Operations over Linear Secret Sharing Schemes

Abstract

A secret sharing scheme implemented in an organisation is designed to reflect the power structure in that organisation. When two organisations merge, this usually requires a number of substantial changes and, in particular, changes to their secret sharing schemes which have to be merged in the way which reflects a new role of each of the organisations. This paper looks at the ways secret sharing scheme can be modified when organisational changes occur. We restrict ourselves with the class of ideal linear secret sharing schemes and describe how matrices of these linear schemes have to be modified when we take the sum, the product or the composition of two linear access structures.