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Share Computing Protocols over Fields and Rings

In this thesis, we explain linear secret sharing schemes, in particular multiplicative threshold linear secret sharing schemes, over fields and rings in a compact and concise way. We explain two characterisations of linear secret sharing schemes, and in particular, we characterise threshold linear secret sharing schemes. We develop an algorithm to generate all multiplicative $(t+1)$-out-of-$n$ threshold linear secret sharing schemes over a field $mathbb{Z}sb{p}$. For the ring $mathbb{Z}sb{2sp{32}}$, we explain the generation of secret sharing schemes for threshold access structures and prove the non-existence of $(t+1)$-out-of-$n$ threshold linear secret sharing schemes with $n > t+1$.

Identiferoai:union.ndltd.org:UPSALLA1/oai:DiVA.org:ntnu-9001
Date January 2009
CreatorsKahrs, Katharina
PublisherNorges teknisk-naturvitenskapelige universitet, Institutt for telematikk, Institutt for telematikk
Source SetsDiVA Archive at Upsalla University
LanguageEnglish
Detected LanguageEnglish
TypeStudent thesis, info:eu-repo/semantics/bachelorThesis, text
Formatapplication/pdf
Rightsinfo:eu-repo/semantics/openAccess

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