Security issues in visual cryptography scheme with known random number sequence

The visual cryptography scheme (VCS) is usually considered unconditionally secure, meaning that participants in the forbidden subset cannot access any secret information. However, this assumes that the random number sequence (RNS) used in the secret sharing process is completely inaccessible to attackers. In reality, the random number generator could have vulnerabilities or backdoors, allowing attackers to obtain RNS. Thus, we study an extreme scenario where attackers successfully acquire RNS. Our work explores the relationship between VCS security and RNS, revealing intriguing findings when there is complete or partial leakage of secret information. To enhance VCS security, we propose three innovative algorithms designed to prevent attackers from accessing all original secret image information, even when they possess RNS and shares within the forbidden subset. Theoretical and experimental results demonstrate the effectiveness of these proposed schemes in enhancing the security of existing VCSs.