Short Secret Sharing Using Repeatable Random Sequence Generators

TL;DR

This paper introduces a secret sharing method combining the storage efficiency of IDAs with perfect secrecy by using repeatable random sequence generators to mix messages with randomness and enhance polynomial evaluations.

Contribution

The novel approach integrates RRSGs into secret sharing, enabling efficient storage and perfect secrecy, and explores polynomial evaluations on random isomorphic fields.

Findings

Achieves storage efficiency comparable to IDAs

Provides perfect secret sharing with added randomness

Supports polynomial evaluations on isomorphic fields

Abstract

We present a new secret sharing algorithm that provides the storage efficiency of an Information Dispersal Algorithm (IDA) while providing perfect secret sharing. We achieve this by mixing the input message with random bytes generated using Repeatable Random Sequence Generator (RRSG). We also use the data from the RRSG to provide random polynomial evaluation points and optionally compute the polynomials on random isomorphic fields rather than a single fixed field.