Revisiting the Constant-Sum Winternitz One-Time Signature with Applications to SPHINCS⁺ and XMSS

Hash-based signatures offer a conservative alternative to post-quantum signatures with arguably better-understood security than other post-quantum candidates. As a core building block of hash-based signatures, the efficiency of one-time signature (OTS) largely dominates that of hash-based signatures. The WOTS⁺ signature scheme (Africacrypt 2013) is the current state-of-the-art OTS adopted by the signature schemes standardized by NIST—XMSS, LMS, and SPHINCS⁺. A natural question is whether there is (and how much) room left for improving one-time signatures (and thus standard hash-based signatures). In this paper, we show that WOTS⁺ one-time signature, when adopting the constant-sum encoding scheme (Bos and Chaum, Crypto 1992), is size-optimal not only under Winternitz’s OTS framework, but also among all tree-based OTS designs. Moreover, we point out a flaw in the DAG-based OTS design previously shown to be size-optimal at Asiacrypt 1996, which makes the constant-sum WOTS⁺ the most size-efficient OTS to the best of our knowledge. Finally, we evaluate the performance of constant-sum WOTS⁺ integrated into the SPHINCS⁺ (CCS 2019) and XMSS (PQC 2011) signature schemes which exhibit certain degrees of improvement in both signing time and signature size.