Flip visual cryptography (FVC) with perfect security, conditionally-optimal contrast, and no expansion

This paper proposes a flip visual cryptography (FVC) scheme with perfect security, conditionally optimal contrast, and no expansion of size. The proposed FVC scheme encodes two secret images into two dual-purpose transparencies. Stacking the two transparencies can reveal one secret image. Flipping one of the two transparencies and then stacking with the other transparency can reveal the second secret image. The proposed scheme is proved to have conditionally optimal contrast: its contrast is optimal if the double-secrets non-expanded FVC scheme is required to have perfect security. The perfect security is also proved.

Research highlights
► Opaque-oriented and non-opaque-oriented FVC schemes are both anasysed in this paper.
► The paper proves that both schemes (opaque oriented VC and non-opaque-oriented VC) satisfy perfect security and they have optimal contrast under security constraint.
► The paper improves the problem of the other multi-VC methods that leaks some information from one of the generated transparencies.