Paper 2022/086

PlonKup: Reconciling PlonK with plookup

Luke Pearson and Joshua Fitzgerald and Héctor Masip and Marta Bellés-Muñoz and Jose Luis Muñoz-Tapia

Abstract

In 2019, Gabizon, Williamson, and Ciobotaru introduced PlonK – a fast and flexible ZK-SNARK with an updatable and universal structured reference string. PlonK uses a grand product argument to check permutations of wire values, and exploits convenient interactions between multiplicative subgroups and Lagrange bases. The following year, Gabizon and Williamson used similar techniques to develop plookup – a ZK-SNARK that can verify that each element from a list of queries can be found in a public lookup table. In this paper, we present PlonKup, a fully succinct ZK-SNARK that integrates the ideas from plookup into PlonK in an efficient way.