A Zero-Dimensional Gröbner Basis for Poseidon

ePrint Report: A Zero-Dimensional Gröbner Basis for Poseidon

Matthias Johann Steiner

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 …

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