@misc{DERBISZ_Jakub_REMARKS_2014-12-05, author={DERBISZ Jakub}, howpublished={online}, year={2014-12-05}, abstract={We introduce methods that use Grobner bases for secure secret sharing schemes. The description is based on polynomials in the ring R = K[X1, . . . , Xl] where identities of the participants and shares of the secret are or are related to ideals in R. Main theoretical results are related to algorithmical reconstruction of a multivariate polynomial from such shares with respect to given access structure, as a generalisation of classical threshold schemes. We apply constructive Chinese remainder theorem in R of Becker and Weispfenning. Introduced ideas find their detailed exposition in our related works}, title={REMARKS ON MULTIVARIATE EXTENSIONS OF POLYNOMIAL BASED SECRET SHARING SCHEMES}, doi={10.37055/sbn/135238}, }