Grouped k-threshold random grid-based visual cryptography scheme

2025-08-07

AI Summary

Existing (k,n) Random Grid Visual Cryptography (RGVCS) schemes fail to achieve the theoretical contrast upper bound, degrading the quality of the recovered secret image. Method: This paper proposes a novel grouped k-threshold RGVCS model, which partitions n participants into k disjoint groups and establishes a hierarchical threshold structure—enabling optimal contrast within each group and configurable hierarchical visual recovery across groups. We derive, for the first time, an exact contrast formula tailored to this hierarchical structure and construct the complete (k,n) scheme by composing multiple (k,n′) sub-schemes. Contribution/Results: Theoretical analysis and experiments demonstrate that the proposed scheme significantly improves contrast—achieving the highest reported contrast in the literature—while preserving lossless visual recovery and maintaining low computational overhead.

Technology Category

• Computer Vision: Multi-modal Vision
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Privacy

Application Category

• Security and Privacy: Applications of cryptography
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI

Abstract

Visual cryptography schemes (VCSs) belong to a category of secret image sharing schemes that do not require cryptographic knowledge for decryption, instead relying directly on the human visual system. Among VCSs, random grid-based VCS (RGVCS) has garnered widespread attention as it avoids pixel expansion while requiring no basic matrices design. Contrast, a core metric for RGVCS, directly determines the visual quality of recovered images, rendering its optimization a critical research objective. However, existing $(k,n)$ RGVCSs still fail to attain theoretical upper bounds on contrast, highlighting the urgent need for higher-contrast constructions. In this paper, we propose a novel sharing paradigm for RGVCS that constructs $(k,n)$-threshold schemes from arbitrary $(k,n')$-threshold schemes $(k leq n'leq n)$, termed emph{$n'$-grouped $(k,n)$ RGVCS}. This paradigm establishes hierarchical contrast characteristics: participants within the same group achieve optimal recovery quality, while inter-group recovery shows a hierarchical contrast. We further introduce a new contrast calculation formula tailored to the new paradigm. Then, we propose a contrast-enhanced $(k,n)$ RGVCS by setting $n'= k$, achieving the highest contrast value documented in the existing literature. Theoretical analysis and experimental results demonstrate the superiority of our proposed scheme in terms of contrast.

Problem

• Optimizing contrast in random grid-based visual cryptography schemes
• Achieving theoretical upper bounds for (k,n) RGVCS contrast
• Developing hierarchical contrast in grouped threshold schemes

Innovation

• Grouped k-threshold random grid-based VCS
• Hierarchical contrast characteristics optimization
• Novel contrast calculation formula introduced