In order to study non-perfect secret sharing schemes in all generality, we describe their structure through their access function, a real function that measures the amount of information that every subset of participants obtains about the secret value. We prove that there exists a secret sharing scheme for every access function.
Uniform access functions, that is, the ones whose values depend only on the number of participants, generalize the threshold access strcutures. Our main result is to determine the optimal information ratio of the uniform access functions. Moreover, we present a construction of linear secret sharing schemes with optimal information ratio for the rational uniform access functions.Category / Keywords: Secret sharing, Non-perfect secret sharing, Information Ratio, Polymatroid Date: received 17 Feb 2014, last revised 24 Apr 2014 Contact author: oriol farras at urv cat Available format(s): PDF | BibTeX Citation Version: 20140424:182844 (All versions of this report) Short URL: ia.cr/2014/124 Discussion forum: Show discussion | Start new discussion