PLONKup vs Turbo PLONK

Supports custom gates and lookups: Integrates Plookup for efficient non-arithmetic operations (e.g., bitwise, range checks). This matters for complex application logic like zkEVMs (Scroll, Aztec) where you need to prove arbitrary computations beyond field arithmetic.

Reduces circuit size for specific operations: Lookup arguments can replace thousands of multiplication gates. This matters for high-throughput DApps like on-chain gaming or privacy-preserving DeFi (e.g., Tornado Cash) where proving costs dominate.

Focuses on raw arithmetic gate efficiency: Uses a standardized, simpler gate structure optimized for common operations. This matters for high-performance rollups (e.g., zkSync Era) where predictable proving time and fast recursion are critical.

Easier circuit writing and auditing: More constrained design leads to fewer bugs and clearer code. This matters for protocols prioritizing security and maintainability, especially when building with frameworks like Halo2.

Key advantage: Enables custom, non-arithmetic gates (like lookups) within a single proof system. This matters for protocols with complex, non-uniform logic (e.g., zkEVMs, zkDEXs) where you need to efficiently prove operations like bitwise AND or range checks without bloating the circuit.

Key advantage: Integrates Plookup natively, making it the superior choice for applications dominated by table lookups (e.g., Merkle proofs, signature verification, precomputed function evaluation). This can reduce circuit size by orders of magnitude for specific operations compared to pure arithmetic representation.

Key advantage: Mature, battle-tested implementations in frameworks like Halo2 (used by Zcash, Polygon zkEVM). This matters for teams prioritizing developer velocity, proven security, and a large ecosystem of libraries and documentation over cutting-edge theoretical optimizations.

Key advantage: More efficient for circuits composed primarily of standard arithmetic gates (additions, multiplications). For applications like private payments or simple DeFi logic, Turbo PLONK's streamlined architecture avoids the extra proving cost of supporting generalized custom gates you may not use.

Key trade-off: The flexibility of custom gates and integrated lookups adds complexity to the prover algorithm. This can result in ~15-30% slower proving times for circuits that don't heavily leverage its specialized features, impacting user experience in high-frequency applications.

Key trade-off: Lacks native support for non-arithmetic operations. Implementing lookups or custom constraints requires workarounds that dramatically increase circuit size (and thus cost). This is a poor fit for protocols like zkBridge or zkOracle that need to prove facts about pre-existing data structures.

Key advantage: Enables lookup arguments alongside custom arithmetic gates. This allows developers to prove complex operations (e.g., bitwise operations, range checks) in a single constraint, drastically reducing circuit size. This matters for protocols with non-arithmetic-heavy logic, like privacy-preserving verifiable credentials or custom cryptographic primitives.

Key advantage: Optimized for high-throughput arithmetic computations by using a wider set of pre-defined, specialized gates. For circuits dominated by field operations (e.g., elliptic curve cryptography, Merkle proofs), Turbo PLONK can generate proofs faster and with smaller verification keys than a comparable vanilla PLONK circuit. This matters for high-frequency DeFi applications or consensus mechanisms.