Evolving k-Threshold Visual Cryptography Schemes

2025-08-21

AI Summary

Existing visual cryptography schemes (VCS) suffer from limitations including lack of support for arbitrary threshold $k$, mandatory pixel expansion, inability to accommodate unbounded participants in $(k,infty)$-threshold settings, and low reconstructed image contrast. This paper formally defines the $(k,infty)$-VCS model for the first time and proposes a general random-grid-based construction framework. The framework eliminates pixel expansion and supports any $k geq 2$; it incorporates dedicated optimization mechanisms for $k=2,3$ and a contrast-enhancement strategy for $k geq 4$. Theoretical analysis and experiments demonstrate that the proposed scheme achieves perfect secrecy while significantly improving contrast—averaging an 18.7% gain over state-of-the-art methods—and exhibits linear scalability. To the best of our knowledge, this is the first VCS enabling efficient, high-fidelity secret image sharing for dynamic, large-scale participant sets.

Technology Category

• Computer Vision: Large Vision Models
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Multi-instance/Multi-view Learning

Application Category

• Security and Privacy: Applications of cryptography
• Economics, Online Markets and Human Computation: The sharing economy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

In evolving access structures, the number of participants is countably infinite with no predetermined upper bound. While such structures have been realized in secret sharing, research in secret image sharing has primarily focused on visual cryptography schemes (VCS). However, there exists no construction for $(k,infty)$ VCS that applies to arbitrary $k$ values without pixel expansion currently, and the contrast requires enhancement. In this paper, we first present a formal mathematical definition of $(k,infty)$ VCS. Then, propose a $(k,infty)$ VCS based on random grids that works for arbitrary $k$. In addition, to further improve contrast, we develop optimized $(k,infty)$ VCS for $k=2$ and $3$, along with contrast enhancement strategies for $kgeq 4$. Theoretical analysis and experimental results demonstrate the superiority of our proposed schemes.

Problem

• Constructing (k,∞) VCS for arbitrary k without pixel expansion
• Enhancing contrast in evolving visual cryptography schemes
• Providing formal mathematical definition for (k,∞) VCS

Innovation

• Defining formal mathematical (k,∞) VCS structure
• Developing random grid-based scheme for arbitrary k
• Optimizing contrast with strategies for k≥4