On the Secret Sharing Scheme Based on Supercodes Decoding

Abstract Secret sharing schemes have been studied intensively for the last 20 years, and these schemes have a number of real-world applications. There are a number of approaches to the construction of secret sharing schemes. One of them is based on codes of forward error correction (FEC). In fact, every linear code can be used to construct secret sharing schemes. For instance original Shamir secret sharing scheme is based on erasure decoding of Reed-Solomon codes. One of the main drawbacks of secret sharing schemes based on FEC is a dependence between number of users (participants) and field size of FEC. In this paper we propose a new scheme of secret sharing based on iterative decoding of LDPC codes in terms of supercodes decoding concept. In this scheme a field size can be made arbitrary and independent on the number of participants.