A Unified Model for Collusion-Permissible and Nonpermissible Secret Sharing Systems

Abstract

A unified mode US2 which contains a pair of encoder-decoder and a channel is presented to emulate the secret sharing systems of various schemes. Depending on collusion is permitted or not in the particular system, the encoder-decoder pair and channel vary. The channel for collusion-nonpermissible US2 is developed. Its capacity is derived and used to establish the bounds on the (1,p,r,n) secret sharing scheme. The channel and a possible coding scheme in investigated as well for US2 which allows players collude. Secret sharing scheme (t,n) threshold scheme (1,p,r,n) secret sharing scheme non-systematic linear code Reed-Solomon code t-private t-resilient code Reed-Solomon code t-private t-resilient collusion-permissible secret sharing model collusion-nonpermissible secret sharing model