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 on the secret value that is obtained by each subset of players. We prove that there exists a secret sharing scheme for every access function.
Uniform access functions, that is, access functions whose values depend only on the number of players, generalize the threshold access structures. The optimal information ratio of the uniform access functions with rational values has been determined by Yoshida, Fujiwara and Fossorier. By using the tools that are described in our work, we provide a much simpler proof of that result and we extend it to access functions with real values.Category / Keywords: Secret sharing, Non-perfect secret sharing, Information Ratio, Polymatroid Date: received 17 Feb 2014, last revised 2 Sep 2016 Contact author: oriol farras at urv cat Available format(s): PDF | BibTeX Citation Version: 20160902:082159 (All versions of this report) Short URL: ia.cr/2014/124 Discussion forum: Show discussion | Start new discussion