Claiming bounties on small scale Poseidon and Poseidon2 instances using resultant-based algebraic attacks

Antoine Bak; Augustin Bariant; Aurélien Boeuf; Maël Hostettler; Guilhem Jazeron

Paper 2026/150

Claiming bounties on small scale Poseidon and Poseidon2 instances using resultant-based algebraic attacks

Antoine Bak, French Institute for Research in Computer Science and Automation, Direction Générale de l'Armement

Augustin Bariant

Aurélien Boeuf, French Institute for Research in Computer Science and Automation

Maël Hostettler, Telecom SudParis, Institut Polytechnique de Paris, Evry, France

Guilhem Jazeron, French Institute for Research in Computer Science and Automation

Abstract

In november 2024, the Ethereum foundation (EF) issued a bounty program with challenges on Poseidon and Poseidon2. The goal of these challenges is to find CICO solutions on different round-reduced instances of Poseidon and Poseidon2, defined on different prime fields. We denote the four main instances Poseidon-256, Poseidon2-64, Poseidon2-31m and Poseidon2-31k. In the challenges, the goal is to solve CICO-1 for Poseidon-256 and Poseidon-64, and CICO-2 for Poseidon-31m and Poseidon-31k. We found CICO solutions to the first 3 proposed instances of Poseidon2-31m and Poseidon2-31k, along with solutions for the first two Poseidon-256 instances. These solutions have been confirmed to be correct and eligible for bounty by the Ethereum fundation, except for the first instance of Poseidon-256, which was claimed by another team before us. In order to solve the instances of Poseidon2-31m and Poseidon2-31k, we used a new resultant-based approach, whereas our attacks on Poseidon-256 only relies on already-known univariate root finding.

Metadata

Available format(s): PDF
Category: Attacks and cryptanalysis
Publication info: Preprint.
Keywords: oseidon CICO Problem Cryptanalysis hash function polynomial solving algebraic attack resultant
Contact author(s): antoine bak @ inria fr
aurelien boeuf @ inria fr
mael hostettler @ telecom-sudparis eu
guilhem jazeron @ inria fr
History: 2026-02-11: revised; 2026-01-30: received; See all versions
Short URL: https://ia.cr/2026/150
License: CC BY-SA

BibTeX

@misc{cryptoeprint:2026/150,
      author = {Antoine Bak and Augustin Bariant and Aurélien Boeuf and Maël Hostettler and Guilhem Jazeron},
      title = {Claiming bounties on small scale Poseidon and Poseidon2 instances using resultant-based algebraic attacks},
      howpublished = {Cryptology {ePrint} Archive, Paper 2026/150},
      year = {2026},
      url = {https://eprint.iacr.org/2026/150}
}