OR-based Visual Cryptographic Schemes (OVCS) suffer from poor visual quality of the reconstructed image. XOR-based visual secret sharing (XVCS) can be thought of as an alternative where the relative contrast of the reconstructed image is much better. Moreover, it is possible to achieve optimum relative contrast equal to 1 in XVCS which is an impossibility in case of OVCS. Although there are examples of XVCSs where optimum relative contrast is achieved but to the best of our knowledge, this is the first theoretical work to find a necessary and sufficient condition for a XOR-based VCS to achieve optimum relative contrast equal to 1 in terms of the underlying access structure. © Springer International Publishing AG. 2017.