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PLONKish Arithmetization

Description

The constraint system underlying the PLONK family. Uses a table of columns (wires) and rows (gates), with polynomial constraints checking gate correctness and copy constraints (permutation argument) checking wiring. Supports custom gates (TurboPLONK), lookup arguments (plookup/UltraPLONK), and more. More flexible than R1CS for expressing complex operations efficiently.

Technical Characteristics

Complexity: - Prover: O(n log n) for most variants - Verifier: O(1) - Proof Size: ~500 bytes – a few KB depending on variant - Setup: trusted (universal CRS)

Security: - Assumption: computational - Post-quantum: no

Based On

PLONK, plookup

Used by Proof Systems

PLONK, TurboPLONK, UltraHonk, HyperPlonk

Supported by Tools

Noir, Barretenberg, Halo2

Resources