Halo2

Halo2 is a zero-knowledge succinct non-interactive argument of knowledge (zk-SNARK) proving system that eliminates the need for a trusted setup, a major advancement in cryptographic protocols. It builds upon its predecessor, Halo, by introducing a novel polynomial commitment scheme and a more efficient proof recursion mechanism. This architecture allows for the creation of complex, scalable zero-knowledge proofs without the security risks and logistical overhead associated with a one-time trusted ceremony, making it a trustless and more secure foundation for privacy-preserving applications.

At its core, Halo2 utilizes a Plonkish arithmetization and a custom polynomial commitment scheme based on the Inner Product Argument (IPA). This combination allows developers to express computational statements as constraint systems over a finite field. The proving system is highly flexible, supporting custom gates and lookup arguments, which are essential for optimizing proofs of complex operations like hash functions or range checks. Its design prioritizes prover efficiency and recursive proof composition, enabling proofs to verify other proofs, a key technique for building scalable blockchains and rollups.

The primary application of Halo2 is within the Zcash blockchain, where it powers the Orchard shielded transaction protocol, providing strong cryptographic privacy for users. Beyond cryptocurrency, its framework is a foundational component for zk-rollups and zkEVMs, such as those explored by Scroll and Taiko, which aim to scale Ethereum by bundling transactions into succinct proofs. The system's library, often referred to as the halo2 proving system, is implemented in Rust and provides APIs for circuit developers to build custom zero-knowledge applications, from private smart contracts to verifiable machine learning models.

At its core, Halo2 is a plonkish proving system, building upon the PLONK protocol's universal trusted setup. Its architecture is defined by a constraint system where a prover demonstrates they have performed a correct computation by generating a proof that all polynomial constraints are satisfied. The system's flexibility comes from its use of custom gates and lookup arguments, allowing developers to design highly efficient circuits for specific computations like cryptographic operations or state transitions.

A key innovation of Halo2 is its support for recursive proof composition without requiring a pairing-friendly elliptic curve. This is enabled by its inner product argument and a polynomial commitment scheme based on the IPA (Inner Product Argument) from Bulletproofs. Recursion allows proofs to verify other proofs, enabling scalable zk-rollups and infinite proof aggregation, which is critical for building L2 scaling solutions on blockchains like Ethereum.

The development workflow involves writing a circuit using a domain-specific language (DSL), such as the halo2_proofs library in Rust. Developers define advice columns, fixed columns, and instance columns to represent private inputs, constants, and public inputs/outputs, respectively. The prover then generates a proof by committing to these polynomials, and the verifier checks the proof against the public instances. This process ensures the computation is valid without revealing the private inputs.

Unlike earlier zk-SNARKs like Groth16, Halo2 employs a universal and updatable trusted setup, meaning a single ceremony can be used for all circuits, and the toxic waste can be safely removed by a sequence of participants. Its performance is characterized by fast proving times and small proof sizes, making it a foundational technology for projects like Zcash (for its shield pool) and various zkEVM implementations aiming to scale Ethereum with zero-knowledge cryptography.

Recursive proof composition is a cryptographic technique where one zero-knowledge proof verifies the correctness of another, creating a chain or tree of proofs that can be aggregated into a single, final proof. In the context of Halo2, this is implemented without requiring a trusted setup, using its polynomial commitment scheme and a recursive verifier circuit. The core idea is that the verification logic of a proof is itself encoded as a circuit; proving that this verification check passes becomes the next step in the recursive chain. This allows for incremental verifiability, where large computations are broken into smaller, provable chunks.

The Halo2 proving system achieves recursion efficiently through its use of the Inner Product Argument (IPA) and a technique called accumulation. Instead of verifying each proof from scratch, the verifier's work is offloaded into an accumulator, which collects the verification equations. A single, final proof is then generated to demonstrate that all accumulated equations are satisfied. This process drastically reduces the overall verification cost and proof size, as the final proof's size remains constant regardless of the number of composed sub-proofs. This is critical for scaling zk-rollups and building zkEVMs.

