Cryptology ePrint Archive: Report 2013/082
Secret Sharing, Rank Inequalities, and Information Inequalities
Sebastia Martin and Carles Padro and An Yang
Abstract: Beimel and Orlov proved that all information inequalities on four or five variables, together with all information inequalities on more than five variables that are known to date, provide lower bounds on the size of the shares in secret sharing schemes that are at most linear on the number of participants. We present here another two negative results about the power of information inequalities in the search for lower bounds in secret sharing. First, we prove that all information inequalities on a bounded number of variables can only provide lower bounds that are polynomial on the number of participants. And second, we prove that the rank inequalities that are derived from the existence of two common informations can provide only lower bounds that are at most cubic in the number of participants.
Category / Keywords: cryptographic protocols / Secret sharing, Information inequalities, Rank inequalities, Polymatroid.
Original Publication (with major differences): IACR-CRYPTO-2013
Date: received 17 Feb 2013, last revised 6 Nov 2015
Contact author: carles padro at upc edu
Available format(s): PDF | BibTeX Citation
Version: 20151106:121224 (All versions of this report)
Short URL: ia.cr/2013/082
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