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We say a tuple of NP statements satisfies a monotone policy if , where if and only if is in the NP language. A monotone-policy batch argument (monotone-policy BARG) for NP is a natural extension of regular batch arguments (BARGs) that allows a prover to prove that satisfy a monotone policy P with a proof of size , where is the size of the Boolean circuit computing the NP relation . Previously, Brakerski, Brodsky, Kalai, Lombardi, and Paneth (CRYPTO 2023) and Nassar, Waters, and Wu (TCC 2024) showed how to construct monotone-policy BARGs from (somewhere-extractable) BARGs for NP together with a leveled homomorphic encryption scheme (Brakerski et al.) or an additively homomorphic encryption scheme over a sufficiently-large group (Nassar et al.). In this work, we improve upon both works by showing that BARGs together with additively homomorphic encryption over any group suffices (e.g., over). For instance, we can instantiate the additively homomorphic encryption with the classic Goldwasser-Micali encryption scheme based on the quadratic residuosity (QR) assumption. Then, by appealing to existing compilers, we also obtain a monotone-policy aggregate signature scheme from any BARG and the QR assumption.