International Association
for Cryptologic Research

Rescue-XLIX is an Arithmetization-Oriented Substitution-Permutation Network over prime fields $\mathbb{F}_p$ which in one full round first applies a SPN based on $x \mapsto x^d$ followed by a SPN based on the inverse power map $x \mapsto x^\frac{1}{d}$. In a recent work, zero-dimensional Gröbner bases for SPN and Poseidon sponge functions have been constructed by utilizing weight orders. Following this approach we construct zero-dimensional Gröbner bases for Rescue-XLIX ciphers and sponge functions.