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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.

The five-minute read

The defect

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

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.

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.

Where the claim stops

FRI is a component, not a virtual machine.

One action, walked through

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

The argument, unpacked

Why it is still on the desk

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

After the text

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

What has to be true

  • 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.

What happened after the paper

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

What to check before you use the idea

  • How many queries does the verifier make?
  • What hash commits to the polynomial?
  • Is there a setup string at all?

Terms

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

The problem the paper 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 a venture studio still reads it

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

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.