# Transactions Root Hash

The transactionsRoot field in the block header contains the root hash of the Merkle tree of transactions of the block. The root hash is the proof that the block contains all the transactions in the proper order.

The transactions root hash in the block header has the following purposes:

To prove the integrity of transactions in the block without presenting all transactions.
To sign the block header only, separately from its transactions.

⚠️ transactionsRoot is enabled by feature #15 “Ride V4, VRF, Protobuf, Failed transactions”.

# transactionsRoot Calculation

The hash of each transaction in the block is calculated. For example:

H_A = hash(T_A)

H_B = hash(T_B)

etc.
Each pair of adjacent hashes is concatenated, and the hash is calculated for each resulting concatenation:

H_AB = hash(H_A + H_B)

If the last hash does not have a pair, it is concatenated with the zero byte hash:

H_GH = hash(H_G + hash(0))
Step 2 is repeated until the root hash is obtained:

H_ABCDEFGH

The root hash is written in the transactionsRoot field.

If the block is empty, then transactionsRoot = hash(0).

Waves blockchain uses BLAKE2b-256 hashing function.

# Proof of Transaction in Block

Let's suppose that side 1 stores the full blockchain data and side 2 stores the block headers only.

To prove that the block contains a given transaction, side 1 provides the following data:

T: Transaction to check.
merkleProofs: Array of sibling hashes of the Merkle tree, bottom-to-top.
index: Index of the transaction in the block.

For example, for the T_D transaction:

merkleProofs = [ H_C, H_AB, H_EFGH ]
index = 3

Side 2 checks the proof:

It calculates the hash of the transaction being checked (all the transaction data is hashed, including the signature):

H_D = hash(T_D)
It concatenates the current hash with the corresponding hash of the merkleProofs array and calculates the hash of concatenation.

index determines in which order to concatenate the hashes:

• If the nth bit of index from the end is 0, then the order is: the current hash + the nth hash of the merkleProofsarray (proof hash is on the right). • If the nth bit is 1, the order is: the nth hash of the merkleProofsarray + the current hash (proof hash is on the left).

For example, index = 3₁₀ = 11₂ , thus:

• merkleProofs[0] = H_C is on the left, • merkleProofs[1] = H_AB is on the left, • merkleProofs[2] = H_EFGH is on the right.
It repeates Step 2 until the root hash is obtained:

H_ABCDEFGH
It compares the root hash obtained with the already known transactionsRoot from the block header. If the hashes match, then the transaction exists in the block.

# Tools

The following Node API methods accept transaction IDs and provide the proof that the transaction is in a block for each transaction:

GET /transactions/merkleProof
POST /transactions/merkleProof

The methods are described in the Transaction article.

You can check a transaction on the same blockchain without using a root hash, since the Waves node stores the full blockchain data, including all transactions. Use the following built-in Ride function:

transactionHeightById(id: ByteVector): Int|Unit

The function returns the block height if the transaction with the specified id exists. Otherwise, it returns unit. See the function description in the Blockchain functions article.

To check a transaction in a block on the external blockchain you can use the following built-in Ride function:

createMerkleRoot(merkleProofs: List[ByteVector], valueBytes: ByteVector, index: Int): ByteVector

This function is applicable if the external blockchain uses the same algorithm for calculating the root hash of transactions (for instance, external blockchain is Waves-based). The createMerkleRoot function calculates the root hash from the transaction hash and sibling hashes of the Merkle tree (see Steps 1–3). To check a transaction in a block, compare the calculated root hash with the transactionsRoot value in the block header. See the function description in the Verification functions article.