# Trustless Trust with Verifiable Computation

*This a piece by** Derek Zhang**, Cofounder, President & Chief Scientist@ARPA, a privacy-preserving blockchain infrastructure enabled by Multiparty Computation(MPC). Derek can be reached at **derekz@arpachain.io**.*

**Keywords**: Blockchain, Ethererum, Verifiable Computation, Consensus algorithm, Incentive Compatibility, cryptoeconomics

# Abstract

Ethereum has implemented a blockchain system which reaches consensus on the state of a general purpose virtual machine, the EVM, allowing users to execute functions to support dApps beyond simple token transactions.

While these functions can reach consensus by Proof-of-Work consensus algorithm, we find out that when the execution requires non-trivial computation effort, practical attacks exist which lead to incorrect results. The reason is that the PoW system is not designed with Incentive Compatibility. We call this the V*erifier’s Dilemma*[1]. And a solution is proposed for this dilemma through a *prover-verifier* consensus scheme. We will then further discuss several constructions for this scheme, by using different cryptographic tools or cryptoeconomics. Finally, we will compare related works, and discuss how ARPA solves this problem.

# The Verifier’s Dilemma

In Nakamoto’s PoW, miners are rewarded for solving computationally hard problems, which is to find the correct hash value. In order to race ahead of others, miners are incentivized to allocate their computation resource to the puzzle game written in the consensus algorithm. When a leader finds the correct hash value, it will broadcast it to the entire network. All other mining nodes will check the validity of this block before mining the next block. The philosophy is that if miners skip checking, they risk of investing in an invalid forked chain and jeopardize their own fate of mining (on the wrong chain).

If the block is simply composed of transactions, it requires negligible computation resources for verification. Miners can do this extra check without spending any significant computation work. The benefit of avoiding ending up in an invalid attackers side chain overweights the cost of validation.

On the other hand, if the broadcasted block contains complex smart contracts that require significant computation resources to validate, the miner can decide to skip the validation to gain an advantage on mining the next block. To prevent this, Ethereum introduced the *gas system* to limit resource exhaustive attack in the system.

**However, this still does not prevent the attacker from creating and including resource-intensive contracts in his newly mined block. **If following the consensus protocol, other miners will validate the block for free. As a consequence, the attack not only exhausts miners’ resource, but also give the attacker some time ahead of other miners in the race for the next block.

Learned that validating an exhaustive contract may lead an inferior position at mining, miners have a strong incentive to skip expensive contracts. Let’s say a complex computation task in the form of a smart contract was initiated by requester **R**, a prover **P** found has just mined the current block, and other validators **V** (miners) are required to check the new block. In this case, **P** can pick a random number as the result of the contract, and **V**s will skip the validation, resulting in an inconsistent state in the blockchain. In addition, **R** will get an incorrect answer and thus wasted its money.

As we mentioned earlier, Ethereum introduced constraints using *gasLimit*. Unfortunately, however, it is not a fool-proof mitigation against this attack. Thus, Nakamoto consensus permits unverified blocks.

# Autonomy on Classic Blockchain Systems

Ethereum and other Turing-complete computation blockchain system assume that the computation and verification of a function are equivalent, *e.g.*, to validate a result from peers in the network, one needs to compute the function again. Indeed, in a trustless network, the only way to agree with the result is to run the Smart Contract (the function) again. Furthermore, to trust others’ validation result, one node needs to validate it again. This leads to a never-ending cycle of validation and that no consensus can converge from that cycle.

In a permissionless network, the biggest contribution of Nakamoto consensus, to decades of research on BFT algorithm, is that it transformed the endless validation cycle to a hash prover-validator model, where the proof is extremely hard to find, but the validation work has the complexity of O(1). Therefore, blockchain network can reach consensus by validating the only *one* block mined from a leader.

In Bitcoin, the block only contains transactions, which is very easy to verify, and thus verifiers are not subject to the dilemma introduced earlier. However, in Ethereum, Turing-complete smart contract can include resource-intensive computation. This results in a situation where the verifiers need to run every computation in order to verify the block, and thus raise the issue of *verifier’s dilemma*.

