Quantum-access security of the Winternitz one-time signature scheme

TL;DR

This paper analyzes the quantum-access security of the Winternitz one-time signature scheme, extending previous work on Lamport OTS, and introduces a new analysis tool for hash chains in the quantum random oracle model.

Contribution

It fills a gap in the quantum-access security analysis of Lamport OTS and generalizes the approach to Winternitz OTS, developing a new tool for hash chain analysis in the QROM.

Findings

Extended security analysis to Winternitz OTS in QROM

Developed a new hash chain analysis tool for QROM

Filled a gap in quantum-access security understanding

Abstract

Quantum-access security, where an attacker is granted superposition access to secret-keyed functionalities, is a fundamental security model and its study has inspired results in post-quantum security. We revisit, and fill a gap in, the quantum-access security analysis of the Lamport one-time signature scheme (OTS) in the quantum random oracle model (QROM) by Alagic et al.~(Eurocrypt 2020). We then go on to generalize the technique to the Winternitz OTS. Along the way, we develop a tool for the analysis of hash chains in the QROM based on the superposition oracle technique by Zhandry (Crypto 2019) which might be of independent interest.