We generalize secret-sharing models that rely on correlated randomness and public communication, originally designed for a fixed access structure, to support a sequence of dynamic access structures, which we term an Additive Access Structure. Specifically, the access structure is allowed to monotonically grow by having any subset of participants added to it at a given time step, and the dealer only learns of these changes to the access structure on the time step that they occur. For this model, we prove the existence of a secret sharing strategy that achieves the same secret rate at each time step as the best known strategy for the fixed access structure version of this model. We also prove that there exists a strategy that is capacity-achieving at any time step where the access structure is a threshold access structure.

翻译：我们推广了依赖相关随机性和公共通信的秘密共享模型，该模型最初设计用于固定访问结构，现扩展为支持一系列动态访问结构，我们称之为可加访问结构。具体而言，访问结构被允许单调增长，即在给定时间步将任意参与者子集加入其中，而分发者仅在访问结构发生变化的对应时间步获知这些变更。针对该模型，我们证明存在一种秘密共享策略，其在每个时间步实现的秘密速率与该模型固定访问结构版本的最优已知策略相同。我们还证明存在一种策略，在访问结构为阈值访问结构的任何时间步均能达到容量极限。