An efficient implementation of the Shamir secret sharing scheme

TL;DR

This paper proposes a simplified and faster implementation of the Shamir secret sharing scheme by replacing Reed-Solomon codes with XOR-based array codes, reducing complexity and improving efficiency.

Contribution

It introduces a novel approach that drops the MDS condition and utilizes XOR-based array codes, enhancing the speed and simplicity of secret sharing implementations.

Findings

Encoding can be simplified without MDS constraints

XOR-based array codes improve speed and efficiency

Implementation is more straightforward and faster

Abstract

The Shamir secret sharing scheme requires a Maximum Distance Separable (MDS) code, and in its most common implementation, a Reed-Solomon (RS) code is used. In this paper, 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 XOR operations instead of RS codes.