Crucial and Redundant Shares and Compartments in Secret Sharing

TL;DR

This paper introduces crucial and redundant shares in Shamir's secret sharing, extending to compartmented schemes, reducing complexity and share size while enabling complex access structures.

Contribution

It proposes new share types and a compartmented scheme that enhance efficiency and flexibility in secret sharing systems.

Findings

Reduces computational complexity of secret sharing schemes.

Allows for fewer shares and ideal share sizes.

Enables complex access structures with improved efficiency.

Abstract

Secret sharing is the well-known problem of splitting a secret into multiple shares, which are distributed to shareholders. When enough or the correct combination of shareholders work together the secret can be restored. We introduce two new types of shares to the secret sharing scheme of Shamir. Crucial shares are always needed for the reconstruction of the secret, whereas mutual redundant shares only help once in reconstructing the secret. Further, we extend the idea of crucial and redundant shares to a compartmented secret sharing scheme. The scheme, which is based on Shamir's, allows distributing the secret to different compartments, that hold shareholders themselves. In each compartment, another secret sharing scheme can be applied. Using the modifications the overall complexity of general access structures realized through compartmented secret sharing schemes can be reduced. This improves the computational complexity. Also, the number of shares can be reduced and some complex access structures can be realized with ideal amount and size of shares.