In this paper, we study an information-theoretic secret sharing problem, where a dealer distributes shares of a secret among a set of participants under the following constraints: (i) authorized sets of users can recover the secret by pooling their shares, and (ii) non-authorized sets of colluding users cannot learn any information about the secret. We assume that the dealer and participants observe the realizations of correlated Gaussian random variables and that the dealer can communicate with participants through a one-way, authenticated, rate-limited, and public channel. Unlike traditional secret sharing protocols, in our setting, no perfectly secure channel is needed between the dealer and the participants. Our main result is a closed-form characterization of the fundamental trade-off between secret rate and public communication rate.
翻译:在本文中,我们研究一个信息理论秘密共享问题,即经销商在一系列参与者中分配秘密股份,其限制如下:(一)经授权的用户群可以通过集股收回秘密,和(二)未经授权的串通用户群无法了解任何关于秘密的信息。我们假设经销商和参与者观察相关高斯随机变量的实现情况,经销商可以通过单向、认证、限息和公共渠道与参与者沟通。与传统的秘密共享协议不同,在我们这个背景下,经销商和参与者之间不需要完全安全的渠道。我们的主要结果是秘密利率和公共通信率之间的基本权衡。