Paper 2024/693

A Note on Anemoi Gröbner Bases

Abstract

This paper focuses on algebraic attacks on the $\mathsf{Anemoi}$ family of arithmetization-oriented permutations [Crypto '23]. We consider a slight variation of the naive modeling of the $\mathsf{CICO}$ problem associated to the primitive, for which we can very easily obtain a Gröbner basis and prove the degree of the associated ideal. For inputs in $\mathbb{F}_{q}^2$ when $q$ is an odd prime, we recover the same degree as conjectured for alternative polynomial systems used in other recent works [eprint/2024/250][eprint/2024/347]. Furthermore, our approach can be adapted to cases which have not been studied there, i.e., even characteristic fields and inputs in $\mathbb{F}_q^{2\ell}$ for $\ell > 1$.

Note: 26/06/24 : longer version (experiments and expanded introduction)