Title:

REMARKS ON MULTIVARIATE EXTENSIONS OF POLYNOMIAL BASED SECRET SHARING SCHEMES

Creator:

DERBISZ Jakub

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

Date issued:

2014-12-05

Identifier:

doi:10.37055/sbn/135238 ; oai:editorialsystem.com:article-135238

Print ISSN:

2082-2677

Publisher ID:

135238

License:

click here to follow the link

Starting page:

285

Ending page:

297

Volume:

6

Issue:

2

Journal:

SBN

Keywords:

Grobner bases ; Chinese remainder theorem ; Secret Sharing Scheme ; access ; structure ; multivariate interpolation