This is a Python port of merkle-tools.

Tools for creating Merkle trees, generating merkle proofs, and verification of merkle proofs.

import merkletools

mt = MerkleTools(hash_function=hashlib.sha512)  # default is sha256 

Adds a value as a leaf or a list of leafs to the tree. All values are hashed prior to being added to the tree.

list_data = ['Some text data', 'perhaps']
mt.add_leaf(list_data, True)

Returns the number of leaves that are currently added to the tree.

leaf_count =  mt.get_leaf_count();

Returns the value of the leaf at the given index as a hex string.

leaf_value =  mt.get_leaf(1)

Generates the merkle tree using the leaves that have been added.

mt.make_tree();

.is_ready is a boolean property indicating if the tree is built and ready to supply its root and proofs. The is_ready state is True only after calling 'make_tree()'. Adding leaves or resetting the tree will change the ready state to False.

is_ready = mt.is_ready 

Returns the merkle root of the tree as a hex string. If the tree is not ready, None is returned.

root_value = mt.get_merkle_root();

Returns the proof as an array of hash objects for the leaf at the given index. If the tree is not ready or no leaf exists at the given index, null is returned.

proof = mt.get_proof(1)

The proof array contains a set of merkle sibling objects. Each object contains the sibling hash, with the key value of either right or left. The right or left value tells you where that sibling was in relation to the current hash being evaluated. This information is needed for proof validation, as explained in the following section.

Returns a boolean indicating whether or not the proof is valid and correctly connects the target_hash to the merkle_root. proof is a proof array as supplied by the get_proof method. The target_hash and merkle_root parameters must be a hex strings.

proof = [
   { r: '09096dbc49b7909917e13b795ebf289ace50b870440f10424af8845fb7761ea5' },
   { r: 'ed2456914e48c1e17b7bd922177291ef8b7f553edf1b1f66b6fc1a076524b22f' },
   { l: 'eac53dde9661daf47a428efea28c81a021c06d64f98eeabbdcff442d992153a8' },
]
target_hash = '36e0fd847d927d68475f32a94efff30812ee3ce87c7752973f4dd7476aa2e97e'
merkle_root = 'b8b1f39aa2e3fc2dde37f3df04e829f514fb98369b522bfb35c663befa896766'

is_valid = mt.validate_proof(proof, targetHash, merkleRoot)

The proof process uses all the proof objects in the array to attempt to prove a relationship between the target_hash and the merkle_root values. The steps to validate a proof are:

1. Concatenate target_hash and the first hash in the proof array. The right or left designation specifies which side of the concatenation that the proof hash value should be on.
2. Hash the resulting value.
3. Concatenate the resulting hash with the next hash in the proof array, using the same left and right rules.
4. Hash that value and continue the process until you’ve gone through each item in the proof array.
5. The final hash value should equal the merkle_root value if the proof is valid, otherwise the proof is invalid.

mt = MerkleTools()

mt.add_leaf("tierion", True)
mt.add_leaf(["bitcoin", "blockchain"], True)

mt.make_tree()

print "root:", mt.get_merkle_root()  # root: '765f15d171871b00034ee55e48ffdf76afbc44ed0bcff5c82f31351d333c2ed1'

print mt.get_proof(1)  # [{l: '2da7240f6c88536be72abe9f04e454c6478ee29709fc3729ddfb942f804fbf08'},
                       #  {r: 'ef7797e13d3a75526946a3bcf00daec9fc9c9c4d51ddc7cc5df888f74dd434d1'}] 

print mt.validate_proof(mt.get_proof(1), mt.get_leaf(1), mt.get_merkle_root())  # True

1. Internally, leaves are stored as bytes. When the tree is built, it is generated by hashing together the bytes values.

2. Lonely leaf nodes are promoted to the next level up, as depicted below.

                     ROOT=Hash(H+E)
                     /        \
                    /          \
             H=Hash(F+G)        E
             /       \           \
            /         \           \
     F=Hash(A+B)    G=Hash(C+D)    E
      /     \        /     \        \
     /       \      /       \        \
    A         B    C         D        E
   

This module uses Python's hashlib for hashing. Inside a MerkleTools object all hashes are stored as Python bytes. This way hashes can be concatenated simply with + and the result used as input for the hash function. But for simplicity and easy to use MerkleTools methods expect that both input and outputs are hex strings. We can convert from one type to the other using default Python string methods. For example:

hash = hashlib.sha256('a').digest()  # '\xca\x97\x81\x12\xca\x1b\xbd\xca\xfa\xc21\xb3\x9a#\xdcM\xa7\x86\xef\xf8\x14|Nr\xb9\x80w\x85\xaf\xeeH\xbb'
hex_string = hash.hex()  # 'ca978112ca1bbdcafac231b39a23dc4da786eff8147c4e72b9807785afee48bb'
back_to_hash = hex_string.decode('hex')  # '\xca\x97\x81\x12\xca\x1b\xbd\xca\xfa\xc21\xb3\x9a#\xdcM\xa7\x86\xef\xf8\x14|Nr\xb9\x80w\x85\xaf\xeeH\xbb'