Paper 2024/310

A Zero-Dimensional Gröbner Basis for Poseidon

Matthias Johann Steiner, University of Klagenfurt
Abstract

In this paper we construct dedicated weight orders $>$ so that a $>$-Gröbner bases of Poseidon can be found via linear transformations for the preimage as well as the CICO problem. In particular, with our Gröbner bases we can exactly compute the $\mathbb{F}_q$-vector space dimension of the quotient space for all possible Poseidon configurations. This in turn resolves previous attempts to assess the security of Poseidon against Gröbner basis attacks, since the vector space dimension quantifies the complexity of computing the variety of a zero-dimensional polynomial system.

Metadata
Available format(s)
PDF
Category
Attacks and cryptanalysis
Publication info
Preprint.
Keywords
Gröbner basisSponge functionSubstitution-Permutation NetworkPoseidon
Contact author(s)
matthias steiner @ aau at
History
2024-03-20: last of 3 revisions
2024-02-23: received
See all versions
Short URL
https://ia.cr/2024/310
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2024/310,
      author = {Matthias Johann Steiner},
      title = {A Zero-Dimensional Gröbner Basis for Poseidon},
      howpublished = {Cryptology {ePrint} Archive, Paper 2024/310},
      year = {2024},
      url = {https://eprint.iacr.org/2024/310}
}
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