Abstract
AbstractDetermining the optimal complexity of secret sharing schemes for every given access structure is a difficult and long-standing open problem in cryptology. Lower bounds have been found by a combinatorial method that uses polymatroids. In this paper, we point out that the best lower bound that can be obtained by this method can be determined by using linear programming, and this can be effectively done for access structures on a small number of participants. By applying this linear programming approach, we present better lower bounds on the optimal complexity and the optimal average complexity of several access structures. Finally, by adding the Ingleton inequality to the previous linear programming approach, we find a few examples of access structures for which there is a gap between the optimal complexity of linear secret sharing schemes and the combinatorial lower bound.KeywordsSecret sharingOptimization of secret sharing schemes for general access structures
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
