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Entropy 2017, 19(11), 601; https://doi.org/10.3390/e19110601

Secret Sharing and Shared Information

Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany
Received: 21 June 2017 / Revised: 2 November 2017 / Accepted: 5 November 2017 / Published: 9 November 2017
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Abstract

Secret sharing is a cryptographic discipline in which the goal is to distribute information about a secret over a set of participants in such a way that only specific authorized combinations of participants together can reconstruct the secret. Thus, secret sharing schemes are systems of variables in which it is very clearly specified which subsets have information about the secret. As such, they provide perfect model systems for information decompositions. However, following this intuition too far leads to an information decomposition with negative partial information terms, which are difficult to interpret. One possible explanation is that the partial information lattice proposed by Williams and Beer is incomplete and has to be extended to incorporate terms corresponding to higher-order redundancy. These results put bounds on information decompositions that follow the partial information framework, and they hint at where the partial information lattice needs to be improved. View Full-Text
Keywords: information decomposition; partial information lattice; shared information; secret sharing information decomposition; partial information lattice; shared information; secret sharing
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Rauh, J. Secret Sharing and Shared Information. Entropy 2017, 19, 601.

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