How not to share a set of secrets

TL;DR

This paper critically examines a space-efficient secret sharing scheme, identifies its vulnerabilities, compares it with Krawczyk's scheme, and introduces two new attack methods highlighting the importance of randomness in security.

Contribution

It reveals vulnerabilities in an existing secret sharing scheme, advocates for Krawczyk's scheme as a robust alternative, and proposes novel attack strategies under specific assumptions.

Findings

Existing scheme fails for certain secret sets

Krawczyk's scheme is space optimal and universally applicable

Two new attack methods exploit lack of randomness

Abstract

This note analyses one of the existing space efficient secret sharing schemes and suggests vulnerabilities in its design. We observe that the said algorithm fails for certain choices of the set of secrets and there is no reason for preferring this particular scheme over alternative schemes. The paper also elaborates the adoption of a scheme proposed by Hugo Krawczyk as an extension of Shamir's scheme, for a set of secrets. Such an implementation is space optimal and works for all choices of secrets. We also propose two new methods of attack which are valid under certain assumptions and observe that it is the elimination of random values that facilitates these kinds of attacks.