Introduction to Zero Knowledge

Introduction to Zero Knowledge

In recent years, the field of cryptography known as "zero knowledge" has made remarkable strides, offering innovative methods to enhance application development while boosting efficiency, security, and privacy across various protocols.

This exploration will delve into the captivating realm of zero knowledge proofs (ZKPs), highlighting their significance in solving complex challenges faced by engineers and developers in modern computing environments.

Trustless Blockchains and Verifiability

Blockchains operate by processing transactions submitted by users, which typically trigger computational tasks for the network. For a blockchain to function in a trustless manner—meaning participants do not have to rely on any single party—network participants must verify the validity of transactions and ensure that the computations resulting from those transactions are executed correctly.

Validating a transaction generally requires digital signature verification, confirming that the purported sender is indeed the originator of the transaction. However, to verify that the transaction's computations were correctly executed, participants often need to re-run the transaction locally, which can be inefficient and impractical.

Limitations of Traditional Verifiability

This traditional verification process can falter under certain circumstances. A participant may be unable to re-execute computations for various reasons:

1. Privacy Concerns: Sensitive data might not be suitable for disclosure, thus hindering re-execution.

2. Resource Constraints: The computational cost of re-executing all transactions can be prohibitively expensive, especially in high-throughput blockchains with numerous transactions per second.

The Transformative Power of Zero Knowledge Proofs

Zero knowledge proofs offer a powerful solution to these limitations. With ZKPs, participants can verify the outcome of a computation while achieving two critical objectives:

1. Data Privacy: Sensitive information involved in the computation remains confidential.

2. Cost Efficiency: Verifying a proof is significantly less resource-intensive than re-executing the computation.

These characteristics—privacy (zero knowledge) and efficiency (succinctness)—position ZKPs as invaluable tools for enhancing the verifiability of trustless blockchains. By utilizing ZKPs, one party can perform the computation and generate a proof of correctness. Other participants can then verify this proof without needing to re-execute the computation themselves. This not only protects sensitive data but also allows for higher transaction throughput within the network.

Components of Zero Knowledge Proofs

While implementing ZKPs can be intricate, understanding their fundamental components is crucial:

• Circuit: This is a program that takes input data and asserts its validity against specified constraints. Inputs can be classified as public (known to all), private (known only to the prover), or a combination of both.

• Proof: A proof is generated to assert that a specific input satisfies the circuit's conditions. Importantly, it reveals no details about private inputs and is compact in size.

• Verifier: The verifier checks three essential criteria:

  1. The validity of the proof.

  2. Whether the proof adheres to the constraints outlined in the circuit.

  3. Confirmation that the public inputs used to generate the proof align with those used by the verifier.

The verification process typically requires minimal computational resources and simply results in a determination of “valid proof” or “invalid proof.”

Example: Zero Knowledge Proofs in Action

Consider the game of Sudoku as an illustrative example. Suppose Alice possesses a solution to a Sudoku puzzle but wishes to demonstrate her knowledge of the solution to Bob without revealing it.

In this scenario, the specific Sudoku puzzle acts as a public input (known to both Alice and Bob), while the solution remains private (only known to Alice). The circuit checks the validity of the solution according to standard Sudoku rules, verifying the correctness row-by-row and column-by-column.

Alice can generate a proof stating that she has a valid solution for the public puzzle. This proof, along with the puzzle, can be sent to Bob. He can then use a verifier linked to the Sudoku circuit to confirm the proof's validity, thereby validating Alice's claim without learning the actual solution.

Zero Knowledge Proofs and Their Impact on Blockchains

One of the driving forces behind recent advancements in ZKPs is their application in blockchain technology. Two significant challenges that decentralized blockchains encounter are:

1. Privacy: All data is publicly accessible, raising concerns about sensitive information.

2. Scalability: Every node in the network is required to re-run each computation, which can limit performance.

ZKPs offer potential solutions to these issues. Several projects leverage the properties of ZKPs to develop privacy-preserving applications. At Wischain, we utilize the succinctness property of ZKPs to enhance the scalability of Ethereum.

Wischain and Zero Knowledge Proofs

The underlying concept of Wischain is straightforward yet powerful: what if we could utilize an Ethereum smart contract to verify all computations from an alternate version of Ethereum? This would allow us to operate a separate network that offers faster and more cost-effective access to an Ethereum Virtual Machine (EVM), with Ethereum itself providing the necessary security for validating computations and ensuring compliance with EVM standards.

Subsequent sections within the Learn and Technology categories will elaborate on this framework in greater depth. However, it is crucial to remember that zero knowledge relies on the components of circuits, proofs, and verifiers.

In our architecture, the circuit (comprising a set of circuits) encodes the rules of the EVM to constrain acceptable behaviors for processing input transactions in relation to the blockchain state. Using a “zkEVM,” a network of GPUs processes transactions for sets of blocks and generates proofs. Subsequently, a smart contract on Ethereum verifies that these proofs align with the circuit defined within the contract. If the proofs are valid, the transactions can be deemed "finalized," enabling the network to progress while ensuring fast, secure, and affordable block space for the growth of Ethereum.