A dealer aims to share a secret with participants so that only predefined subsets can reconstruct it, while others learn nothing. The dealer and participants access correlated randomness and communicate over a one-way, public, rate-limited channel. For this problem, we propose the first explicit coding scheme able to handle arbitrary access structures and achieve the best known achievable rates, previously obtained non-constructively. Our construction relies on lossy source coding coupled with distribution approximation to handle the reliability constraints, followed by universal hashing to handle the security constraints. We stress that our coding scheme does not require symmetry or degradation assumptions on the correlated random variables, and does not need a pre-shared secret among the participants and dealer. As a by-product, our construction also yields explicit coding schemes for secret-key generation under one-way, rate-limited public communication that, unlike prior work, achieves the capacity for arbitrary source correlations and do not require a pre-shared secret to ensure strong secrecy.

翻译：一个分发者旨在与参与者共享一个秘密，使得只有预定义的子集能够重构该秘密，而其他子集无法获得任何信息。分发者与参与者可访问相关随机性，并通过单向、公共、速率受限的信道进行通信。针对该问题，我们提出了首个能够处理任意访问结构并达到已知最佳可实现速率的显式编码方案，该速率先前仅以非构造性方式获得。我们的构造依赖于结合分布近似的有损信源编码来处理可靠性约束，再通过通用哈希处理安全性约束。我们强调，该编码方案不需要对相关随机变量作对称性或退化性假设，且无需在参与者与分发者之间预共享秘密。作为副产品，该构造还产生了在单向速率受限公共通信下生成密钥的显式编码方案；与先前工作不同，该方案能够实现任意信源相关性的容量，且无需预共享秘密即可确保强保密性。