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Enhancing Data Security through Rainbow Antimagic Graph Coloring for Secret-Share Distribution and Reconstruction

Raul M. Falcon, K. Abirami, N. Mohanapriya, Dafik

TL;DR

This work introduces the Rainbow Antimagic Connection Number (RACN) as a novel tool for securing secret-sharing in multi-party settings by combining rainbow edge-coloring with antimagic labeling. It frames secret distribution under a $(k,m)$-threshold scheme and leverages RACN to route and reconstruct shares along rainbow paths across multiple communication rounds. The authors derive exact RACN values for several path-graph operations (shadow, splitting, and Mycielski), provide related auxiliary metrics such as minimum share counts and reconstruction phases, and discuss reconstruction via longest rainbow paths. They also address practical considerations like privacy, dynamic participant changes, and secure dissemination, while highlighting NP-hardness in RACN computation and proposing open problems for robustness and optimization.

Abstract

Now-a-days, ensuring data security has become an increasingly formidable challenge in safeguarding individuals' sensitive information. Secret-sharing scheme has evolved as a most successful cryptographic technique that allows a secret to be divided or distributed among a group of participants in such a way that only a subset of those participants can reconstruct the original secret. This provides a safe level of security and redundancy, ensuring that no single individual possesses the complete secret. The implementation of Rainbow Antimagic coloring within these schemes not only safeguards the data but also ensures an advanced level of information security among multi-participant groups. Additionally, the retrieved data is reconstructed and can be disseminated to all group participants via multiple rounds of communication.

Enhancing Data Security through Rainbow Antimagic Graph Coloring for Secret-Share Distribution and Reconstruction

TL;DR

This work introduces the Rainbow Antimagic Connection Number (RACN) as a novel tool for securing secret-sharing in multi-party settings by combining rainbow edge-coloring with antimagic labeling. It frames secret distribution under a -threshold scheme and leverages RACN to route and reconstruct shares along rainbow paths across multiple communication rounds. The authors derive exact RACN values for several path-graph operations (shadow, splitting, and Mycielski), provide related auxiliary metrics such as minimum share counts and reconstruction phases, and discuss reconstruction via longest rainbow paths. They also address practical considerations like privacy, dynamic participant changes, and secure dissemination, while highlighting NP-hardness in RACN computation and proposing open problems for robustness and optimization.

Abstract

Now-a-days, ensuring data security has become an increasingly formidable challenge in safeguarding individuals' sensitive information. Secret-sharing scheme has evolved as a most successful cryptographic technique that allows a secret to be divided or distributed among a group of participants in such a way that only a subset of those participants can reconstruct the original secret. This provides a safe level of security and redundancy, ensuring that no single individual possesses the complete secret. The implementation of Rainbow Antimagic coloring within these schemes not only safeguards the data but also ensures an advanced level of information security among multi-participant groups. Additionally, the retrieved data is reconstructed and can be disseminated to all group participants via multiple rounds of communication.
Paper Structure (4 sections, 3 theorems, 24 equations, 5 figures)

This paper contains 4 sections, 3 theorems, 24 equations, 5 figures.

Table of Contents

  1. Introduction
  2. RACN in Secret-Sharing
  3. RACN of some Graph Operations on Path graph
  4. Conclusion

Key Result

Theorem 3.1

For $p \geq 2$, the RACN of shadow graph of path graph is,

Figures (5)

  • Figure 1: Illustration of Reconstruction phase using RACN
  • Figure 2: Illustration of Communication process
  • Figure 3: Illustration of RACN of shadow graph of Path graph
  • Figure 4: Illustration of RACN of splitting graph of Path graph
  • Figure 5: Illustration of RACN of mycielski graph of Path graph

Theorems & Definitions (6)

  • Theorem 3.1
  • proof
  • Theorem 3.2
  • proof
  • Theorem 3.3
  • proof