A Modified Shamir Secret Sharing Scheme With Efficient Encoding

Abstract

The Shamir secret sharing (SSS) scheme requires a Maximum Distance Separable (MDS) code, and in its most common implementation, a Reed-Solomon (RS) code is used. In this letter, we observe that the encoding procedure can be made simpler and faster by dropping the MDS condition and specifying the possible symbols that can be shared. In particular, the process can be made even faster by using array codes based on exclusive-or (XOR) operations instead of RS codes.