A comment on group independent threshold sharing

Abstract

Secret sharing is important in the cases where a secret needs to be distributed over a set of n devices so that only authorized subsets of devices can recover the secret. Some secret sharing schemes can be used with only certain algebraic structures (for example fields). Group independent linear threshold sharing refers to a t out of n linear threshold secret sharing scheme that can be used with any finite abelian group. Group independent secret sharing schemes were introduced in [16] and a formal definition was given in [25] and [10]. Here we describe additional properties of group independent sharing schemes. In particular, we discuss how to construct the dual from the shareholder reconstruction matrix, new bounds on the computational requirements of group independent sharing and new necessary and sufficient conditions to test if a matrix will provide a group independent sharing scheme. © Springer-Verlag 2004.