Formally, the advantage for a rational miner by skipping the verification of a computation *f* is:

We can claim that by skipping validation, **V** also suffers from mining on the wrong chain. Knowing other miners are faithfully working on the due diligence work, the probability that the block is invalid is small, but still non-zero. The optimal decision of whether skipping the validation largely depends on how computation-intense the task is, if the percentage of faithful miner in the network is constant.

# Verifiable Computation

To reach consensus, this is a simple matter of checking a number of hashes, signatures, and account balances in Bitcoin network. For Ethereum, things are more complex. As the state is the state of a powerful virtual machine, verifying it is done by recomputing the steps the virtual machine must take[2].

*Verifiable computation* provides a means to prove the correctness of a computation, such that verifying this proof is less complex computationally than performing the computation itself [3]. Furthermore, verifiable computation enables a weak computer to offload the computation of some functions, to other perhaps untrusted clients, while maintaining verifiable results. The other clients evaluate the function and return the result with a proof that the computation of the function was carried out correctly[4].

Formally, if a cloud service has been tasked with computing the result of a function f, how can the client be sure that the result for an input x they receive is correct? They could recompute f(x) themselves and compare the values, but this would defeat the purpose of using a cloud service for the computation in the first place. It is possible, of course, that there is an easy way to check if the output is correct for some particular f . For instance, if f=h’ for some hash function h, f would be very difficult to compute, while h would be easy. And this is exactly how Nakamoto consensus solved this verification problem: by transforming a W(f) = V(f) problem to a W(f) >> V(f) hash puzzle.

However, blockchain-based transaction verification does not work for arbitrary computation and is situation-specific. The high-level solution is to delegate the computation to someone, and the rest of the network nodes only need to verify the computation with a simple verification function. We call this process the *off-chain computation*. To achieve this goal, a computation proof is needed in the delegation process. For example, if you want to prove that you have been somewhere, the best proof is an item that is unique to that place. We can think off-chain computation as a delegation process, and the envoy has to prove that he actually did finish the task. Similar to this concept, an off-chain computation scheme needs a verification scheme that:

- Can prove that the computation is faithfully done,
- The amount of work done cannot be exaggerated, and optionally,
- The privacy of the content is guaranteed and nothing is revealed to the participants.

This relationship is illustrated in Figure 1.

Figure 1 The off-chain computation process, a proof is the vital part in trustless computation.

With verifiable computation, instead of just computing y=f (x), a computation node will compute a proof p as well: (y,p)=**P**(f,x). And the verifier can check the proof using a verification function **V**(f,x,y,p). The verification function **V **must be such that it returns true only if y=f (x)and (y,p)=**P**(f,x). And the executing **V **should be computationally less complex than f*.*

# Multiparty Computation

Multiparty Computation(MPC) is a way by which multiple parties can compute some function of their individual secret inputs, without any party revealing anything to the other parties about their input other than what can be learned from the output. As mentioned earlier, the current state of smart contract execution is duplicated across all nodes on the blockchain. **However, using MPC, the computation is verifiable and can be safely delegated to other nodes**. In other words, the process can be trusted by the third party, as long as they provide proof that the process is done in the correct way. This proof can be further breaking down in two conceptual parts:

- The computation is conducted with prescribed function and correct input data,
- The proof cannot be forged.

In ARPA MPC, Message Authentication Code (MAC) is a value that can be used to confirm a message has been created by a certain party, and to detect if a message has been changed. The main tool to achieve active security in modern, secret sharing-based protocols is information-theoretic MAC. MACs convey the correctness of computation, so that the computation is verifiable. The validation complexity is O(1), which means it consumes constant time to compute. Therefore it is possible to be executed in any VM. A typical information-theoretic MAC scheme is listed as Alg.3:

If computation nodes deviate from the protocol, such as sending incorrect result, the proof-carrying MAC will not be reconciled and the validation process cannot be passed. Therefore, part 1 is guaranteed by MPC protocol cryptographically.

After the computation nodes finish their work, they sign their MACs with their own private key and store them on the DHT-based distributed storage. This prevents the MAC from being forged by the third party. Therefore, the proof cannot be forged and can be trusted that it is the authentic proof even on a public-accessible storage. This produces the desired property of part 2.

In summary, we now can conclude that the secure computation can be broken down into computation and verification parts. With part 1 and part 2 solved, it is clear that the computation work can be delegated to any party, without pre-existing trust. Thus, the trustless trust is achieved with MAC verification scheme using MPC.

