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Most cheating immune visual cryptography schemes (CIVCS) are based on a traditional visual cryptography scheme (VCS) and are designed to avoid cheating when the secret image of the original VCS is to be recovered. However, all the known CIVCS have some drawbacks. Most usual drawbacks include the following: the scheme needs an online trusted authority, or it requires additional shares for the purpose of verification, or it has to sacrifice the properties by means of pixel expansion and contrast reduction of the original VCS or it can only be based on such VCS with specific access structures. In this study, the authors propose a new CIVCS that can be based on any VCS, including those with a general access structure, and show that their CIVCS can avoid all the above drawbacks. Moreover, their CIVCS does not care about whether the underlying operation is OR or XOR.