# Validium By [yektin.eth](https://paragraph.com/@yektin) · 2024-05-06 --- ![](https://storage.googleapis.com/papyrus_images/93c37d224dd169b64a411848f47063b094521c142877d70119f2d355287ed54d.png) Blockchains have to be created around a thing called blockchain trilemma. The point that they approach, the closer 2 will be the more powerful and the 3rd will be the least powerful specialty for them. ![Blockchain Trilemma](https://storage.googleapis.com/papyrus_images/d962c683b7e81cfbd07f5b70aa8d1ec9dc908efaecf2dcabd7ea3f1d65a5be92.png) Blockchain Trilemma Ethereum technology chooses security and decentralization besides scalability in the blockchain trilemma. So, there are some developments around Ethereum to solve the scalability issues of the network. We’ll talk about a scalability solution, Validium’s in this essay. Ethereum’s current roadmap is based on a scalability solution called Rollups. Validiums are likely in several ways to Rollups however, they have a different approach for scalability. We can say that Validium’s exists until Rollup’s become affordable. Why? Like Rollups, Validiums tries to work with a slight amount of Ethereum mainnet usage but besides Rollups, data execution and data availability parts are done off-chain. Transactions proofs used zero-knowledge proofs, like how Zero-Knowledge Rollup does, and after executing the proofs they verify the proofs on Ethereum mainnet. In favor of Ethereum’s security infrastructure, verifying proofs on Ethereum mainnet makes security conditions better. We said that Validium’s likelihood with ZK-Rollup’s execution and verification methods. That proof type is called Validity Proof. **Validity Proof** Validity Proof or Zero Knowledge Proof is a proof type for verifying transactions with standing between the verifier and prover. In the proving process, none of the proving data will be exported out of the system. With polynomial equations, they provide encryption and verification. Generally, they use 3 major polynomial hash schema: **1- KZG (Kate-Zaverucha-Groth) Polynomial Commitments:** The Prover puts up a polynomial, provides the proof, and commits the result. The verifier tests polynomials by sending a random value to the prover. In this case, the prover knows the equation of the polynomial and the verifier knows the output value of the point from the polynomial equation that he/she gave. So, how the proof unknown can be known? Proof unknown stands as a polynomial equation too. We’re trying to create a relation between this proof equation and the polynomial equation at the beginning. In this point, we’ll work like how we find the roots of a polynomial equation, we find the point that makes the polynomial equation zero. Division of this point and multiplication of this point with the polynomial equation at the beginning will give us the point that the polynomial equation equals zero. As a result, we’ll get this equation: ![](https://storage.googleapis.com/papyrus_images/4096c936cf9d9ec1e9614520af500bc0a5ef5ad1d1e777afbedd3920a6b54305.png) Here, the q(s) value is our proof. If you want to learn more about this topic and see what happens in the further work you can work with [Elliptic Curve Pairing](https://blog.subspace.network/kzg-polynomial-commitments-cd64af8ec868). **2- Bulletproof:** Bulletproof, is a zero-knowledge argument that proves the interval of knowledge. This can be used; to convince the verifier that a number exists in an interval without providing any information about the encoded data itself. This idea was created in 2017 by a group of cryptographical researchers at Stanford. Bulletproof, works with a discrete logarithm problem and Fiat-Shamir conversion to achieve the goal of itself. The discrete logarithm problem makes the calculation of the input impossible with a one-way execution. And Fiat-Shamir conversion creates a digital signature with the achieved proof. Unlike the KZG schema, there is no need for a relation between the prover and the verifier. `Small like a bullet but provides security like bullet-proof. - Shashank Agrawal` **3- FRI (Fast Reed-Solomon Interactive Oracle Proofs of Proximity):** According to the small degree polynomial’s degree, makes us calculate the function’s value in a certain orbit. We can create validity proof by using this schema. Generally, the KZG schema is in use. Validium users’ assets are controlled by a smart contract that is deployed on the Ethereum network. Users can take their assets from Validiums using Merkle proofs. Data accessibility management can choose not to provide users with off-chain transaction data, freezing their assets or preventing them from withdrawing them. The main difference between ZK-Rollups and Validiums is the data availability issue that we talked about here. Rollups and ZK-Rollups store the data on-chain but Validiums stores the data off-chain. **How Validiums Interact with Ethereum?