pymerkle

Merkle-tree in Python

⚠️ This library requires security audit. Use at youn own risk for the moment.

Documentation at pymerkle.readthedocs.org.

Storage agnostic implementation capable of generating inclusion and consistency proofs.

Install

pip3 install pymerkle

This will also install cachetools as a dependency.

Basic API

Let MerkleTree be any class implementing the BaseMerkleTree interface; e.g.,

from pymerkle import InmemoryTree as MerkleTree

tree = MerkleTree(algorithm='sha256')

Append data into the tree and retrieve the corresponding hash value:

index = tree.append_entry(b'foo')   # leaf index

value = tree.get_leaf(index)        # leaf hash

The examples below assume that the tree contains at least five entries.

Current tree size:

size = tree.get_size()    # number of leaves

Current and intermediate states:

state = tree.get_root()    # current root-hash

state = tree.get_root(5)   # root-hash for the first 5 leaves

Inclusion proof

Prove inclusion of the 3-rd leaf hash in the state of size 5:

proof = tree.prove_inclusion(3, 5)

Verify the proof against the base hash and the corresponding state:

from pymerkle import verify_inclusion

base = tree.get_leaf(3)
root = tree.get_root(5)

verify_inclusion(base, root, proof, index=3, size=5)

The proof structure is recomputed from the leaf index and size and must match exactly. Passing index and size additionally ensures that the proof refers to the expected leaf position and state.

Consistency proof

Prove consistency between the states with size 3 and 5:

proof = tree.prove_consistency(3, 5)

Verify the proof against the respective root-hashes:

from pymerkle import verify_consistency

prior_state = tree.get_root(3)
later_state = tree.get_root(5)

verify_consistency(prior_state, later_state, proof, prior_size=3,
    later_size=5)

The proof structure is recomputed from the sizes and must match exactly. Passing prior_size and later_size additionally ensures that the proof refers to the expected states; omit them only if the states are not bound to known sizes.

Supported hash functions

sha224, sha256, sha384, sha512, sha3_224, sha3_256, sha3_384, sha3_512

Support for Keccak beyond SHA3

Installing the keccak extra, which pulls in safe-pysha3 (a maintained fork of pysha3),

pip3 install pymerkle[keccak]

makes available the following hash functions:

keccak_224, keccak_256, keccak_384, keccak_512

Security

⚠️ This library requires security audit. Use at youn own risk for the moment.

Resistance against second-preimage attack

This consists in the following standard technique:

• Upon computing the hash of a leaf node, prepend 0x00 to the payload
• Upon computing the hash of an interior node, prepend 0x01 to the payload

Note: For, say, testing purposes, you can disable this feature by passing disable_security=True when initializing the BaseMerkleTree superclass. Proofs generated this way are rejected upon verification unless security=False is explicitly passed to verify_inclusion or verify_consistency. Pass algorithm as well to make sure that proofs are resolved with the expected hash function. Refer here to see how to perform second-preimage attack against the present implementation.

Resistance against CVE-2012-2459 DOS

Contrary to the bitcoin specification, lonely leaves are not duplicated while the tree is growing. Instead, a bifurcation node is created at the rightmost branch (see next section). As a consequence, the present implementation should be invulnerable to the CVE-2012-2459 DOS attack (see also here for insight).

Topology

Interior nodes are not assumed to be stored anywhere and storage backends need not create links between them. The tree structure is determined by the recursive function which computes intermediate states on the fly and is essentially the same as RFC 9162 (Section 2). It turns out to be that of a binary Sakura tree (Section 5.4).

Optimizations

The performance of a Merkle-tree depends on how efficiently it computes the root-hash for arbitrary leaf ranges on the fly. The recursive version of this operation (e.g., RFC 9162, Section 2) is slow.

A key remark is that the above operation can be made iterative by combining the root-hashes for ranges whose size is a power of two ("subroots") and can as such be computed efficiently. Subroot computation has significant impact on performance (about six times faster proof generation on a database with 100,000 entries) while keeping memory usage reasonably low (e.g., less than 150 MiB for the whole process when generating proofs against one million entries).

Note: For, say, comparison purposes, you can disable this feature by passing disable_optimizations=True when initializing the BaseMerkleTree superclass.

Caching

In view of the above technique, subroot computation is the only massively repeated and relatively costly operation. It thus makes sense to apply memoization for ranges whose size is at least a certain threshold (128 leaves by default). For example, on a database with one million entries, proof generation becomes several times faster after a few thousand proofs, with the cache occupying a few MiB. Practically, a tree with sufficiently long uptime will respond considerably faster with little penalty in memory usage.

Note: For, say, comparison purposes, you can disable this feature by passing disable_cache=True when initializing the BaseMerkleTree superclass.

Storage

This library is unopinionated on how leaves are appended to the tree, i.e., how data is stored in concrete. Cryptographic functionality is encapsulated in the BaseMerkleTree abstract class, which admits pluggable storage backends through subclassing.

It is the developer's choice to decide how to store data by implementing the internal storage interface of this class. Any contiguously indexed dataset should do the job. Conversely, given any such dataset, we should be able to trivially implement a Merkle-tree that is operable with it.

Example

This is a simple non-persistent implementation utilizing a list as storage. It expects entries to be strings, which are utf-8-encoded before hashing.

from pymerkle import BaseMerkleTree


class MerkleTree(BaseMerkleTree):

    def __init__(self, algorithm='sha256'):
        """
        Storage setup and superclass initialization
        """
        self.hashes = []

        super().__init__(algorithm)


    def _encode_entry(self, data):
        """
        Prepares data entry for hashing
        """
        return data.encode('utf-8')


    def _store_leaf(self, data, digest):
        """
        Stores data hash in a new leaf and returns index
        """
        self.hashes += [digest]

        return len(self.hashes)


    def _get_leaf(self, index):
        """
        Returns the hash stored by the leaf specified
        """
        value = self.hashes[index - 1]

        return value


    def _get_leaves(self, offset, width):
        """
        Returns hashes corresponding to the specified leaf range
        """
        values = self.hashes[offset: offset + width]

        return values


    def _get_size(self):
        """
        Returns the current number of leaves
        """
        return len(self.hashes)

Concurrency

Public tree operations are serialized by means of a reentrant lock, so that a tree can be shared between threads. Concrete implementations should decorate any additional public method accessing their storage with pymerkle.core.synchronized.

Development

In what follows, you need to have locally installed the package and dev requirements:

pip3 install -r requirements.txt -r requirements-dev.txt

Tests

./test.sh [--help]

Performance

In order to capture the effect of I/O operations, performance measurements are run against a SQLite database as leaf storage. Create it using the following script:

python benchmarks/init_db.py [--help]

Benchmarks

Assuming a local leaf database has been created as above, run

./benchmark.sh [--help]

Profiling

Assuming valgrind and massif-visualizer are installed, use

./profile.sh [--help]

to do memory profiling. Pass --time to profile execution times instead of memory allocations.

Documentation

pymerkle.readthedocs.org.

Build locally

Documentation is built with sphinx.

Assuming dev requirements have been installed, build the docs with

./build-docs.sh [--help]

and browse at

docs/target/build/html/index.html

to view them.