A primary application is in blockchain scalability, particularly for zk-rollups. Here, recursive composition allows a rollup to generate a single succinct proof that validates an entire batch of transactions, which can then be verified on-chain with minimal gas cost. It also enables infinite proof recursion or proof aggregation, where proofs from multiple provers or over long time periods can be merged. This creates a proof of proofs, providing a cryptographic guarantee for a vast history of state transitions without requiring the verifier to re-execute the entire chain of logic.

In the context of zero-knowledge proof systems like Halo2, a trustless or transparent setup refers to a configuration that does not require a one-time trusted setup ceremony to generate initial cryptographic parameters, thereby eliminating a critical security assumption and potential single point of failure. Unlike systems that rely on a trusted setup—where a secret parameter must be generated and then securely destroyed—Halo2's transparent setup uses publicly verifiable, updatable parameters that anyone can generate and verify, ensuring no party ever possesses toxic waste that could compromise the system's security.

The core innovation enabling this is the accumulation scheme, a recursive proof composition technique that allows the prover to iteratively combine proofs without needing secret trapdoors. This mechanism, built upon the Inner Product Argument (IPA) and polynomial commitments, creates a chain of proofs where each step verifies the previous one. Consequently, the system's security relies solely on standard cryptographic assumptions, such as the hardness of the discrete logarithm problem, rather than on the correct execution of a secret ceremony. This makes the setup process updatable and universally composable.

This architectural choice has profound implications for decentralization and long-term security. Projects built with Halo2, such as the zcash blockchain, can launch without organizing a complex multi-party computation (MPC) ceremony, reducing coordination overhead and launch risk. Furthermore, the system's security is not anchored to a specific point in time; the proving and verification keys are generated from public randomness, and the protocol remains secure even if the initial parameters were somehow compromised, as they contain no secrets. This property is sometimes described as post-quantum secure in the sense that the setup itself does not introduce quantum-vulnerable secrets.

From a developer's perspective, the trustless setup simplifies the deployment and maintenance of zk-SNARK applications. There is no need to manage or audit a ceremony, and the verification key is succinct and constant-sized, regardless of the circuit complexity. This contrasts with other transparent systems like STARKs, which may have larger proof sizes. The Halo2 proving system, particularly in its PLONKish arithmetization form, thus provides a powerful and practical toolkit for creating scalable, private applications on public blockchains without foundational trust assumptions.

Halo2 is a zero-knowledge succinct non-interactive argument of knowledge (zk-SNARK) proving system that introduced recursive proof composition without requiring a trusted setup, building upon the innovations of its predecessor, Halo. Developed primarily for the Zcash blockchain, its core advancement is the use of a polynomial commitment scheme based on the Inner Product Argument (IPA), which allows for more efficient proof generation and verification compared to earlier pairing-based systems like Groth16. This design eliminates the need for a persistent toxic waste ceremony, making the system more trust-minimized and sustainable for long-running networks.

The architecture of Halo2 is built around a Plonkish arithmetization, a flexible method for translating computational statements into polynomial equations that a zero-knowledge proof can verify. This arithmetization supports custom gates and lookup arguments, enabling highly efficient circuits for complex operations like hashing and digital signatures. A key feature is recursion, where proofs can verify other proofs, enabling applications like incremental verification and rollup scalability. This allows blockchains to bundle thousands of transactions into a single, compact proof, dramatically increasing throughput.

Halo2's impact extends far beyond Zcash, forming the cryptographic foundation for major Layer 2 scaling solutions and zkEVM implementations. Its library, implemented in Rust, has been adopted and forked by projects like Scroll, Taiko, and Polygon zkEVM to build Ethereum-compatible rollups. The system's efficiency and active developer ecosystem have made it a leading choice for teams building general-purpose zk-rollups, cementing its role in the evolution of zero-knowledge cryptography from a niche privacy tool to a cornerstone of blockchain scalability.