The Hong Kong University of Science and Technology
Department of Computer Science


PhD Thesis Defence


"Secret Sharing Schemes from Linear Codes"

By

Mr. Jin Yuan


Abstract

Secret sharing schemes have been studied for over twenty years. An
important approach to the construction of secret sharing schemes is based
on linear codes. The access structure of the secret sharing scheme based
on a linear code is determined by the minimal codewords of the dual code.
However, it is very hard in general to determine the minimal codewords of
linear codes. Although every linear code gives rise to a secret sharing
scheme, the access structure of secret sharing schemes based on only a few
classes of codes are determined.

The main contributions of this thesis are a new characterization of the
minimal codewords of linear codes, the construction of several classes of
linear codes that are either optimal or almost optimal, and the
determination of the access structures of the secret sharing schemes based
on the duals of these linear codes. The access structures of the secret
sharing schemes presented in this thesis are of two types and are very
nice.


Date:			Friday, 23 September 2005

Time:			3:00p.m.-5:00p.m.

Venue:			Room 4480
			Lifts 25-26

Chairman:		Prof. Ophelia Tsui (PHYS)

Committee Members:	Prof. Cunsheng Ding (Supervisor)
			Prof. Mordecai Golin
			Prof. Yunhao Liu
			Prof. Wai-Ho Mow (ELEC)
			Prof. Chaoping Xing (Math.,
					     National Univ. of Singapore)


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