A Monotone Circuit Construction for Individually-Secure Multi-Secret Sharing

TL;DR

This paper presents a novel method to convert single-secret sharing schemes into multi-secret schemes with individual security, significantly improving information rate while maintaining access structure constraints.

Contribution

It introduces a technique to transform single-secret sharing schemes into multi-secret schemes with enhanced information rate and individual security guarantees.

Findings

Achieves an information rate of m/|S| with m-1 share replacements.

Provides a method to ensure zero mutual information with each secret.

Improves upon the original scheme's information rate of 1/|S|.

Abstract

In this work, we introduce a new technique for taking a single-secret sharing scheme with a general access structure and transforming it into an individually secure multi-secret sharing scheme where every secret has the same general access structure. To increase the information rate, we consider Individual Security which guarantees zero mutual information with each secret individually, for any unauthorized subsets. Our approach involves identifying which shares of the single-secret sharing scheme can be replaced by linear combinations of messages. When $m-1$ shares are replaced, our scheme obtains an information rate of $m/|S|$, where $S$ is the set of shares. This provides an improvement over the information rate of $1/|S|$ in the original single-secret sharing scheme.