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**2024/398**

**Title:**

The Last Challenge Attack: Exploiting a Vulnerable Implementation of the Fiat-Shamir Transform in a KZG-based SNARK

**Authors:**
Oana Ciobotaru, Vesselin Velichkov, Maxim Peter

**Abstract:**

The Fiat-Shamir transform [1] is a well-known and widely employed technique for converting sound public-coin interactive protocols into sound non-interactive protocols. Even though the transformation itself is relatively clear and simple, some implementations choose to deviate from the specifications, for example for performance reasons. In this short note, we present a vulnerability arising from such a deviation in a KZG-based PLONK verifier implementation. This deviation stemmed from the incorrect computation of the last challenge of the PLONK protocol [2], where the KZG batching proof challenge was computed before, and, hence, independently from the KZG evaluation proofs. More generally, such a vulnerability may affect any KZG [3] implementation where one uses batched KZG proof evaluations for at least two distinct evaluation points. We call an attack enabled by such a deviation a Last Challenge Attack. For concreteness, we show that when a PLONK verifier implementation presents such a deviation, a malicious PLONK prover can mount a Last Challenge Attack to construct verifiable proofs of false statements. The described vulnerability was initially discovered as part of an audit, and has been responsibly disclosed to the developers and fixed. A proof of concept of the vulnerability, in which a proof is forged for an arbitrary public input, is made available.

In addition to the above, in this work we also provide a security proof of the knowledge-soundness of the batched KZG scheme with evaluations for at least two distinct values.

**ePrint:**
https://eprint.iacr.org/2024/398

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