# RFC-0201/TariScript

## Tari Script

Maintainer(s): Cayle Sharrock

# Licence

Copyright 2020 The Tari Development Community

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## Language

The keywords "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY" and "OPTIONAL" in this document are to be interpreted as described in BCP 14 (covering RFC2119 and RFC8174) when, and only when, they appear in all capitals, as shown here.

## Disclaimer

This document and its content are intended for information purposes only and may be subject to change or update without notice.

This document may include preliminary concepts that may or may not be in the process of being developed by the Tari community. The release of this document is intended solely for review and discussion by the community of the technological merits of the potential system outlined herein.

## Goals

This Request for Comment (RFC) presents a proposal for introducing Tari Script into the Tari base layer protocol. Tari Script aims to provide a general mechanism for enabling further extensions such as side chains, the DAN, one-sided payments and atomic swaps.

## Introduction

It is hopefully clear to anyone reading these RFCs that the ambitions of the Tari project extend beyond a Mimblewimble-clone-coin.
It should also be fairly clear that basic Mimblewimble does not have the feature set to provide functionality such as:

• One-sided payments
• Atomic swaps (possible with scriptless scripts, but not easy)
• Hash time-locked contracts (possible with scriptless scripts, but not easy)
• Multiparty side-chain peg outs and peg-ins
• Generalised smart contracts

Extensions to Mimblewimble have been proposed for most of these features, for example, David Burkett's one-sided payment proposal for LiteCoin (LIP-004), this project's HTLC RFC, the pegging proposals for the Clacks side-chain, and Scriptless scripts.

This RFC makes the case that if Tari were to implement a scripting language similar to Bitcoin script, then all of these use cases collapse and can be achieved under a single set of (relatively minor) modifications and additions to the current Tari and Mimblewimble protocol.

## Scripting on Mimblewimble

To the author's knowledge, none of existing Mimblewimble projects have employed a scripting language. The reasons for this are unclear, but there is at least one narrative in the space that it is not possible with Mimblewimble. Given that Grin styles itself as a "Minimal implementation of the Mimblewimble protocol", this status is unlikely to change soon.

As of this writing, the Beam project also considers Scriptless Script to be the extent of their scripting capabilities.

Mimblewimble coin is a fork of Grin and "considers the protocol ossified".

Litecoin is in the process of adding Mimblewimble as a side-chain. As of this writing, there appear to be no plans to include general scripting into the protocol.

### Scriptless scripts

Scriptless script is a wonderfully elegant technology and inclusion of Tari script does not preclude the use of Scriptless script in Tari. However, scriptless scripts are difficult to reason about and development of them are best left to experts in cryptographic proofs, leaving the development of Mimblewimble smart contracts in the hands of a very select group of people.

However, it is the opinion of the author that there is no reason why Mimblewimble cannot be extended to include scripting.

## Tari script - a basic motivation

The essential idea of Tari script is as follows:

Given a standard Tari UTXO, we add additional restrictions on whether that UTXO can be included as a valid input in a transaction.

As long as those conditions are suitably committed to, and are not malleable throughout the existence of the UTXO, then in general, these conditions are no different to the requirement of having range proofs attached to UTXOs, which require that the value of Tari commitments is non-negative.

Note that range proofs can be discarded after a UTXO is spent, since the global security guarantees of Mimblewimble are not concerned that every transaction in history was valid from an inflation perspective, but that the net effect of all transactions lead to zero inflation. This sounds worse than it is, since locally, every individual transaction is checked for validity at the time of inclusion in the blockchain.

This argument is independent of the nature of the additional restrictions. Specifically, if these restrictions are manifested as a script that provides additional constraints over whether a UTXO may be spent, the same arguments apply.

This means that from a philosophical viewpoint, there ought to be no reason that Tari Script is not workable, and further, that pruning spent outputs (and possibly the scripts associated with them) is not that different from pruning range proofs.

There is one key difference though that we need to address.

If it somehow happened that two illegal transactions made it into the blockchain (perhaps due to a bug), and the two cancelled each other out, such that the global coin supply was still correct, one would never know this when doing a chain synchronisation in pruned mode.