** Validium works with the smart contracts deployed on the Ethereum mainnet. **1- Verifier Smart Contract:** Verifies the validity proofs of the transactions with state updates via Validium operators. This verification includes the transaction that is held off-chain and matching the data availability proofs with the off-chain transactions data. **2- Main Smart Contract:** Executes the committed states (Merkle proofs) via block producers. Besides this, this smart contract updates the Validium’s state after the validity proofs are proved on-chain. **Commitment to Ethereum** Because of is a scalability solution for Ethereum, Validium is connected to the Ethereum network at several points. The transactions on Validium are not valid until verified at the mainnet. In Validiums, the inability to reverse or modify transactions made off-chain is evaluated as a result of on-chain approval, and the settlement is secured by the Ethereum chains’s settlement layer. Besides this, for verification of these transactions on-chain, the Ethereum chain needs to know of the Validiums’ states. **How a Validium Works?** In Validiums, the users' transactions using the consensus mechanism PoS (Proof-of-Stake, a consensus mechanism that leans to the asset locking to the network) the transactions stored off-chain. Validium chains’ operators, make the whole transactions on the chain to a chunk and accept these as input. As an output, they create valid proof for verifying that the transactions are valid or not. Validium state hashed and stored with Merkle tree roots in the smart contract that deployed on Ethereum mainnet. Merkle trees are used to represent the current state of the Validiums. For a state update, operators create a new root and deploy it to the smart contract. After the validation of the validity proof provided, this root is accepted as a new state root. If users want to send their assets to Validium from the Ethereum network, they will send their assets to the smart contracts. They will show this transaction to the off-chain data and the sent assets show up on the users’ portfolio in the Validium network. If the request is sending the asset on the Validium chain to the Ethereum chain, the user does a transaction to take the assets back and sends this transaction to the operator. The operator executes the transaction here and adds to a chunk. In this sending process, if a validity proof can be provided the users’ assets on the Validium chain are erased and the assets that are sent can be seen on the Ethereum mainnet. Also, the Validium structure can remove the bond with the operator and can make users directly interact with the Validium smart contract with Merkle proof. The operator sends the chunk, that is filled with these transactions, to the verifier smart contract with validity proof and then proposes to create a new root to the main smart contract. If the proof is valid, the main smart contract updates the state of Validium and finalizes the transactions that are inside the chunk. As a difference from ZK-Rollups, block producers won’t share the data inside the transaction chunk in Validium chains. They just share the header of the blocks. **Data Availability and Validiums** Storing the data off-chain may cause some issues about the control of the assets of users in Validiums. Several Validium protocol aims to solve this issue by making the state data storing decentralized. Blok producers send the data to the managers chosen for the data availability and these managers are responsible for storing these data off-chain and at the same time making these data available for users' wants. **Data Availability Committee (DAC):** Several Validium protocols choose a trust-based system for the issue of stored data availability on off-chain data storage. This group is responsible for storing the states of data and a copy of the proofs for the data availability. **Bonded Data Availability:** As a data availability solution used in Validium’s. It requires participants who provide assistance for data accessibility to lock tokens into a smart contract to store off-chain data. This method is more sensible and decentralized rather than creating a trust-based committee. **Volitions and Validiums** Validiums should be chosen wisely for more valuable areas. So that Volition’s are created. Volitions are a structure that combination of ZK-Rollups’ and Validiums’ chains. Users can choose between these scalability solution chains. More freedom can be provided by using the different benefits of ZK-Rollups and Validiums. Especially the usage of the Volition structure in decentralized exchange platforms makes more sense in scalability, privacy, security, and non-trust-based systems. ![Source: StarkEx](https://storage.googleapis.com/papyrus_images/edfecb595fbd91d04a94edfaa5a4c25b9d75fcef5ace9078da9704892f09c7db.png) Source: StarkEx **Validiums and EVM Equivalency** The problem of not working with smart contracts on ZK-Rollups that was talked about in [Ethereum’s current roadmap live stream in ITU Blockchain](https://www.youtube.com/watch?v=ppq35e-NPWU) exists in Validiums too. Execution of smart contracts and implementation of them is hard work under the Validium structure. To overcome this problem, some Validium protocols aim to create custom bytecodes on top of smart contract languages that are already EVM-compatible (e.g. Solidity, Viper) to provide an efficient processing structure. However, this would require developers to work in a completely new development environment, which is not preferred. In this topic, the zkEVM (Zero-Knowledge EVM) structure’s development is a living idea. The goal with it is producing and verifying zero-knowledge proofs with EVM-compatible machines. With a zero-knowledge compatible EVM, we can work with smart contracts on zero-knowledge proof used protocols (ZK-Rollups and Validiums). **How Validiums Participate in Scaling Ethereum?