Welcome to the resource topic for 2025/937
Title:
Attacking Poseidon via Graeffe-Based Root-Finding over NTT-Friendly Fields
Authors: Antonio Sanso, Giuseppe Vitto
Abstract:This paper explores the algebraic structure of the Poseidon and Poseidon2 permutations
over NTT-friendly finite fields, with a focus on preimage recovery via root-finding
techniques. We introduce an algorithm for efficiently identifying single roots of high-degree
univariate polynomials that emerge from these constructions, based on the Graeffe transform
and the tangent Graeffe method. Our approach is evaluated on reduced-round bounty
instances of these permutations at various security levels, as proposed by the Ethereum
Foundation, demonstrating practical effectiveness. These results yield new insights into the
security of permutation-based cryptographic primitives instantiated over NTT-friendly prime
fields.
ePrint: https://eprint.iacr.org/2025/937
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