Evolving k-Threshold Visual Cryptography Schemes

TL;DR

This paper introduces a new class of visual cryptography schemes for infinite participant groups, providing formal definitions, constructions for arbitrary k, and contrast improvements, validated through analysis and experiments.

Contribution

It presents the first formal definition and construction of $(k,inity)$ VCS applicable to any k, with optimized contrast strategies for specific k values.

Findings

Proposed $(k,inity)$ VCS schemes work for arbitrary k.

Enhanced contrast for $k=2$ and $3$ schemes.

Experimental results confirm scheme superiority.

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 $k\geq 4$. Theoretical analysis and experimental results demonstrate the superiority of our proposed schemes.