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Fast Reed-Solomon Interactive Oracle Proofs of Proximity

FRI. Eli Ben-Sasson, Iddo Bentov, Yinon Horesh and Michael Riabzev.

FRI is the proximity test: fold the polynomial in rounds until a constant remains, and sample enough points that a cheating polynomial is caught.

A reading of the public document. Not a copy of it, and not a claim about a later network that reused the name.

A STARK pitch that cannot name the proximity test is skipping the part that replaces the trusted setup.
Evidence
Primary paper
Re-measured
No
Assumptions
3
Records linked
4

Code

Source, repository, and what is actually hosted

  • ECCC 2017/134https://eccc.weizmann.ac.il/report/2017/134/
  • 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

    A STARK has to show that a function is close to a low-degree polynomial without a trusted setup.

  2. Claim 02 · Paper model

    The rule

    FRI is the proximity test: fold the polynomial in rounds until a constant remains, and sample enough points that a cheating polynomial is caught.

  3. Claim 03 · Paper model

    How it is put together

    No trapdoor. The security is hash-based. Each round reduces the degree. The proof size depends on the number of queries and the folding.

  4. Claim 04 · Paper model

    Where the claim stops

    FRI is a component, not a virtual machine.

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

    A STARK has to show that a function is close to a low-degree polynomial without a trusted setup.

    Model

    What has to hold

    Post-quantum here means hash assumptions, not a claim about every STARK parameter.

    Falsifier

    What would retire it

    What hash commits to the polynomial?

  2. 02 The rule

    Observation

    What the study says

    FRI is the proximity test: fold the polynomial in rounds until a constant remains, and sample enough points that a cheating polynomial is caught.

    Model

    What has to hold

    Post-quantum here means hash assumptions, not a claim about every STARK parameter.

    Falsifier

    What would retire it

    What hash commits to the polynomial?

  3. 03 How it is put together

    Observation

    What the study says

    No trapdoor. The security is hash-based. Each round reduces the degree. The proof size depends on the number of queries and the folding.

    Model

    What has to hold

    Query count is a security parameter. Cutting it to save bytes cuts the proof.

    Falsifier

    What would retire it

    How many queries does the verifier make?

  4. 04 Where the claim stops

    Observation

    What the study says

    FRI is a component, not a virtual machine.

    Model

    What has to hold

    FRI is a component, not a virtual machine.

    Falsifier

    What would retire it

    How many queries does the verifier make?

03 Sequence

One action, as an operating tape

  1. 01Commit to a polynomial with a Merkle tree.
  2. 02Fold evaluations and commit again.
  3. 03The verifier queries both sides and checks consistency.
  4. 04How many queries does the verifier make?

04 Load-bearing

The argument, and where a pitch drops it

  1. Why it is still on the desk

    The cut

    A STARK pitch that cannot name the proximity test is skipping the part that replaces the trusted setup.

    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

    Post-quantum here means hash assumptions, not a claim about every STARK parameter.

  2. After the text

    The cut

    STARKs, and later FRI optimisations, sit on this test. Cairo and others are languages on top.

    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

    FRI is a component, not a virtual machine.

  • Cryptography · Not re-measured

    Post-quantum here means hash assumptions, not a claim about every STARK parameter.

  • Cryptography · Not re-measured

    Query count is a security parameter. Cutting it to save bytes cuts the proof.

06 Divergence

What happened after the paper

STARKs, and later FRI optimisations, sit on this test. Cairo and others are languages on top.

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

A STARK has to show that a function is close to a low-degree polynomial without a trusted setup.

What the design proposes

  • No trapdoor. The security is hash-based.
  • Each round reduces the degree.
  • The proof size depends on the number of queries and the folding.

How the mechanism is specified

  • Commit to a polynomial with a Merkle tree.
  • Fold evaluations and commit again.
  • The verifier queries both sides and checks consistency.

What this page does not treat as proven

  • FRI is a component, not a virtual machine.
  • Post-quantum here means hash assumptions, not a claim about every STARK parameter.
  • Query count is a security parameter. Cutting it to save bytes cuts the proof.

Why the desk still reads it

A STARK pitch that cannot name the proximity test is skipping the part that replaces the trusted setup.

09 Lexicon

Terms, opened into the record

Proximity
Evidence that a committed function is close to low degree.
Folding
Combining evaluations so the next round has lower degree.

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.