标题： 基于相关随机变量和速率限制的公共通信的秘密共享方案 显示英文标题

标题： Secret Sharing Schemes from Correlated Random Variables and Rate-Limited Public Communication

摘要： 一个经销商旨在与参与者共享一个秘密，以便只有预定义的子集能够重建它，而其他人则无法获取任何信息。 经销商和参与者访问相关随机性，并通过单向、公共、速率受限的信道进行通信。 针对此问题，我们提出了第一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，这些速率之前是通过非构造性方法获得的。 我们的构建依赖于损失源编码与分布逼近相结合以处理可靠性约束，然后使用通用散列来处理安全性约束。 我们强调，我们的编码方案不需要关于相关随机变量的对称性或退化假设，也不需要参与者和经销商之间预先共享的秘密。 作为副产品，我们的构建还产生了用于在单向、速率受限的公共通信下生成密钥的显式编码方案，与先前的工作不同，该方案实现了任意源相关性的容量，并且不需要预先共享的秘密来确保强保密性。 显示英文摘要

摘要： 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.