CEU Electronic Theses and Dissertations, 2011
| Author | Dibert, Alexander |
|---|---|
| Title | Generalized secret sharing |
| Summary | In this thesis we discussed secret haring for infinite secret domains. The first part of the thesis is devoted to the result by Chor and Kushilevitz. We proved an impossibility of secret haring over countable set of secrets and shares. Our result is slightly more general the the one by Chor and Kushilevitz. Also we gave several counterexamples which show an importance of assumptions in our theorem. Later we discussed possible definition of secret sharing over continuum set of secrets. Particularly, using the idea by Gabor Tardos, we constructed a scheme that shows that the definition by Chor and Kushilevitz is ”intuitively incorrect”. Namely, it is possible that an unqualified set of players can reconstruct the secret. We suggested a modified definition and showed that the positive result by Chor and Kushilevitz holds for the new definition. Finally we gave an introduction to Lebesgue-Rokhlin probability spaces and showed that a secret from such spaces can be shared. We suggest a further research in this direction. It seems that the converse is true. Namely, if a secret sharing scheme exists for a secret picked up from a probability space, then this space is Lebesgue-Rokhlin. As a short digression we presented a nice scheme for the situation when a secret is a branch of a binary tree(possible infinite). This scheme seems to be useful as it allows to compute several primitives on a secret without any communication between participants. In the last part of the thesis we presented our concept of perfect uniform non-probabilistic secret sharing, in which we avoid the idea of probability and concentrate on cardinalities. We showed that there exists a perfect uniform non-probabilistic secret sharing scheme for any secret domain and any access structure(possibly infinite). |
| Supervisor | Csirmaz, Laszlo |
| Department | Mathematics MSc |
| Full text | https://www.etd.ceu.edu/2011/dibert_alexander.pdf |
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