatches event will be emitted.

event TrustedVerifyBatches (
  uint64 indexed numBatch,
  bytes32 stateRoot,
  address indexed aggregator

Once the batches have been successfully aggregated in L1, all zkEVM nodes can validate their local L2 state by retrieving and validating consolidated roots directly from the L1 consensus contract (PolygonZkEVM.sol). As a result, the L2 consolidated state has been reached.

Last update: December 11, 2023
Authors: EmpieichO (69.77%), kmurphypolygon (26.36%), Nadim Kobeissi (3.88%)