Systematic Construction of Adaptively Decodable Visual Secret Sharing Scheme on Background Color

Recently, we have proposed an adaptively decodable visual secret sharing scheme (VSSS) on background color. In this scheme, the secret cannot be decrypted when the share images are overlaid in white background and the secret can be decrypted when the share images are overlaid in black background. In this paper, to extend (2, 2)-threshold VSSS to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(k,\ n)$</tex>-threshold VSSS, we propose a systematic construction of adaptively decodable VSSS. Furthermore, we show examples of (3, 3), (2, 4), and (3, 4)-threshold VSSS.