Linear threshold schemes, visual cryptography, and parasite-host cryptosystems

This dissertation consists of three parts.;The first part is a study of Blakley's vector threshold scheme (BVTS) and a generalization of it to linear threshold schemes (LTS). This first part generalizes the BVTS, shows that Shamir's threshold scheme (STS) is a special case of the BVTS, and shows that the generalized BVTS is Shannon perfectly secure. It shows that the STS can be modified so as to increase the number of its participants by at least one, and also studies the relationship between rigid and nonrigid BVTS.;The second part, a study of visual cryptography schemes (VCS), proposes a new method for constructing uniform visual threshold schemes (VTS) in such a way that the constructor can exercise control over the above-threshold behavior of the scheme. It presents fast algorithms for constructing such VTS, and introduces two new notions in VTS, verifier and wild card. It presents fast algorithms for constructing VTS with verification and VTS with wild card. It also combines VTS and ramp schemes to produce the concept of Generalized Visual Threshold Scheme (GVTS), which exhibits Shannon relative security.;The third part extends the ideas of subliminal channels and kleptography and introduces parasite-host cryptosystems (PHC). A PHC consists of a host cryptosystem, as well as a parasite cryptosystem resident within the host cryptosystem. The host cryptosystem works in the ordinary manner. The (legitimate) users of the host cryptosystem can decrypt (verify, recover) the output of the PHC. The parasite cryptosystem relies on the output of the host cryptosystem. However, the (ab)users, who hold the keys peculiar to the parasite cryptosystem, can decrypt (verify, recover) an additional parasite output implicit in the aforementioned output of the host cryptosystem. This third part of the dissertation also defines three kinds of security with respect to the parasite cryptosystem belonging to a given PHC. They are called plain, computational, and perfect security. It presents several constructions of PHC related to threshold schemes.