Secret Sharing and Shared Information

Johannes Rauh

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Submission date: 10. Nov. 2017
Pages: 15
published in: Entropy, 19 (2017) 11, art-no. 601 
DOI number (of the published article): 10.3390/e19110601
Bibtex
MSC-Numbers: 94A17, 94A62
Keywords and phrases: information decomposition, partial information lattice, shared information, secret sharing
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Link to arXiv: See the arXiv entry of this preprint.

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.