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Title:
Revisiting the Constant-sum Winternitz One-time Signature with Applications to SPHINCS+ and XMSS
Authors: Kaiyi Zhang, Hongrui Cui, Yu Yu
Abstract: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.
ePrint: https://eprint.iacr.org/2023/850
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