Constash: A Post-Quantum Hash Function from Constacyclic Codes over \( R = \mathbb{F}_q + u\mathbb{F}_q + v\mathbb{F}_q + uv\mathbb{F}_q \)

Abstract

In this work, we introduce \emph{Constash}, a new syndrome-based hash construction built from $\lambda$-constacyclic codes over a finite Frobenius ring. The proposed design maps each input to a sparse vector over the ring and computes its syndrome with respect to a public parity-check matrix. In this setting, preimage resistance is related to bounded-weight syndrome decoding, while collision resistance is related to low-weight kernel relations. The ring structure also supports efficient evaluation in the negacyclic case. We discuss concrete parameter choices and practical attack baselines, giving a ring-based perspective on post-quantum syndrome hashing.