But if there was a steady inflation bug due to invalid range proofs making it into the blockchain, a pruned mode sync would still detect that something was awry, because the global coin supply balance acts as another check.

With Tari script, once the script has been pruned away, and then there is a re-org to an earlier point on the chain, then there's no way way to ensure that the script was honoured.

However, a single honest archival node would be able to detect any fraud on the same chain and provide a simple proof that a transaction did not honour the redeem script.

The assumptions that broadly equate scripting with range proofs in the above argument are:

• The script (hash) must be committed to in the blockchain.
• The script must not be malleable in any way without invalidating the transaction.
• The creator of the UTXO must commit to and sign the script (hash).

The script commitment, which can be adequately represented by the hash of the canonical serialisation of the script in binary format, could be placed in the transaction kernel, or in a dedicated merkle mountain range for scripts.

Range proofs are not malleable because one must have knowledge of the UTXO blinding factor in order to generate a valid range proof. However, it's trivial to replace scripts with other valid scripts, potentially to the point that miners or malicious actors could take the UTXO for themselves.

Therefore, it's imperative that the UTXO creator sign the script.

Further, this signature must be present in the kernel in some form, otherwise miners will be able to remove the script via cut-through, whereas kernels are never pruned.

One approach to commit to the script hashes is to modify the output commitments using the data commitments approach suggested by Phyro. In this approach, when creating a new UTXO, the owner also calculates the hash of the locking script, s, such that s = H(script). The script hash gets stored in the UTXO itself.

## Protocol modifications

The current definition of a Tari UTXO is:

pub struct TransactionOutput {
/// Options for an output's structure or use
features: OutputFeatures,
/// The homomorphic commitment representing the output amount
commitment: Commitment,
/// A proof that the commitment is in the right range
proof: RangeProof,
}

Under Tari script, this would change to

pub struct TransactionOutput {
features: OutputFeatures,
commitment: Commitment,
proof: RangeProof,
/// New: The hash of the locking script on this UTXO.
script_hash: HashOutput,
}

Now when calculating the transaction or block balance, we calculate a different set of commitments. The current commitment,

$$C = v.H + k.G$$

is modified with a commitment to the script hash, so

$$\hat{C} = C + \mathrm{H}(C \Vert s).G$$

and wallets will sign the kernel with $$k + \mathrm{H}(C \Vert s)$$ rather than just k.

The overall and block balance checks must also be modified to use $\hat{C}$ rather than C.

### Transaction balance

The new transaction balance is thus

\begin{align} & \sum(\mathrm{Inputs}) - \sum(\mathrm{Outputs}) - \sum(\mathrm{fee}_i.G) \\ =& \sum\hat{C_i} - \sum\hat{C_j} - \sum(\mathrm{fee}_i.G) \\ =& \sum(C_i + \mathrm{H}(C_i \Vert s_i).G) - \sum(C_j + \mathrm{H}(C_j \Vert s_j).G) - \sum(\mathrm{fee}.G) \end{align}

If the accounting is correct, all values will cancel

$$= \sum(k_i + \mathrm{H}(C_i \Vert s_i).G) - \sum(k_j + \mathrm{H}(C_j \Vert s_j).G)$$

The sum of all the blinding factors (times G) is the definition of the standard Mimblewimble excess,

$$x_s\cdot G = X_s$$

If we define, $$\Lambda = \sum(\mathrm{H}(C_i \Vert s_i).G) - \sum(\mathrm{H}(C_j \Vert s_j).G)$$

then the new transaction excess can be written as $$X_\mathrm{new} = X_s + \Lambda$$

The kernels are unmodified, except that the excess will now include $\Lambda$, representing the sum of all the commitments to the UTXO script hashes. This also means that the kernel signatures are calculated slightly differently:

\begin{align} s_i &= r_i + e.\bigl(k_i + \mathrm{H}(C_i \Vert s_i) \bigr) \\ s_i.G &= r_i.G + e.\bigl(k_i + \mathrm{H}(C_i \Vert s_i) \bigr).G \\ s_i.G &= R_i + e.\bigl(P_i + \mathrm{H}(C_i \Vert s_i)\bigr) \\ \end{align}

Summing the signatures, one can easily confirm that $X_s + \Lambda$ signs the kernel correctly. The kernel offset is not included in this treatment, but it does not affect the result. One of the input commitments will be offset by a value selected by the sender and provided with the transaction data as usual. The signatures will still validate as usual, and the kernel offset will correct the overall excess balance.

