Introduction to Halo2

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Introduction to Halo2
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Introduction

Halo2 builds on the foundation of earlier zk-SNARKs (Zero-Knowledge Succinct Non-Interactive Arguments of Knowledge) like Groth16 and Plonk but introduces significant innovations in flexibility, scalability, and composability. It is particularly well-suited for applications that require recursive proofs, privacy-preserving computations, and efficient proof generation.

Developed as a part of the Zcash ecosystem, Halo2 addresses some of the key limitations of earlier ZK proof systems, such as the need for a trusted setup and limited composability. By removing the need for a trusted setup and supporting proof recursion, Halo2 enables the creation of more modular and scalable zero-knowledge applications.

Key Features of Halo2

  1. Flexibility
  • General-Purpose Proofs: Unlike older systems like Groth16, which require specialized circuit generation, Halo2 supports general-purpose proof construction. Developers can design circuits for a wider range of applications, from privacy-preserving transactions to verifiable computations.
  • Custom Gates and Lookups: Halo2 allows developers to define custom gates and use lookup tables. This enables more efficient circuit design and reduces the number of constraints required for certain types of operations.
  1. Efficiency
  • Reduced Proof Sizes: Halo2 enables smaller proof sizes, which are cheaper to verify and more efficient to transmit. This is especially important for blockchain-based applications where transaction size impacts network fees.
  • Batch Proofs: Halo2 supports batching multiple proofs into a single proof, thereby reducing the computational overhead associated with verifying multiple statements at once.
  1. Support for Recursive Proofs
  • Proof Composition: One of the most revolutionary features of Halo2 is its support for recursive proof composition. Recursive proofs allow one proof to attest to the correctness of another proof, enabling powerful applications like rollups and verifiable computation.
  • Scalability and Aggregation: Recursion allows developers to create proof systems that “stack” smaller proofs into larger, composite proofs. This is a foundational concept for zk-rollups, where multiple transactions are aggregated into a single proof to be submitted to a blockchain.

What is a zk Circuit?

A zk circuit is a logical structure that defines how a zero-knowledge proof is generated and verified. At its core, a zk circuit encodes mathematical constraints that must be satisfied for a certain statement to be proven true. The circuit defines the logic that governs what can be proven, and its structure ensures that the proof is both verifiable and privacy-preserving.

The Role of Constraints

Constraints are the mathematical rules that define the behaviour of the zk circuit. They specify the conditions that must be met for a proof to be valid. For example, if you want to prove knowledge of two numbers whose sum is 10, the circuit would enforce a constraint like a + b = 10 . Constraints are essential because they ensure the integrity of the proof while maintaining privacy.

Inputs, Outputs, and Witnesses

  1. Inputs: These are public values that are known to both the prover and the verifier. Inputs are part of the public data that define the statement being proven. For instance, in a zk-SNARK that proves knowledge of a solution to a Sudoku puzzle, the initial puzzle grid might be a public input.
  2. Witnesses: Witnesses are private, hidden values known only to the prover. They are critical to maintaining privacy in zero-knowledge proofs. Witnesses provide the secret information required to satisfy the constraints of the circuit. For example, the solution to a Sudoku puzzle would be a witness.
  3. Outputs: Outputs are the final values that result from running the inputs and witnesses through the constraints of the circuit. They are typically part of the public data shared with the verifier.

Why Witnesses Are Hidden but Provable

The key to zero-knowledge proofs is that witnesses are hidden from the verifier but still provable. This is achieved using cryptographic commitments, which allow the prover to “commit” to a witness without revealing it. The proof demonstrates that the witness satisfies the circuit’s constraints without disclosing any additional information. This property maintains privacy while still ensuring that the proof is valid.

Key Concepts in zk Circuits

  1. Selectors
  • Selectors determine when certain constraints are active in the circuit. They are like “switches” that turn constraints on or off depending on the current state of the circuit.
  1. Columns
  • Columns are storage structures used to hold inputs, fixed data, or advice (dynamic data). There are different types of columns for different purposes:
    • Fixed Columns: Store constant values that do not change during proof generation.
    • Advice Columns: Store dynamic, prover-specific data that changes with each proof.
    • Instance Columns: Represent public inputs known to both the prover and the verifier.
  1. Constraints
  • Constraints are the mathematical conditions that must be satisfied to “satisfy” the circuit. Each row of the circuit’s table corresponds to a step in the logical process, and constraints enforce the relationships between the values in the columns. For example, a constraint might state that c = a + b , where a and b are stored in advice columns and c is stored in an instance column.

Together, selectors, columns, and constraints form the building blocks of a zk circuit. These elements work in harmony to define the logic, input-output relationships, and privacy guarantees of the proof system.

Why Learn Halo2 for zk Circuits?

Demand for ZK Development Skills

The demand for developers skilled in zero-knowledge proofs (ZKPs) is rapidly growing. Blockchain privacy solutions, decentralized finance (DeFi) applications, and privacy-preserving AI systems are driving this need. Developers with knowledge of Halo2 are especially valuable as it supports advanced features like recursive proofs and general-purpose circuit design.

Why Halo2 is a Powerful Tool for Developers

Halo2’s flexibility, efficiency, and composability make it a crucial tool for developers entering the ZK space. It allows developers to create circuits for a wide variety of applications and supports the design of highly efficient, privacy-preserving computations. With its recursive proof capabilities, Halo2 enables scalable, verifiable computation for projects like rollups and recursive zk-proofs.

Advantages of Learning Halo2 Early

  1. High-Demand Skill: Knowledge of Halo2 positions developers for roles in cutting-edge cryptography and privacy technology.
  2. Access to High-Impact Projects: Halo2 is used in prominent projects like Zcash and zk-rollups, opening opportunities to contribute to impactful blockchain technologies.
  3. Career Growth: Expertise in Halo2 provides access to high-paying roles in DeFi, blockchain privacy, and decentralized application development.

Conclusion

Halo2 stands as a transformative proving system for zero-knowledge proofs, enabling privacy, scalability, and efficiency for modern cryptographic applications. Its unique features, such as recursive proof support and composability, make it a vital tool for developers and organizations alike. By learning Halo2, developers can position themselves at the forefront of the growing demand for privacy-preserving technologies and play a critical role in the development of future blockchain, AI, and cryptography innovations.

We encourage you to continue your exploration of topics on zk proofs. If you’re interested in diving deeper, you can follow up on the pathway here Zero-Knowledge Proofs on the Celo Blockchain: A Comprehensive Tutorial Series - Pathways - Celo Academy

Resources

Circom docs
SnarkJS
0xparc Circom Workshop

About the author

I’m Jonathan Iheme, A full stack block-chain Developer from Nigeria. With a great passion for Zero Knowledge Technology.

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