Almost-perfect secret sharing

TL;DR

This paper explores relaxed secret sharing schemes allowing minimal information leaks, investigates their relation to Kolmogorov complexity, and demonstrates how to reduce secret size and leakage simultaneously.

Contribution

It introduces notions of non-perfect secret sharing, connects them to Kolmogorov complexity, and shows methods to decrease secret size and leakage together.

Findings

Established connections between non-perfect secret sharing and Kolmogorov complexity

Proved that secret size and information leak can be reduced simultaneously

Analyzed effects of secret size changes on security and leakage

Abstract

Splitting a secret s between several participants, we generate (for each value of s) shares for all participants. The goal: authorized groups of participants should be able to reconstruct the secret but forbidden ones get no information about it. In this paper we introduce several notions of non- perfect secret sharing, where some small information leak is permitted. We study its relation to the Kolmogorov complexity version of secret sharing (establishing some connection in both directions) and the effects of changing the secret size (showing that we can decrease the size of the secret and the information leak at the same time).