PLONK

PLONK, whose name is an acronym for Permutations over Lagrange-bases for Oecumenical Noninteractive arguments of Knowledge, was published in 2019 by Ariel Gabizon, Zachary J. Williamson and Oana Ciobotaru. Its distinctive feature is a universal structured reference string: instead of requiring a fresh setup per circuit, a single powers-of-tau-style ceremony serves any circuit up to a maximum size. It is also updatable, so anyone can add randomness and just one honest participant is enough for the setup to be secure.

Internally, PLONK uses a permutation argument to enforce copy constraints between circuit wires, polynomials in the Lagrange basis over evaluation domains, and KZG polynomial commitments, which are the part that requires the trusted reference string. This design cleanly separates the one-time initial ceremony from the per-circuit work, which no longer needs additional trust.

The comparison with Groth16 captures its profile. Groth16 produces more compact proofs, just three group elements, and very cheap verification, but it forces a circuit-specific ceremony. PLONK trades some proof size for a universal setup that does not need to be redone when the circuit changes. That is why it fits platforms with many or continually evolving circuits, and projects such as zkSync, Aztec, Dusk Network and Mina have adopted or adapted it; Zcash's Halo 2 uses a PLONKish-style arithmetization without a trusted setup.