The same treatment extends to be block validation check. Note that since the individual kernel excesses can still be summed to obtain the overall block balance, the de-association of kernels and their outputs is maintained.

### Checking the requirements

Miners cannot modify the script hash, because it is committed to in the public excess value. Moreover, the $C_i \Vert s_i$ pair is committed to, so miners can't, for example swap script hashes on commitments to keep the overall excess the same but still manipulate specific outputs.

The UTXO creator(s) are also committing to the script hash by including it in the kernel signature.

Thus all three requirements are satisfied and Tari Script, using this formulation should offer the same security guarantees that range proofs do.

In particular, UTXOs can still be pruned because the $\Lambda$ values change sign when used as inputs and will
cancel out in the overall balance in the same way that the pruned out excesses are.

However, a problem arises now in that as it stands, the UTXOs cannot be pruned because we would lose some data needed to verify the kernel signatures, i.e. $\mathrm{H}(C_i \Vert s_i)$ and that data only exists in the UTXOs. However, we can salvage this situation fairly easily by noticing that we only need that hash of the commitment and script hash. If we track an MMR of $C_i \Vert s_i$, then those hashes are always available, even after the UTXOs themselves have been discarded. In terms of additional block space required, this amounts to a single 32 byte hash per header (the MMR root). A more detailed storage assessment is given below.

## Tari Script semantics

The proposal for Tari Script is straightforward. It is based on Bitcoin script and inherits most of its ideas.

The main properties of Tari script are

• The scripting language is stack-based. At redeem time, the UTXO spender must supply an input stack. The script runs by operating on the the stack contents.
• If an error occurs during execution, the script fails.
• After the script completes, it is successful if and only if it has not aborted, and there is exactly a single element on the stack with a value of zero. In other words, the script fails if the stack is empty, or contains more than one element, or aborts early.
• It is not Turing complete, so there are no loops or timing functions.
• The Rust type system ensures that only compatible data types can be operated on, e.g. A public key cannot be added to an integer scalar. Errors of this kind cause the script to fail.

### Opcodes

Tari Script opcodes are enumerated from 0 to 255 and are represented as a single unsigned byte. The opcode set is initially limited to allow for the applications specified in this RFC, but can be expanded in future.

pub enum Opcode {
/// Push the current chain height onto the stack
PushHeight,
/// Push the associated 32-byte value onto the stack
PushHash(Box<HashValue>),
/// Hash the top stack element with the Blake256 hash function and push the result to the stack
HashBlake256,
/// Fail the script immediately. (Must be executed.)
Return,
/// Drops the top stack item
Drop,
/// Duplicates the top stack item
Dup,
/// Reverse rotation. The top stack item moves into 3rd place, abc => bca
RevRot,
/// Pop two items and push their sum
/// Pop two items and push the second minus the top
Sub,
/// Pop the public key and then the signature. If the signature signs the script, push 0 to the stack, otherwise
/// push 1
CheckSig,
/// As for CheckSig, but aborts immediately if the signature is invalid. As opposed to Bitcoin, it pushes a zero
/// to the stack if successful
CheckSigVerify,
/// Pushes 0, if the inputs are exactly equal, 1 otherwise
Equal,
/// Pushes 0, if the inputs are exactly equal, aborts otherwise
EqualVerify,
}

### Serialisation

Tari Script and the execution stack are serialised into byte strings using a simple linear parser. Since all opcodes are a single byte, it's very easy to read and write script byte strings. If an opcode has a parameter associated with it, e.g. PushHash then it is equally known how many bytes following the opcode will contain the parameter. So for example, a pay-to-public-key-hash script (P2PKH) script, when serialised is

71b07aae2337ce44f9ebb6169c863ec168046cb35ab4ef7aa9ed4f5f1f669bb74b09e58170ac

which maps to

71  b0           7a       ae2337ce44f9ebb6169c863ec168046cb35ab4ef7aa9ed4f5f1f669bb74b09e5  81          70   ac
Dup HashBlake256 PushHash(ae2337ce44f9ebb6169c863ec168046cb35ab4ef7aa9ed4f5f1f669bb74b09e5) EqualVerify Drop CheckSig

Input parameters are serialised in an analogous manner.

