Taro is primarily an on-chain protocol. Assets are issued on the bitcoin blockchain using taproot transactions.
To understand Taro, we will need to make ourselves familiar with several concepts, some of which are novel, in the context of the bitcoin blockchain.
Learn about the basic concepts here: Public-key cryptography Cryptographic Hashes Merkle trees Bitcoin UTXO
Taproot is a new transaction type defined in BIP 341 and fully functional on Bitcoin mainnet as of November 2021. The main difference of Taproot transactions to conventional Bitcoin transactions is that scripts controlling coins are contained within a tree structure called the 'tapScript branch' which is privately committed into the transaction. These scripts don’t need to be revealed if the KeySpend path is used to move the coins.
While a conventional transaction requires the entire script to be revealed, a Taproot transaction can be spent with a key to abstain from revealing the scripts and if the keyspend path is infeasible, only the executed portion of the script is revealed on the blockchain. All other script paths can remain private, or be selectively revealed off-chain.
This makes it possible to create more complicated scripts without the added cost of submitting extra data to the blockchain in the keySpend path, and efficient verification of a pruned script data. In the context of Taro, it allows us to provably attach arbitrary data to a transaction without revealing this data on-chain.
We refer to a transaction that includes such arbitrary data as a commitment. Once the transaction has been included in a block, we have committed to this data and can no longer change or amend it.
To commit to data, we tweak the public key of our Taproot spending key using a trick known as “Taptweak.” It allows us to selectively reveal the data without revealing the private key, or to spend the output without revealing the commitment.
This technique is used in Taproot transactions to commit to the Taproot script tree, and can be used to commit to any arbitrary data.
Q= P+H(P|c)GQ = the final Taproot public key P = the internal public key H(P|c) = A hash of the internal public key and the commitment
To sign a transaction with our private key, the private key needs to be tweaked with the same hash of the public key and commitment, H(P|c).
A Sparse (meaning ‘thinly scattered’) Merkle tree is a data structure in which it can be proven that specific data doesn't exist within a merkle tree. An SMT is an authenticated key-value store, meaning that the key, or location, of a leaf and the content of the leaf are bound to each other.
To achieve this property, the contents of the leaf are hashed and a merkle tree is created in which the leaf's position corresponds to the bitmap of the hash digest. By necessity, this requires a tree of 256 levels and 2^256 leaves. Generation of the tree is efficient--despite the apparently large size--because the overwhelming majority of the branches contain empty leaves and can be represented with nil hashes.
Constructing a Sparse Merkle tree
For example, we may create a Sparse Merkle tree using a fictitious hashing function of sha002, which results in a number between 0 and 3. We generate a Sparse Merkle tree with 4 leaves: 0, 1, 2 and 3. Only leaf 2 is populated, all other leaves are empty. To find leaf 2 (written 10 in binary), we go right at the first branch (1), then left at the second branch (0).
Identifying leaves in a Sparse Merkle tree
To verify leaf 2, we now only need to reveal the value at this leaf, plus the hash of leaf 3 and the hash of branch 0.
In Sparse Merkle trees, every leaf can be described as a guide to itself through a map when expressed in binary form. The map is the Sparse Merkle tree itself, and the guide is represented by instructions on whether to turn left or right at each fork. The 9th leaf in a 2^4 large Sparke Merkle tree for example is expressed in binary as 1001, meaning we find the appropriate leaf by turning left, then right, right and finally left.
This property is extremely useful for constructing and reconstructing the Sparse Merkle tree, as it describes precisely which parts of the Sparse Merkle tree we have to reconstruct. More importantly, the data in each leaf can now be described by their location in the tree.
Using the Sparse Merkle tree, we can associate data with public keys, and prove that we have deleted this data in an easily verifiable way without having to reveal the entire tree.
Because every item has its predetermined location, the tree’s root hash is not dependent on the order in which items are inserted.
Merkle sum trees are a type of merkle tree that contains numeric values at each leaf, and each node also carries the sum of the values below it. At the root of the Merkle sum tree is the sum of total values in the tree.
Merkle Sum trees allow efficient verification of conservation (non-inflation) by committing to quantities associated with leaves.
Taro makes use of a combination of the concepts above to allow for the issuance of Bitcoin-native assets. Sparse Merkle trees and Merkle sum trees are combined into sparse Merkle sum trees.
The root of this tree is added to a taproot tapscript, and together a taproot address is created.
Instead of its own blockchain, Taro issuers store sparse Merkle sum trees off-chain and issue proofs to asset holders out of band. The owners of such assets can independently verify that their account is included in the tree, is filled with the appropriate amount and the corresponding taproot transaction exists and is confirmed on the Bitcoin blockchain.
To issue a Taro asset , we must first create its identifier. We create a 32-byte asset ID which is produced by hashing three elements: the outpoint being spent to mint the asset, an asset tag of the minter’s choice (e.g. a hash of a brand name) and meta information associated with the asset--such as links, images or documents.
asset_id = sha256(genesis_outpoint || asset_tag || asset_meta)
The asset script can have inputs and outputs, similar to a Bitcoin transaction. A newly created asset does not contain any Taro inputs, while an asset transfer does.
The output of the asset script defines who the newly created assets are issued to. More precisely, this is done through a sparse Merkle sum tree, in which each account is identified by its 256-bit key, and each leaf corresponding to this key contains information about the amount the account holds.
It is possible to issue multiple assets in one transaction, but each asset will have its own asset script and within it, sparse Merkle tree. Assets can be unique or non-unique.
