A New Generalized Group-Oriented Cryptosystem Based on the Systematic Block Codes

Abstract

Secret Sharing has been well-studied over the past decade. From the view point of sharing policy, these schemes can be classified into two types: the threshold-based scheme and the generalized group-oriented cryptosystem. Based on the systematic block code, we had designed an efficient general threshold-based scheme[23]. In this article, based on the result of previous work, we further extend our result to the cases of the generalized group-oriented cryptosystem. This scheme has several merits: (1) It allows parallel secret reconstruction. (2) The SD can dynamically decides the number of distributed secrets depending on the requirement. (3) The construction of the generator matrix is simple and efficient. (4) Users secret shares will not be disclosed after multiple-secret reconstruction operations. (5) The computation is efficient and the quantity of public values in our scheme is low.