Vol. 13, No. 2, 2020

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New generalized secret-sharing schemes with points on a hyperplane using a Wronskian matrix

Weston Loucks and Bahattin Yildiz

Vol. 13 (2020), No. 2, 257–279
Abstract

A new secret-sharing scheme is constructed using elementary tools from different fields of mathematics. A method is introduced which uses the assignment of points on a hyperplane, serving as terminal points of vectors which meet an outlined criterion for linear independence. Submatrices of a Wronskian matrix are used in the assignment of these points. This method is also generalized to include a weighted scheme and a multilevel hierarchical model.

Keywords
secret-sharing schemes, hyperplane, Wronskian, hierarchical secret-sharing schemes, generalized cross product
Mathematical Subject Classification 2010
Primary: 94A60
Secondary: 11T71, 34A30
Milestones
Received: 19 April 2019
Revised: 16 December 2019
Accepted: 24 February 2020
Published: 30 March 2020

Communicated by Kenneth S. Berenhaut
Authors
Weston Loucks
Department of Mathematics and Statistics
Northern Arizona University
Flagstaff, AZ
United States
Bahattin Yildiz
Department of Mathematics and Statistics
Northern Arizona University
Flagstaff, AZ
United States