# Related Work

Several technologies existed as candidates of secure computation., namely Fully Homomorphic Encryption(FHE), Zero-Knowledge Proof(ZKP), and Trust Execution Environment. Our discoveries indicate that, while some technologies have advantages such as computation efficiency, some of them are not offering security and verifiable features needed in a permissionless network. In essence, we need to be able to verify the secureness, correctness and privacy-preservingness of computation. The details of each item are explained below:

**Efficiency**: The speed of computation**Privacy-preserving**: Privacy-preserving here refers to the capability to evaluate a function on a dataset while not revealing the detail**Proof of Correctness**: Prove the computation work is actually using the prescribed function**Proof of Computation**: Prove the amount of work the participating node has done**Proof of Security**: Prove that the computation is actually carried out in a secure environment

# Conclusion

The main contribution of Bitcoin is that it created a decentralized public ledger and it reached the consensus in a trustless network. We discovered that with Nakamoto consensus, the system is not Incentive Compatible, especially when the block contains computation-intensive transaction: the best strategy for a rational miner is to skip the verification in order to catch up with the leading miner. We call this *The Verifier's Dilemma*. Further analysis has shown that classic blockchain system assumes the Proving and Validation have the same amount of work, and PoW consensus solved this issue by transforming the work to a hash verification, where the validation has a constant O(1) complexity. With verifiable computation, where the proof-carrying result is significantly easier to validate, we found a path to solve this dilemma. Multiparty Computation, first created to solve secure computation between multiple untrusted parties, was modified to support computation proof. We discussed the properties of MAC and illustrated how to use MAC to support verifiable computation. And further discussed the possibility of using computation delegation to reach trustless trust even for resource-intensive tasks.

# Further work

We at ARPA are a multi-national team focused on secure multiparty computation and its blockchain solution for a general purpose privacy-preserving computation network. While it is a challenging work on the cryptography side, we aim to improve blockchain in the following aspects:

**Secure Computation**Computation is carried out securely so that no participating nodes should learn anything more than its prescribed output.**Verifiable Computation**The computation can be audited publicly, and its correctness can be proved. Therefore, it is possible to outsource the computation from the blockchain network.**Layer2 Solution**Combining secure and verifiable computation, the heavy-lifting work of computation is done off-chain, essentially making our secure computation protocol adaptable to any existing blockchain network.**Scalability**ARPA is designed as a layer2 solution. The on-chain network will never reach its computation (gas) limit. Therefore, we can improve the computation scalability and TPS(transaction per second) of any network. The computation capacity is increased linearly to participating nodes.**Efficiency**State-of-the-art implementation of MPC protocol is used to speed-up the secure computation.**Availability**World’s first general-purpose MPC network for secure computation. With high availability and low cost, we promote data security and privacy practice that is difficult to achieve otherwise.

[1]Demystifying Incentives in the Consensus Computer

[2]Gavin Wood. Ethereum: A secure decentralised generalised transaction ledger. Ethereum Project Yellow Paper, 151, 2014.

[3]Bryan Parno, Mariana Raykova, and Vinod Vaikuntanathan. How to delegate and verify in public: Verifiable computation from attribute-based encryption. In Theory of Cryptography Conference, pages 422–439. Springer, 2012.

[4]https://en.wikipedia.org/wiki/Verifiable_computing

**ABOUT AUTHOR**

Derek Zhang is a serial entrepreneur, president and chief scientist at ARPA. Before his startup journey, he served as data scientist at the World Bank, PineBridge Investments, AIG and CircleUp, in D.C., NYC, Silicon Valley and Beijing, specializing in machine learning, big data and capital markets.

**ABOUT ARPA**

**ARPA** **is the privacy-preserving solution for blockchain**. ARPA’s secure computation network enables 1) private smart contract, 2) unprecedented privacy protection for data-at-use, 3) scalable computational sharding via Verifiable Computation.

ARPA enables numerous use cases including secure data renting/exchange, secure cloud computation, identity protection, computation outsourcing, etc. These cases are applicable to AI, banking, insurance, healthcare, IoT, government etc.

*To get more information about ARPA, or to join our team please contact us at **about@arpachain.io*

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