The types of input parameters that are accepted are:

pub enum StackItem {
Number(i64),
Hash(HashValue),
Commitment(PedersenCommitment),
PublicKey(RistrettoPublicKey),
Signature(RistrettoSchnorr),
}

### Storage impact of script hash MMR

Adding another MMR to track the script commitments, $\mathrm{H}(C \Vert s_i$ has the following impacts on bandwidth and storage:

Additional data transferred in each block would be:

• 32 bytes for every UTXO (The script hash itself)
• 32 bytes for every header (The MMR root).

The storage impact is the size of the scripts, plus $(2^{\log_2 k + 1}-1)$ * 32 bytes, where k = total number of UTXOs, or, if we just store the leaves it's k * 32 bytes.

For 10 million UTXOs, this adds an additional 620 MB or so to the blockchain database if the entire MMR is stored, or 305 MB if just the hashes are stored.

## Extensions

### Covenants

Tari script places restrictions on who can spend UTXOs. It will also be useful for Tari digital asset applications to restrict how or where UTXOs may be spent in some cases. The general term for these sorts of restrictions are termed covenants. The Handshake white paper has a fairly good description of how covenants work.

It is beyond the scope of this RFC, but it's anticipated that Tari Script would play a key role in the introduction of generalised covenant support into Tari.

### Lock-time malleability

The current Tari protocol has an issue with Transaction Output Maturity malleability. This output feature is enforced in the consensus rules but it is actually possible for a miner to change the value without invalidating the transaction.

The lock time could also be added to the script commitment hash to solve this problem.

## Applications

### One-sided transactions

One-sided transactions are Mimblewimble payments that do not require the receiver to interact in the transaction process. LIP-004 describes how this will be implemented in Litecoin's Mimblewimble implementation. The main thrust is that the sender uses Diffie-Hellman exchange to generate a shared private key that is used as the receiver's blinding factor.

To prevent the sender from spending the coins (since both parties now know the spending key), there is an additional commitment balance equation that is carried out on the block and transaction that requires the spender to know the receiver's private key.

To implement one-sided payments in Tari, we propose using Diffie-Hellman exchange in conjunction with Tari Script to achieve the same thing.

In particular, if Alice is sending some Tari to Bob, she generates a shared private key as follows:

$$k_s = \mathrm{H}(k_a P_b)$$

where $P_b$ is Bob's Tari node address, or any other public key that Bob has shared with Alice. Alice can generate an ephemeral public-private keypair, $P_a = k_a\cdot G$ for this transaction.

Alice then locks the output with the following script:

where P_B is Bob's public key. As one can see, this Tari script is very similar to Bitcoin script.
The interpretation of this script is, "Given a Public key, and a signature of this script, the public key must be equal to the one in the locking script, and the signature must be valid using the same public key".

This is in effect the same as Bitcoin's P2PK script. To increase privacy, Alice could also lock the UTXO with a P2PKH script:

Dup HashBlake256 PushHash(HB) EqualVerify CheckSig Add

where HB is the hash of Bob's public key.

In either case, only someone with the knowledge of Bob's private key can generate a valid signature, so Alice will not be able to unlock the UTXO to spend it.

Since the script is committed to and cannot be cut-through, only Bob will be able to spend this UTXO unless someone is able to discover the private key from the public key information (the discrete log assumption), or if the majority of miners collude to not honour the consensus rules governing the successful evaluation of the script (the 51% assumption).

### Credits

Thanks to @philipr-za and @SWvheerden for their input and contributions to this RFC.