Year

2001

Degree Name

Doctor of Philosophy

Department

School of Information Technology and Computer Science

Abstract

In this thesis, we consider the traitor tracing problem.

We study c-frameproof codes and c-traceability schemes. We derive lower bounds on the maximum number of codewords in a class of frameproof codes and traceability schemes, and give constructions for both with more codewords than the best known.

We propose a new kind of traitor tracing scheme, called sequential traitor tracing, that can efficiently identify all traitors and requires small real-time computation. We analyse the scheme and give constructions. We obtain the convergence time of these schemes and compare it with the convergence time of the known dynamic schemes.

We study unconditionally secure asymmetric and anonymous traceability schemes. In asymmetric schemes the merchant, who embeds the fingerprint, is not trusted. The merchant may attempt to 'frame' a buyer by embedding the buyer's codeword in a second copy of the object. We introduce a third party called the 'arbiter' who is trusted and can arbitrate between the buyer and the merchant when a dispute occurs. We propose a construction and prove its security. In anonymous traceability the buyer only provides his pseudo-identity to the merchant. The model uses two subsystems: an authentication code with arbiter (A3-code) and an asymmetric traceability with unconditional security. We analyse security of the system and show that security parameters of the system can be described in terms of those of the two subsystems. We give an example construction for the model.

We propose q-ary fingerprinting for stored digital objects, such as images, videos and audio clips, where the bit representation of the object may change due to various compression and processing methods. We construct codes that allow correct recovery of the fingerprint when part of the fingerprint is corrupted or removed.

In the appendix chapter, we give new results on asymmetric authentication codes: A2-codes, A3-codes, respectively. We derive information-theoretic lower bounds on success probability of various attacks on A2-code and A3-code, and give combinatorial structure of ℓ-optimal A2-codes and A3-codes. For ℓ-optimal A2-codes, we prove that the transmitter's encoding matrix is a strong partially balanced resolvable design, and the receiver's verification matrix corresponds to an α-resolvable design with special properties. Furthermore, we prove that given an α-resolvable design with certain properties, an ℓ-optimal A2-code can be constructed. For ℓ-optimal A3-codes against collusion attacks, we prove that the transmitter's encoding matrix is a strong partially balanced resolvable design, and the receiver's verification matrix corresponds to an α-resolvable design with special properties.

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