Sharing Graphs

TL;DR

This paper introduces a simple, visual secret sharing scheme for graphs that allows secure reconstruction through graph intersection, offering perfect secrecy and fewer operations than traditional methods like Shamir's.

Contribution

The authors propose a novel graph-based secret sharing scheme using intersection, which is computationally simple, visually verifiable, and suitable for heterogeneous data.

Findings

Achieves perfect secrecy for (2, n) scheme.

Requires fewer operations than Shamir's algorithm.

Allows visual and straightforward secret reconstruction.

Abstract

Almost all known secret sharing schemes work on numbers. Such methods will have difficulty in sharing graphs since the number of graphs increases exponentially with the number of nodes. We propose a secret sharing scheme for graphs where we use graph intersection for reconstructing the secret which is hidden as a sub graph in the shares. Our method does not rely on heavy computational operations such as modular arithmetic or polynomial interpolation but makes use of very basic operations like assignment and checking for equality, and graph intersection can also be performed visually. In certain cases, the secret could be reconstructed using just pencil and paper by authorised parties but cannot be broken by an adversary even with unbounded computational power. The method achieves perfect secrecy for (2, n) scheme and requires far fewer operations compared to Shamir's algorithm. The proposed method could be used to share objects such as matrices, sets, plain text and even a heterogeneous collection of these. Since we do not require a previously agreed upon encoding scheme, the method is very suitable for sharing heterogeneous collection of objects in a dynamic fashion.