Distributed Secret Sharing Over a Public Channel From Correlated Random Variables
Distributed Secret Sharing Over a Public Channel From Correlated Random Variables
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DOI：
10.1109/tit.2024.3363644
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发表时间：
2021-10
影响因子：
2.5
通讯作者：
Rémi A. Chou
中科院分区：
文献类型：
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作者：
Rémi A. Chou
我们考虑一个秘密共享模型，其中交易商将秘密的份额分配给一组参与者，并约束只有预先确定的参与者子集必须能够通过汇集他们的份额来重建秘密。我们的研究从三个方面概括了Shamir的秘密共享模型。首先，我们允许联合设计股份创建和股份分配的协议，而不是将模型限制为独立设计。其次，我们不假设参与者和经销商可以免费访问信息安全通道，而是假设他们可以访问公共通道和相关的随机性。第三，在无线网络设置的激励下，从信道增益测量中获得相关随机性，我们探索了一种分布式设置，其中经销商是由多个子经销商组成的实体。我们的主要结果是经销商和参与者在该模型中可以获得的可实现秘密率的内区域和外区域。为此，我们开发了两种新的可实现性技术，第一种是在分布式设置中连续处理可靠性和安全性约束，第二种是将多经销商设置减少为多个单用户经销商设置。我们的结果得到了当相关随机性对应于每个子交易商和每个参与者之间共享的成对密钥时阈值访问结构的容量区域，以及存在单个交易商和任意相关随机性时全有或全无访问结构的容量。
We consider a secret-sharing model where a dealer distributes the shares of a secret among a set of participants with the constraint that only predetermined subsets of participants must be able to reconstruct the secret by pooling their shares. Our study generalizes Shamir’s secret-sharing model in three directions. First, we allow a joint design of the protocols for the creation of the shares and the distribution of the shares, instead of constraining the model to independent designs. Second, instead of assuming that the participants and the dealer have access to information-theoretically secure channels at no cost, we assume that they have access to a public channel and correlated randomness. Third, motivated by a wireless network setting where the correlated randomness is obtained from channel gain measurements, we explore a distributed setting where the dealer is an entity made of multiple sub-dealers. Our main results are inner and outer regions for the achievable secret rates that the dealer and the participants can obtain in this model. To this end, we develop two new achievability techniques, a first one to successively handle reliability and security constraints in a distributed setting, and a second one to reduce a multi-dealer setting to multiple single-user dealer settings. Our results yield the capacity region for threshold access structures when the correlated randomness corresponds to pairwise secret keys shared between each sub-dealer and each participant, and the capacity for the all-or-nothing access structure in the presence of a single dealer and arbitrarily correlated randomness.