Halo vs Halo2

Pioneered Recursive Proof Composition: Introduced the concept of amortizing verification costs by verifying proofs inside other proofs. This was a foundational breakthrough for building scalable, trustless blockchain clients like zcashd.

Relied on a Trusted Setup: Its original construction required a one-time, circuit-specific trusted setup ceremony. This introduced a trust assumption and complexity barrier for widespread adoption compared to transparent systems.

Eliminated Trusted Setup: Leveraged the Inner Product Argument (IPA) and later KZG commitments to achieve transparent, universal setups. This is a critical feature for protocols like zkSync Era and Scroll that prioritize decentralization.

Modular & Programmable Design: Introduced a flexible PLONKish arithmetization and a powerful API (e.g., halo2_proofs crate). This enables custom constraint systems, making it the go-to choice for complex applications like zkEVMs and zkRollups.

Core advantage: The original Halo proof system is transparent and non-updatable, requiring no trusted setup ceremony. This eliminates a major security and operational risk vector for protocols like Mina Protocol, which prioritize maximal decentralization and censorship resistance.

Specific advantage: Uses inner product arguments for succinct recursive proof composition. This provides a more straightforward theoretical model for verifying proofs of proofs, which was foundational for early zk-rollup designs and recursive SNARK research.

Core advantage: Introduces a flexible, table-based arithmetization (custom gates, lookups). This allows developers to design highly optimized circuits for specific computations (e.g., EVM opcodes in zkEVMs, cryptographic primitives), drastically improving prover efficiency for complex logic.

Specific advantage: Built with efficient recursion as a first-class primitive. This enables scalable proof aggregation (e.g., proof of multiple blocks), which is critical for high-throughput zk-rollups like Scroll and Polygon zkEVM to reduce on-chain verification costs.

Key limitation: Lacks the advanced tooling and prover optimizations of Halo2. Development has largely shifted to Halo2, making it harder to find libraries, examples, and community support for new implementations compared to frameworks like halo2_proofs.

Key trade-off: The popular KZG polynomial commitment implementation requires a trusted setup ceremony (e.g., Perpetual Powers of Tau). This adds ceremony complexity and introduces a (manageable) trust assumption, unlike the original Halo's transparent setup.

Enables incremental verification: Supports folding schemes and proof recursion natively, allowing for parallel proof generation and aggregation of multiple proofs into one. This is critical for building zkRollups like Scroll and zkEVMs that require scalable, verifiable state transitions.

Greater flexibility for custom circuits: Uses a generalized arithmetization (Plonkish) that simplifies the design of complex constraints and custom gates. This matters for protocols like Aztec Network (private DeFi) and Taiko (Type-1 zkEVM) that require optimized, application-specific proof logic.

Relies on a single, updatable Structured Reference String (SRS): The original Halo protocol introduced a recursive proof system that eliminated the need for a perpetual trusted setup, reducing ceremony complexity. This foundational innovation paved the way for more trust-minimized systems.

Proved recursive proof aggregation was practical: Halo's major contribution was a theoretical breakthrough demonstrating efficient proof recursion without trusted setups. It provided the core cryptographic backbone that projects like Celo initially adopted before more feature-rich forks evolved.

Increased complexity for developers: The powerful Plonkish arithmetization and advanced features like lookup arguments require deeper cryptographic knowledge to implement correctly compared to simpler SNARK backends. This can slow initial development for teams without specialized ZK expertise.

Lacks modern proving optimizations: The original protocol does not include now-standard features like custom gates, efficient lookup arguments, or the same level of tooling (e.g., halo2_proofs library, halo2wrong for debugging) that Halo2 offers, making it less suitable for high-performance production applications.