Construction vectors for visual cryptographic schemes

The concept of group construction vector and independent construction vector for visual cryptography is proposed, and the method based on construction vector is presented for constructing basis matrices. The general solutions to construction vectors and the general solutions to k out of n visual cryptographic schemes are obtained. Using the construction vectors, everyone can construct visual cryptographic schemes simply and efficaciously according to the formulas. The concept and the general solutions to construction vector present a good idea for researches on visual cryptographic schemes, including structural properties, the bound of pixel expansion and contrast, and optimal construction.