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HyperPlonk: Plonk with Linear-Time Prover and High-Degree Custom Gates

HyperPlonk. Binyi Chen, Benedikt Bünz, Dan Boneh and Zhenfei Zhang.

HyperPlonk replaces that transform with a sumcheck so the prover is linear in the number of gates, and it allows higher-degree custom gates.

A reading of the public paper. Not a copy, not a benchmark, and not a claim about any later network.

When a team says they left PLONK for prover time, ask whether they mean this sumcheck change or a different arithmetisation.
Evidence
Primary paper
Re-measured
No
Assumptions
3
Records linked
1

Code

Source, repository, and what is actually hosted

  • ePrint 2022/1355https://eprint.iacr.org/2022/1355
  • The source URL is not a GitHub repository. No code remote is invented.
  • Full text is not mirrored. Public availability is not a licence to copy the file onto this site.
  • Add to a reading list

01 Claim ledger

What the paper is allowed to say

Each row is a sentence already in the study. The status is the same on every row: a model claim, not a live measurement.

  1. Claim 01 · Paper model

    The defect

    PLONK's prover does a number-theoretic transform that is quasilinear but painful, and its custom gates are degree-limited.

  2. Claim 02 · Paper model

    The proposal

    HyperPlonk replaces that transform with a sumcheck so the prover is linear in the number of gates, and it allows higher-degree custom gates.

  3. Claim 03 · Paper model

    Sumcheck is the new backbone.

    A custom gate of higher degree can express constraints that previously needed many rows.

  4. Claim 04 · Paper model

    The bound

    Linear time is not free in constants. The paper is not a benchmark of a product.

02 Three cuts

Observation, model, falsifier

A desk does not stop at the summary. Each claim is cut three ways, using only this study's own assumptions and checks. Nothing here is a new figure.

  1. 01 The defect

    Observation

    What the study says

    PLONK's prover does a number-theoretic transform that is quasilinear but painful, and its custom gates are degree-limited.

    Model

    What has to hold

    High-degree gates move work. They do not remove the need to audit the constraint.

    Falsifier

    What would retire it

    What degree of custom gate is allowed?

  2. 02 The proposal

    Observation

    What the study says

    HyperPlonk replaces that transform with a sumcheck so the prover is linear in the number of gates, and it allows higher-degree custom gates.

    Model

    What has to hold

    High-degree gates move work. They do not remove the need to audit the constraint.

    Falsifier

    What would retire it

    Is the prover using an NTT or sumcheck?

  3. 03 Sumcheck is the new backbone.

    Observation

    What the study says

    A custom gate of higher degree can express constraints that previously needed many rows.

    Model

    What has to hold

    High-degree gates move work. They do not remove the need to audit the constraint.

    Falsifier

    What would retire it

    What degree of custom gate is allowed?

  4. 04 The bound

    Observation

    What the study says

    Linear time is not free in constants. The paper is not a benchmark of a product.

    Model

    What has to hold

    Linear time is not free in constants. The paper is not a benchmark of a product.

    Falsifier

    What would retire it

    Is the prover using an NTT or sumcheck?

03 Sequence

One action, as an operating tape

  1. 01Arithmetise the circuit as a PLONK-style constraint system.
  2. 02Prove the sum over the hypercube by sumcheck.
  3. 03Open the committed polynomials at the points the protocol names.
  4. 04What degree of custom gate is allowed?

04 Load-bearing

The argument, and where a pitch drops it

  1. What the paper is for

    The cut

    When a team says they left PLONK for prover time, ask whether they mean this sumcheck change or a different arithmetisation.

    Why it carries weight

    If this cut is skipped, the paper's name is being used without the mechanism that makes the name mean anything.

    Where it is dropped

    This is not vanilla PLONK.

  2. What happened after

    The cut

    Production provers forked the PLONK line in several directions. HyperPlonk is one of them, not all of them.

    Why it carries weight

    If this cut is skipped, the paper's name is being used without the mechanism that makes the name mean anything.

    Where it is dropped

    This is not vanilla PLONK.

05 Register

What has to be true

  • Model · Not re-measured

    Linear time is not free in constants. The paper is not a benchmark of a product.

  • Model · Not re-measured

    High-degree gates move work. They do not remove the need to audit the constraint.

  • Model · Not re-measured

    This is not vanilla PLONK.

06 Divergence

What happened after the paper

Production provers forked the PLONK line in several directions. HyperPlonk is one of them, not all of them.

A later client, parameter set, or reward formula is a different object. Cite this paper for the mechanism. Cite a primary release for the network. This desk has not re-run the proof.

07 Pre-mortem

What to check before you use the idea

  4. 0 of 3 marked on this browser. A mark is a reading note, not a pass, a rating, or a recommendation.

08 Anatomy

The paper, in the order a builder needs

The problem it names

PLONK's prover does a number-theoretic transform that is quasilinear but painful, and its custom gates are degree-limited.

What the design proposes

  • Sumcheck is the new backbone.
  • A custom gate of higher degree can express constraints that previously needed many rows.
  • The verifier still depends on the polynomial commitment.

How the mechanism is specified

  • Arithmetise the circuit as a PLONK-style constraint system.
  • Prove the sum over the hypercube by sumcheck.
  • Open the committed polynomials at the points the protocol names.

What this page does not treat as proven

  • Linear time is not free in constants. The paper is not a benchmark of a product.
  • High-degree gates move work. They do not remove the need to audit the constraint.
  • This is not vanilla PLONK.

Why the desk still reads it

When a team says they left PLONK for prover time, ask whether they mean this sumcheck change or a different arithmetisation.

09 Lexicon

Terms, opened into the record

Sumcheck
An interactive proof that a sum over a boolean hypercube has a claimed value.
Custom gate
A constraint row that is not the plain PLONK equation.

10 Repository

Every linked record on this page

Underlined words open a page that already exists: a concept, a protocol profile, a failure record, or another paper. If a word is not underlined, this desk does not have a record for it.

This is Blockchain Lab's reading of a public design paper. It is not the paper, not a copy of it, and not an offer of tokens, equity, custody or a partnership. Later network behaviour can diverge from the text. Nothing here is investment, legal or technical advice.

Research status: Design paper. Last reviewed: 1 October 2026. This is a reading of a public paper, not investment, legal or security advice.