Each leaf contains a TLV (type, length, value) blob, akin to the TLV used in the Lightning Network. It contains information such as versions, asset id, amount, as well as data pertaining to previous transfers of this asset, such as signatures.
Once we have generated the sparse Merkle sum tree and asset script, we can tweak our internal public key and obtain the contract’s address and finalize the transaction.
Once we publish this transaction and have it confirmed on the bitcoin blockchain, we have irreversibly created the asset. To an observer, this transaction will look like any other standard taproot transaction.
The asset issuer can now selectively reveal what assets were created and to whom they were allotted. Most importantly, the issuer can prove to the recipient that an asset has been transfered to them, by revealing a specific asset proof, which contains the asset script as well as the path of the sparse Merkle sum tree with the recipient’s account as the key.
The recipient can verify the partial sparse Merkle sum tree to recreate the script, tweak the issuer’s public key and verify that the genesis transaction exists on the blockchain, while the partial Merkle tree gives them assurance over the assets issued to them, as well as the total number of assets issued.
Proving non-inclusion in a Sparse Merkle tree
Taro assets can be transferred on-chain, or they can be used to open Lightning Network channels. In this chapter, we will discuss on-chain transactions only.
Exactly how individual account holders interact with each other is not prescribed by Taro, but can be application specific. Issuers are given flexibility in how they define their assets, or how they intend to restrict these assets.
The Asset Root Commitment commits to all assets held inside of the tree as well as their sum. The asset_id is globally unique as it depends on the identifier of its genesis output. The overall root can comprise multiple asset_ids whose conservation of funds is provided by verifying the asset_tree_root.
asset_tree_root = sha256(asset_id || left_hash || right_hash || sum_value)
Taro addresses are bech32m encoded identifiers of the asset ID, the asset script hash, the internal key of the sparse Merkle sum tree and an amount, prefixed with Taro or Tarot (testnet).
bech32(hrp=TaroHrp, asset_id || asset_script_hash || internal_key || amt)
The issuer or asset holder can use the information in your Taro address to create or modify the sparse Merkle sum tree as explained below. This address format can also be used to request a specific proof over the amounts held by the address.
To transfer Taro assets, the recipient communicates their address to the current holder, who can initiate the transfer. The exact interaction between account holders and issuers is not strictly defined at this time. It could be left up to each application or even asset issuer to specify.
The sender of the funds will need to generate a new sparse Merkle sum tree reflecting the new balances. This is done by reducing the balances of certain leafs and increasing the balances of other leafs. The sparse Merkle sum tree guarantees that no new assets are created in such a transaction and that the previous claims to the assets are fully relinquished.
Creating assets requires a single on-chain taproot transaction, in which there is no limit on how many assets can be minted or how many accounts can hold these assets. To transfer assets, as explained above, requires reorganizing the Merkle tree and publishing a new on-chain transaction. There is no limit to how many internal Taro transactions are reflected in this single on-chain transaction.
Using this methodology, funds are allocated to account holders, represented as leafs in the sparse Merkle sum tree, but the ability to make such internal transfers is limited to the owner of the internal taproot private key(s).
Diagram showing the relationship between the Taproot tree, the asset tree, the individual Taro tree and its leaf.
A Universe is a service that provides information about assets as well as proofs for asset holders. It acts similarly to a bitcoin block explorer, but showcases Taro transaction data which is stored off-chain with Taro clients. The main difference is that, as most information related to Taro assets is off-chain, it is easier to conceal.
A Universe may be run by the asset issuer themselves or may be appointed by an issuer. It is also conceivable that community-run Universes aggregate information submitted by asset holders.
Given a known asset ID, the Universe for example may provide information about its Genesis output, as well as current meta information such as documentation, asset scripts or total coins in circulation. A service may also know about multiple assets (Multiverse) or only about a single output (Pocket Universe).
A Universe has no privileges within the Taro protocol. It produces transaction data validated against the bitcoin blockchain. An adversarial Universe could only refrain from returning data requested by clients. Taro transaction data isn’t bound to a Universe. The data availability offerings provided by a Universe is motivated by entities who wish to have fast, cheap verification of their Taro assets.
Assets may be transferred internally within the assets’ sparse Merkle tree, as described above, or they may be sent to another taproot key holder. This is referred to as an asset split.
In an asset split, the sender will again first need to update the sparse Merkle sum tree of their own taproot output, adjusting the balance(s) and recalculating the Merkle root. In the case of a merge, the root sum will also change.
Additionally, there will be a second sparse Merkle sum tree committed to a new taproot output. This second Merkle tree is calculated by the recipient of the assets, who acts similarly to an issuer in the example above, with the difference that these assets aren’t created from nothing, but rather are split from a previous output, for example the asset’s genesis output.
To be able to verify that the asset split has taken place, the operator of the new Universe needs proof that
- assets were created at transaction zero (t0)
- assets existed on a leaf in the original Merkle tree at t0
- the balance of this leaf was set to zero at t1
- the assets existed on a leaf of the new Merkle tree at t1
Once assets are split, the owner of the asset is able to perform internal transactions in the same way as the issuer. Each proof before the split will always need to include the Issuance proof for provenance verification.
Asset proofs grow linearly with each new on-chain transaction. Every asset transaction needs to be audited back to its Genesis output. An asset proof is only valid as long as the output it references is unspent on the blockchain.
An asset is considered invalid as soon as its output has been spent without committing to a new sparse merkle sum tree. This is not obvious for a third party observer, and in some instances it may be preferable to spend outputs to a new empty merkle tree to prove that assets were destroyed, invalidated, or “burned”.