Ethereum: Is the number of transactions in a Merkle Tree always “even”?

The Ethereum Merkle Tree is a data structure used to efficiently verify the integrity and authenticity of blockchain transactions. It allows nodes to quickly determine whether a given block contains valid or corrupted transactions by looking for inconsistencies in the Merkle tree.

According to the definition and construction of a Merkle Tree, one of its main properties is that it must always contain an even number of transactions. This ensures that each node in the tree can be uniquely identified by a hash value that reflects all the transactions in that block.

In Ethereum, this feature is crucial to maintaining the security and integrity of the network. By implementing this limit on the number of transactions that can be inserted into each Merkle Tree structure, nodes can efficiently verify the validity of blocks and ensure that the blockchain remains tamper-proof.

However, there may be situations where the number of transactions in a block does not meet this property. For example, if a node inserts an odd number of transactions into its Merkle tree, this means that there are no valid or corrupt transactions in that block, which can lead to inefficient verification processes.

In practice, most Ethereum network nodes work within this limitation by inserting new blocks into their Merkle trees. However, to further ensure data integrity and prevent potential security issues, other tools, such as smart contract logic, can be used.

For example, some smart contracts use a mechanism called “hash-based proof-of-work,” which does not require every transaction in a block to be sent to the Merkle tree. This method allows network nodes to efficiently verify the validity of blocks without having to hash each individual transaction.

In summary, although it is generally assumed that the number of operations in a Merkle tree should always be “even”, there may be special scenarios where this property is not supported for reasons such as potential security issues or inefficient verification processes. Nevertheless, most nodes on the Ethereum network work within these constraints by inserting new blocks into their Merkle trees.

Code Example

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pragma robustness ^0.8.0;

contract MerkleTreeExample {

// Insert a block into the Merkle tree

function insertBlock(block) public {

// Insert block transactions into the Merkle Tree

MerkleTreeNode[] memory nodes = new MerkleTreeNode[](block.transactions.length);

for (uint256 i = 0; i < block.transactions.length; i++) {

nodes[i] = MerkleTreeNode(block.transactions[i].hash, block.transactions[i].value);

}

// Check if the number of transactions is even

request(nodes.length % 2 == 0, “The number of transactions in the block must be even.”);

// Insert the block into the Merkle tree

for (uint256 i = 0; i < nodes.length; i++) {

MerkleTreeNode memory node = nodes[i];

if (!node.isLeaf()) {

insertMerkleNode(node.hash, i);

}

}

emit BlockInserted(block.hash, block.transactions);

}

// Function to recursively insert a single operation into a Merkle tree

function insertMerkleNode(hash, index) private {

// If this is the last operation in the list, add it to the leaf node

if (index == nodes.length – 1) {

nodes.push(MerkleTreeNode(hash, index.value));

} else {

// Otherwise, recursively insert into the subtree rooted at this hash

MerkleTreeNode memory primary = nodes[index + 1];

MerkleTreeNode memory child = nodes[index];

if (parent.

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