  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.
