Paper 2019/584

2-threshold Ideal Secret Sharing Schemes Can Be Uniquely Modeled by Latin Squares

Lintao Liu, Xuehu Yan, Yuliang Lu, and Huaixi Wang

Abstract

In a secret sharing scheme, a secret value is encrypted into several shares, which are distributed among corresponding participants. It requires that only predefined subsets of participants can reconstruct the secret with their shares. The general model for secret sharing schemes is provided in different forms, in order to study the essential properties of secret sharing schemes. Considering that it is difficult to directly con- struct secret sharing schemes meeting the requirements of the general model, most of current theoretic researches always rely on other mathematical tools, such as matriod. However, these models can only handle with values in a finite field. In this paper, we firstly establish a one-to-one mapping relationship between Latin squares and 2-threshold secret sharing schemes. Afterwards, we utilize properties of Latin squares to further give an exact characterization for the general model of 2-threshold ideal secret sharing schemes. Furthermore, several interesting properties of 2-threshold ideal schemes are provided, which are not induced by any other means, especially nolinear schemes in an arbitrary integer domain.

Note: In this paper, it is proved that there exists a one-to-one mapping between Latin squares and (2,2)-threshold secret sharing schemes. Furthermore, the Latin square can be utilized as a mathematical tool to study the essential characteristics of threshold ideal secret sharing. Therefore, the related researches on secret sharing schemes may not be limited in linear schemes in a finite field.