Paper 2026/1129

pSquare-hash: A Family of Tweakable Hash Functions for Physically Secure PQ Signatures

Abstract

In 2020 and 2024 respectively, NIST released a Special Publication (SP 800-208) and a Federal Information Processing Standard (FIPS 205) specifying hash-based signature schemes with natural quantum resistance thanks to their symmetric foundation. The former recommends the stateful hash-based signature schemes LMS and XMSS, whereas the latter standardizes their stateless counterpart SPHINCS+. While in principle all three constructions can be instantiated with any secure cryptographic hash function, the concrete instances recommended by NIST are currently limited to either the SHA-2 or the SHA-3 family. Building on the maturity of these standardized families is of course a sensible choice. Yet, we argue that neither is particularly well suited for this purpose, especially once physical security matters. As an alternative we suggest pSquare-hash, an arithmetization-oriented family of lightweight tweakable hash functions. We demonstrate that such dedicated tweakable constructions ideally suit the instantiation and security requirements of hash-based signature schemes, potentially leading to efficiency advantages over standard concatenation-based approaches through either a reduction of the permutation size or the number of calls. With respect to physical security, the presence of the tweak enables a clean separation between inputs that need to be protected against leakage/faults and those that are insensitive. The arithmetization-oriented nature and choice of prime enable the effective utilization of masking schemes with superior passive and active attack resistance (e.g., prime-field and/or inner-product masking) and keep the design suitable for zero-knowledge applications. We compare higher-order masked software (Cortex-M4) and hardware (NanGate 15 nm) implementations of pSquare-hash to equivalent SHA-2, SHA-3, SKINNY-Hash, Ascon-Hash and Poseidon2 instances and exhibit favorable characteristics whenever masking is applied.