Slovak University of Technology, Bratislava

Faculty of Electrical Engineering and Information Technology

Degree Course: INFORMATICS

Author: Bc. źubo Matejíček

Diploma thesis: Multilevel schemes for secret sharing

Supervisor: doc. RNDr. Ladislav Satko, PhD.

2003, May

This thesis deals with properties of secret sharing. It aims mostly at multilevel schemes based on Shamir threshold scheme. The algorithm of trusted authority and the algorithm of combiner are described as both are convenient for use with such schemes. Also, preconditions on which the security of secret sharing is based on are described.

We have proved that functionality of a multilevel scheme depends on publicly known scheme parameters. It means that proper selection of these parameters is crucial for construction of such scheme. We have designed and implemented the algorithm which allows us to verify whether a scheme using certain parameters shall be functional.

A drawback of this algorithm is its operational complexity caused by a fact that all potential minimal sets of participants must be traversed through and for each one of them it must be evaluated whether a given set is capable of reconstruction of the key.