No reduction from Fiat-Shamir + GKR to SNARK

A reduction of class unstated from Fiat-Shamir together with GKR to SNARK would imply a contradiction.

Statement

Migrated verbatim from random-oracle-model § Known Results:

• Fiat-Shamir fails for the GKR protocol — Khovratovich, Rothblum, and Soukhanov showed that the Fiat-Shamir transform fails for the GKR succinct interactive argument — a standard, widely-studied protocol, not a contrived one KRS25. They exhibit families of circuits for which the non-interactive GKR argument proves false statements.

Migrated verbatim from fiat-shamir-heuristic:

Natural Protocols (KRS25)

Prior counterexamples to Fiat-Shamir were contrived — protocols specifically engineered to fail. Khovratovich, Rothblum, and Soukhanov gave the first counterexample for a standard, widely-studied protocol KRS25. They showed that the Fiat-Shamir transform applied to the GKR succinct interactive argument (from GKR15) allows an efficient prover to prove false statements for explicit families of circuits. This raises serious questions about the security of deployed non-interactive succinct arguments based on Fiat-Shamir.

Notes

Recorded during migration and not fixed — these are claims about the source text, not changes to it:

• DUPLICATED at content/Glossary/fiat-shamir-heuristic.md:38 with a longer, differently-worded version. Neither page links the other.
• A concrete attack/counterexample rather than a reduction barrier; Q = contradiction only in the sense that soundness fails.
• The fiat-shamir-heuristic.md copy adds an editorial closing sentence (‘This raises serious questions about the security of deployed non-interactive succinct arguments’) that the ROM copy omits — an unsourced editorial judgment.
• Duplicate of content/Glossary/random-oracle-model.md:23.
• Closes with an editorial sentence (‘This raises serious questions about the security of deployed non-interactive succinct arguments based on Fiat-Shamir’) that is an unsourced judgment, not a result.