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Spartan: Efficient and General-Purpose zkSNARKs without Trusted Setup

Spartan. Srinath Setty.

Spartan encodes the circuit as a sparse matrix and uses a polynomial commitment so the prover's work tracks the number of constraints more tightly than a dense encoding.

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

A prover-time claim should say whether the circuit is sparse in the sense this paper uses. Otherwise the comparison is advertising.
Evidence
Primary paper
Re-measured
No
Assumptions
3
Records linked
1

Code

Source, repository, and what is actually hosted

  • ePrint 2019/550https://eprint.iacr.org/2019/550
  • 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

    General-purpose SNARKs without a setup were still too slow in the prover for the circuits people wanted to ship.

  2. Claim 02 · Paper model

    The proposal

    Spartan encodes the circuit as a sparse matrix and uses a polynomial commitment so the prover's work tracks the number of constraints more tightly than a dense encoding.

  3. Claim 03 · Paper model

    Sparsity is the saving. A dense encoding pays for zeros.

    There is no trusted setup.

  4. Claim 04 · Paper model

    The bound

    The paper's costs are asymptotic and experimental for its implementation, not a quote for 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

    General-purpose SNARKs without a setup were still too slow in the prover for the circuits people wanted to ship.

    Model

    What has to hold

    No setup does not mean no cryptographic assumption.

    Falsifier

    What would retire it

    Is there a setup?

  2. 02 The proposal

    Observation

    What the study says

    Spartan encodes the circuit as a sparse matrix and uses a polynomial commitment so the prover's work tracks the number of constraints more tightly than a dense encoding.

    Model

    What has to hold

    No setup does not mean no cryptographic assumption.

    Falsifier

    What would retire it

    Is the encoding sparse?

  3. 03 Sparsity is the saving. A dense encoding pays for zeros.

    Observation

    What the study says

    There is no trusted setup.

    Model

    What has to hold

    No setup does not mean no cryptographic assumption.

    Falsifier

    What would retire it

    Is there a setup?

  4. 04 The bound

    Observation

    What the study says

    The paper's costs are asymptotic and experimental for its implementation, not a quote for a product.

    Model

    What has to hold

    The paper's costs are asymptotic and experimental for its implementation, not a quote for a product.

    Falsifier

    What would retire it

    Is the encoding sparse?

03 Sequence

One action, as an operating tape

  1. 01Compile to R1CS.
  2. 02Treat the matrices as sparse.
  3. 03Prove the satisfying assignment with the polynomial protocol in the paper.
  4. 04Is there a setup?

04 Load-bearing

The argument, and where a pitch drops it

  1. What the paper is for

    The cut

    A prover-time claim should say whether the circuit is sparse in the sense this paper uses. Otherwise the comparison is advertising.

    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

    The paper's costs are asymptotic and experimental for its implementation, not a quote for a product.

  2. What happened after

    The cut

    Later lookups and folding schemes attack the same prover cost from other directions.

    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

    A later client, parameter or reward formula is a different object from this paragraph.

05 Register

What has to be true

  • Model · Not re-measured

    The paper's costs are asymptotic and experimental for its implementation, not a quote for a product.

  • Cryptography · Not re-measured

    No setup does not mean no cryptographic assumption.

  • Model · Not re-measured

    It is not a consensus protocol.

06 Divergence

What happened after the paper

Later lookups and folding schemes attack the same prover cost from other directions.

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

General-purpose SNARKs without a setup were still too slow in the prover for the circuits people wanted to ship.

What the design proposes

  • Sparsity is the saving. A dense encoding pays for zeros.
  • There is no trusted setup.
  • The commitment scheme is part of the proof system, not a chain primitive.

How the mechanism is specified

  • Compile to R1CS.
  • Treat the matrices as sparse.
  • Prove the satisfying assignment with the polynomial protocol in the paper.

What this page does not treat as proven

  • The paper's costs are asymptotic and experimental for its implementation, not a quote for a product.
  • No setup does not mean no cryptographic assumption.
  • It is not a consensus protocol.

Why the desk still reads it

A prover-time claim should say whether the circuit is sparse in the sense this paper uses. Otherwise the comparison is advertising.

09 Lexicon

Terms, opened into the record

Sparse matrix
A constraint matrix that is mostly zeros, which the prover should not have to touch.
Polynomial commitment
A short object that binds a polynomial.

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.

Concepts

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.