In this paper, we construct the first asymptotically efficient two-round n-out-of-n and multi-signatures from lattices in the quantum random oracle model ( \(\textsf{QROM}\) ), using the Fiat-Shamir with Aborts ( \(\textsf{FSwA}\) ) paradigm. Our protocols can be viewed as the improvements on the two-round protocols by Damgård et al. (JoC 2022). \(\textsf{params}\) From a technical perspective, the simulation of \(\textsf{QROM}\)  and the efficient reduction from breaking underlying assumption to forging signatures are the essential challenges to achieving efficient \(\textsf{QROM}\) security for the previously related works. In order to conquer the former one, we adopt the quantum-accessible pseudorandom function ( \(\textsf{QPRF}\) ) to simulate \(\textsf{QROM}\) . Particularly, we show that there exists a \(\textsf{QPRF}\) that is both invertible and programmable, which can simulate \(\textsf{QROM}\) with the same properties. Moreover, we use \(\textsf{QPRF}\) as an intermediate tool to successfully simulate \(\textsf{QROM}\) whose output is separable, even against a quantum adversary. For the latter challenge, we tweak and apply the online extractability by Unruh (Eurocrypt 2015).