Secret Sharing for Generic Theoretic Cryptography

TL;DR

This paper introduces a novel secret sharing scheme that allows for flexible access structures, revealing secrets only to authorized subsets, and offers advantages over traditional threshold schemes by distributing independent shares.

Contribution

It presents a totally generalized ideal secret sharing scheme that is independent of the secret, enabling diverse access control mechanisms beyond threshold limitations.

Findings

Supports arbitrary access structures

Shares are independent of the secret

Enhances access control flexibility

Abstract

Sharing a secret efficiently amongst a group of participants is not easy since there is always an adversary / eavesdropper trying to retrieve the secret. In secret sharing schemes, every participant is given a unique share. When the desired group of participants come together and provide their shares, the secret is obtained. For other combinations of shares, a garbage value is returned. A threshold secret sharing scheme was proposed by Shamir and Blakley independently. In this (n,t) threshold secret sharing scheme, the secret can be obtained when at least t out of n participants contribute their shares. This paper proposes a novel algorithm to reveal the secret only to the subsets of participants belonging to the access structure. This scheme implements totally generalized ideal secret sharing. Unlike threshold secret sharing schemes, this scheme reveals the secret only to the authorized sets of participants, not any arbitrary set of users with cardinality more than or equal to t. Since any access structure can be realized with this scheme, this scheme can be exploited to implement various access priorities and access control mechanisms. A major advantage of this scheme over the existing ones is that the shares being distributed to the participants is totally independent of the secret being shared. Hence, no restrictions are imposed on the scheme and it finds a wider use in real world applications.