arbo

arbo: tree in Esperanto.

Note: There is a fork of this Go module as the tree/arbo package under https://github.com/vocdoni/vocdoni-node. The fork is modified so the tree does not store the orphan nodes and remains as small as the last state. This version of the tree will store all historical nodes, which depending on the use case can be useful or not.

MerkleTree implementation in Go. Compatible with the circomlib implementation of the MerkleTree. Specification: https://docs.iden3.io/publications/pdfs/Merkle-Tree.pdf and https://eprint.iacr.org/2018/955.

Main characteristics of arbo are:

• Allows to define which hash function to use.
  • So for example, when working with zkSnarks the Poseidon hash function can be used, but when not, it can be used the Blake2b hash function, which has much faster computation time.
  • New hash functions can be plugged by just implementing the interface
• Parallelizes computation by CPUs
  • See AddBatch section

AddBatch

The method tree.AddBatch is designed for the cases where there is a big amount of key-values to be added in the tree. It has the following characteristics:

• Parallelizes by available CPUs
  • If the tree size is not too big (under the configured threshold):
    • Makes a copy of the tree in memory (VirtualTree)
    • The VirtualTree does not compute any hash, only the relations between the nodes of the tree
      • This step (computing the VirtualTree) is done in parallel in each available CPU until level log2(nCPU)
    • Once the VirtualTree is updated with all the new leafs (key-values) in each corresponent position, it computes all the hashes of each node until the root
      • In this way, each node hash is computed only once, while when adding many key-values using tree.Add method, most of the intermediate nodes will be recalculated each time that a new leaf is added
      • This step (computing all the hashes) is done in parallel in each available CPU
  • If the tree size is avobe the configured threshold:
    • Virtually splits the tree in n sub-trees, where n is the number of available CPUs
    • Each CPU adds the corresponent new leaves into each sub-tree (working in a db tx)
    • Once all sub-trees are updated, puts them together again to compute the new tree root

As result, the method tree.AddBatch goes way faster thant looping over tree.Add, and can compute the tree with parallelization, so as more available CPUs, faster will do the computation.

As an example, this is the benchmark for adding 10k leaves (with 4 CPU cores, AddBatch would get faster with more CPUs (powers of 2)):

Intel(R) Core(TM) i5-7200U CPU @ 2.50GHz with 8GB of RAM
nCPU: 4, nLeafs: 10_000

Using Poseidon hash function:
(go) arbo.AddBatch:	436.866007ms
(go) arbo.Add loop:	5.341122678s
(go) iden3.Add loop:	8.581494317s
(js) circomlibjs:	2m09.351s

And, for example, if instead of using Poseidon hash function we use Blake2b, time is reduced to 80.862805ms.

Usage

// create new database
database, err := db.NewBadgerDB(c.TempDir())

// create new Tree with maxLevels=100 and Blake2b hash function
tree, err := arbo.NewTree(database, 100, arbo.HashFunctionBlake2b)

key := []byte("hello")
value := []byte("world")
// Add a key & value into the merkle tree
err = tree.Add(key, value)

// There are cases where multiple key-values (leafs) are going to be added to a
// Tree, for these cases is more efficient to use:
invalids, err := tree.AddBatch(keys, values)

// generate the merkle proof of a leaf by it's key
value, siblings, err := tree.GenProof(key)

// verify the proof
verified, err := arbo.CheckProof(tree.hashFunction, key, value, tree.Root(), siblings)
if !verified {
	fmt.Println("proof could not be verified")
}

// get the value of a leaf assigned to a key
gettedKey, gettedValue, err := tree.Get(key)

// update the value of a leaf assigned to a key
err = tree.Update(key, value)

// dump the tree (the leafs)
dump, err := tree.Dump(nil) // instead of nil, a root to start from can be used

// import the dump into a tree
err = tree.ImportDump(dump)

// print graphviz diagram of the tree
err = tree.PrintGraphviz(nil) // instead of nil, a root to start from can be used

Usage with SNARKs compatibility

Arbo is designed to be compatible with circom merkle tree's snark-friendly merkletree. The only change needed is the hash function used for the Tree, for example using the Poseidon hash function:

tree, err := arbo.NewTree(database, 32, arbo.HashFunctionPoseidon)

Be aware of the characteristics of this kind of hashes, such as using values inside the finite field used by the hash, and also the computation time.

The interface of arbo uses byte arrays, and for the case of these kind of hashes (that usually work directly with finite field elements), arbo expects those values to be represented by little-endian byte arrays. There is a helper method to convert a *big.Int to []byte using little-endian:

bLen := tree.HashFunction().Len()
kBigInt := big.NewInt(100)

// convert *big.Int to byte array
kBytes := arbo.BigIntToBytes(bLen, kBigInt)

// convert byte array to *big.Int
kBigInt2 := arbo.BytesToBigInt(kBytes)