Paper 2022/086

PlonKup: Reconciling PlonK with plookup

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


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.

Available format(s)
Cryptographic protocols
Publication info
Preprint. MINOR revision.
zero knowledgelookup tableimplementationapplications
Contact author(s)
luke @ polychain capital
joshua @ heliax dev
hector masip @ upc edu
marta @ dusk network
jose luis munoz @ upc edu
2022-03-12: last of 3 revisions
2022-01-25: received
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Creative Commons Attribution


      author = {Luke Pearson and Joshua Fitzgerald and Héctor Masip and Marta Bellés-Muñoz and Jose Luis Muñoz-Tapia},
      title = {{PlonKup}: Reconciling {PlonK} with plookup},
      howpublished = {Cryptology ePrint Archive, Paper 2022/086},
      year = {2022},
      note = {\url{}},
      url = {}
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