---
title: "Lookup arguments: Plookup, LogUp, cq, Lasso/Shout/Twist"
description: "Lookup arguments: Plookup, LogUp, cq, Lasso/Shout/Twist: Cross-cutting — often the real cost driver."
type: "option"
url: "https://zkpick.com/proof-systems/lookup-arguments/"
section: "01 Choosing a proof system"
authors:
  - "MarketComp"
publisher: "MarketComp"
version: "1.3"
updated: "2026-09-12"
license: "CC-BY-4.0"
json: "https://zkpick.com/data/proof-systems/lookup-arguments.json"
---

*By MarketComp. Updated 2026-09-12. Version 1.3. CC BY 4.0.*

# Lookup arguments: Plookup, LogUp, cq, Lasso/Shout/Twist — *Cross-cutting — often the real cost driver*

> Lookup arguments: Plookup, LogUp, cq, Lasso/Shout/Twist: Cross-cutting — often the real cost driver. Lookup arguments prove that values appear in a table, and are how systems express operations that are expensive as raw arithmetic. Maturity: Plookup and LogUp production; structure-exploiting variants research-stage. Maintained by: Plookup: Gabizon and Williamson (Aztec). LogUp: Haböck (Polygon). cq: Eagen, Fiore and Gabizon. Lasso, Twist and Shout: Setty, Thaler and collaborators (a16z crypto). Choose it when: Evaluate the lookup argument explicitly whenever range checks, bitwise operations or instruction decoding dominate your constraint count.

Lookup arguments prove that values appear in a table, and are how systems express operations that are expensive as raw arithmetic. Plookup is the original and ubiquitous; LogUp uses logarithmic derivatives and is substantially cheaper for wide multi-column lookups; cq makes prover cost independent of table size after preprocessing; Lasso and its successors exploit table structure so huge tables need never be materialised.

**Strengths**

- Frequently determines prover time more than the choice of headline proof system does
- LogUp and its GKR variant dominate modern small-field designs
- Structure-exploiting arguments make instruction-set-sized tables tractable at all

**Tradeoffs**

- Plookup scales poorly with large tables and multi-column lookups
- cq requires a KZG SRS and amortised preprocessing — poor fit for changing tables
- Structure-exploiting schemes are tied to sumcheck arithmetisations, need decomposable tables to deliver their headline benefits, and their reference implementation is self-declared alpha
- Multiplicity handling is a known correctness trap: an unconstrained multiplicity column silently breaks soundness

**Choose it when:** Evaluate the lookup argument explicitly whenever range checks, bitwise operations or instruction decoding dominate your constraint count.

Maintained by: Plookup: Gabizon and Williamson (Aztec). LogUp: Haböck (Polygon). cq: Eagen, Fiore and Gabizon. Lasso, Twist and Shout: Setty, Thaler and collaborators (a16z crypto) · Maturity: Plookup and LogUp production; structure-exploiting variants research-stage · License: n/a (constructions) · Source: https://eprint.iacr.org/2022/1530