** **1- Storing Data Off-Chain:** As from the Rollups’ structure, the scalability level relies on Ethereum mainnet’s data network bandwidth. In the other way, Validiums stores the transactions’ data off-chain and just sends the committed states and validity proofs to the Ethereum mainnet. In this way, they can contribute to scaling by performing minimal transactions on the Ethereum mainnet. **2- Recursive Proof:** This proof type is a validity proof and verifies the other proofs. We can say it is like the proof of the proofs. They can contribute to the scaling in a way that increases the amount of executable transactions on the blockchain. `Validity proofs can make a risky situation because of the needed special hardware.` `Because Validiums creating a new structure on the development part, they can have some issues about onboarding developers to their ecosystem.` The main projects using the Validium structure are StarkEx by StarkWare and zkPorter by Matter Labs. **StarkEx** StarkEx is a Layer-2 scaling solution that relies on validity proofs. As ZK-Rollup and Validium at the same time, it includes different types of data availability methods. **ZK-Rollup & StarkEx:** This architecture is used for StarkEx futures and StarkEx spot tradings. The data is stored on-chain. The benefit of a non-trust setup is used as an advantage. However because of creating a proof for every update, there is an existing fee for each transaction. **Validium & StarkEx:** This architecture is used for StarkEx futures and StarkEx spot tradings. The data is stored off-chain and a Data Availability Committee is preferred. Because of the data stored off-chain, the fee on the chain is pretty low. If we want to change the on-chain state, then we need to pay some fees. Storing the data off-chain provides some commitment about privacy but don’t forget that in this setup this work is done by a trusted setup. **Volition & StarkEx:** This architecture is used for StarkEx spot tradings. This architecture is a combination of two other scaling solutions so if there is a need for something we can change the method whatever we want to. The name of Validium is proposed by StarkWare: [https://twitter.com/VitalikButerin/status/1267455602764251138](https://twitter.com/VitalikButerin/status/1267455602764251138) * StarkEx provides some developments in privacy areas: **OND (Rollup):** Storing the encoded data on-chain. **OFFD (Validium):** Confidentiality can be ensured by ensuring that the data availability committee does not act contrary to its responsibilities. * StarkEx developed two different development designs as a data availability solution: **Minimally Viable Rollback (MVR):** What if the data is inaccessible beyond OFFD solutions? Let's think that both the operator and data availability committee have an issue. In this type of case, this design aims to ensure continuity by returning to a state where data is accessible instead of a state where data is inaccessible. Trustless Off-chain Data Availability (TODA): In this solution, users can choose to be Power Users (PU). Users who choose to become Power Users are authorized to sign for every piece of evidence and can verify their own transaction with this signature. **zkPorter** zkPorter is a Layer-2 solution that develops a hybrid approach to data availability using zkRollup and sharding ideas. zkPorter is thought of as more secure than the Ethereum mainnet (a.k.a. Layer 1). In the worst case, even if 2/3 of locked assets on the network got hacked the execution of this data stopped and the state froze for taking assets back. **Polygon zkEVM Validium** Polygon develops two different solutions: Polygon zkEVM (a Rollup solution) and Polygon zkEVM Validium (old Polygon PoS). They plan to make this solution work with the power of Polygon CDK. Polygon says that: “Let's become Rollup and Validium at the same time. If this both structure uses the same validators and the same liquidity pool, this could be good.” **Manta Network** Manta Network aims to work as a Validium using Polygon zkEVM as zkEVM and Celestia as a data availability solution. **Celo** Celo, originally known as a mobile blockchain (Celo aimed to send crypto assets via phone numbers instead of crypto addresses), is evaluating becoming an Ethereum layer 2 solution as Validium using Polygon CDK, a proposal recently opened by Polygon Labs. Nowadays, they are thinking about the OP Stack to integrate. **Immutable X** Immutable is an NFT-centric blockchain. They are aiming to become a Volition with Validium and ZK-Rollup at the same time. Also, Immutable works on a zkEVM structure beyond Polygon CDK. --- *Originally published on [yektin.eth](https://paragraph.com/@yektin/validium)*