Paper 2024/468

Zero-Dimensional Gröbner Bases for Rescue-XLIX

Abstract

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.