The Algebraic Freelunch Efficient Gröbner Basis Attacks Against Arithmetization-Oriented Primitives

ePrint Report: The Algebraic Freelunch Efficient Gröbner Basis Attacks Against Arithmetization-Oriented Primitives

Augustin Bariant, Aurélien Boeuf, Axel Lemoine, Irati Manterola Ayala, Morten Øygarden, Léo Perrin, Håvard Raddum

In this paper, we present a new type of algebraic attack that applies to many recent arithmetization-oriented families of permutations, such as those used in Griffin, Anemoi, ArionHash, and XHash8, whose security relies on the hardness of the constrained-input constrained-output (CICO) problem. We introduce the FreeLunch approach: the monomial ordering is chosen so …

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