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Secret sharing (SS) is a foundational cryptographic primitive with diverse applications, including secure multiparty computation and conditional disclosure of secrets. While traditional schemes have primarily emphasized information-theoretic security, recent advancements have increasingly leveraged computational assumptions to achieve more efficient constructions and support broader access policies. Despite these successes, most existing computational secret sharing (CSS) schemes are limited to a static security model, where adversaries must commit to their choice of corrupted participants at the outset. A critical challenge in CSS lies in achieving adaptive security, where adversaries can dynamically select participants to corrupt, better reflecting real-world threat models. In this paper, we present a novel transformation that converts any statically secure CSS scheme into an adaptively secure one while preserving the original access policy and computational assumptions, providing a framework for bridging the gap between static and adaptive security. Our construction introduces a multiplicative share size overhead of where is the number of parties. Additionally, we explore trade-offs in efficiency and security, offering more efficient adaptive CSS constructions for specific, restricted policy classes. This work addresses key limitations in the current landscape of CSS and paves the way for broader adoption of adaptively secure secret sharing in cryptographic applications. 

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.