A novel multi-carrier visual cryptography scheme based on XOR and OR operations

The conventional Visual Cryptography Scheme (VCS) relying solely on OR operations suffers from poor recovery quality and severe pixel expansion when implemented on physical transparencies. While XOR-based VCS improves reconstruction fidelity, its dependence on electronic carriers compromises the fundamental “decryption in physical space” principle. To reconcile these trade-offs, we propose a novel Multi-Carrier VCS (MCVCS) that synergistically combines XOR and divides shares into electronic and non-electronic ones. Our scheme introduces a dual-carrier framework where shares are bifurcated into electronic and non-electronic components. During reconstruction, the electronic shares undergo XOR processing in computational devices to generate an intermediate share, which is then physically superimposed with the non-electronic share (OR operation). Theoretical analysis proves our scheme satisfies the security condition and possesses a constant relative difference of $$\alpha $$ = 1/2, independent of participant count. Our scheme bridges the gap between analog physical cryptography and digital security paradigms, and still maintains the features of “decryption is simple” and “decryption in physical space” of VCS.