Cheating on a visual secret sharing scheme under a realistic scenario

Cheating on a (2, n)-threshold visual secret sharing (VSS) schemes is discussed under a realistic scenario. Horng et al. pointed out an ordinary VSS scheme is vulnerable against a certain kind of cheating, and they proposed a countermeasure against it. In their work, so-called Kerckhoffs´s principle and availability of computing power are implicitly assumed in cheating detection. Namely, this work follows a scenario where a victim knows basis matrices and can use computational ability in cheating detection. Under this scenario, Horng et al. showed that their countermeasure attains negligible success probability of generating the victim´s share. However, recalling the fact that the decryption of VSS schemes does not depend on computations but depends on human visual system, we can naturally assume a realistic scenario where the victim does not know the basis matrices and has no computing power. Under this scenario, we show that the cheaters can make the victim recover an arbitrary forged secret image in Horng et al.´s countermeasure with probability 1.