An efficient secret sharing scheme based on Newton’s divided difference interpolation & magic cube properties

Abstract

In the present paper, a secret sharing method depend on mathematical properties of magic cube was proposed. This method allows to share a secret among a group of participants, so that specific group is able to reconstruct the secret parts by the use of Newton's Divided Difference Interpolation mathematical formula. The main aim is to build magic cube with any order (odd, doubly even, or singly even) of six magic square faces. Each face of magic square has a number of features that represented by start value, dimensions, and the difference between the consecutive values. The dimension of the magic cube will be embedded in the polynomial as a secret value. The points of the polynomial will be sent to a set of trusted participants by the dealer to resolve find the secret. The factorial will be calculated to the dimension in order to calculate the start number value. Moreover, the dimension will be calculated as a power value to propagate the difference between consecutive numbers of magic cube. Thus; the participants will be able to rebuild the original magic cube easily. These mathematical properties and the generated complexities that interested by the secret sharing and magic cubes will add more protection stages to the secret information.