Secret sharing over infinite domains
type: Item
instance of: scholarly article
title: Secret sharing over infinite domains
zbMATH Open document ID: 0774.94003
DOI: 10.1007/BF02620136
author: Benny Chor
author: Eyal Kushilevitz
published in: Journal of Cryptology
publication date: 1993-08-29T00:00:00Z
review text: Various schemes for secret-sharing, i.e. distributing a secret among \(n\) parties in a way that allows ``legal'' sets of parties to reconstruct the secret while preventing ``illegal'' sets of parties to get information about the secret, are already known. However, these schemes were designed for cases where the set of secrets and the set of shares are finite. In the article the existence of secret-sharing schemes over infinite domains is studied. It is shown that infinity alone is not sufficient to decide the (im)possibility of secret-sharing schemes, as the cardinality of the domain must be taken into account as well. Particularly, if the sets of secrets and shares are countable then no secret-sharing scheme exists. This result contrasts with another one stating that if the sets of secrets and shares have the cardinality of the reals then perfect (i.e. no illegal set of shares reveals any partial information about the secret) secret-sharing schemes do exist. As a consequence it is shown that perfect private-key encryption (i.e. the one where an eavesdropper gets no partial information about the plaintext by examining the ciphertext) is not possible over a countable domain. On the other hand, over the reals a perfect private-key encryption scheme does exist.
Mathematics Subject Classification ID: 94A60
zbMATH DE Number: 399377
zbMATH Keywords: secret-sharing
zbMATH Keywords: perfect private-key encryption
reviewed by: Jozef Vyskoč
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 399377