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Traceability schemes, frameproof codes, key distribution patterns and related topics: A combinatorial approach
Abstract
In this dissertation, we investigate several recent topics of cryptographic interest, namely Traceability schemes, frameproof codes, key distribution patterns and other related objects such as separating systems, group testing algorithms, perfect hash families etc.. Traceability schemes for broadcast encryption were defined by Chor, Fiat and Naor (20), and frameproof codes for digital fingerprinting were proposed by Boneh and Shaw (14). Traceability schemes were designed to protect against a possible coalition of users producing an illegal encryption key, while frameproof codes were designed to protect against a possible coalition of buyers making an illegal copy. In this dissertation, these topics are investigated by combinatorial methods which are quite different from the previous tools used. Thus we are able to obtain many new results about the constructions and properties of these two objects. The combinatorial descriptions of these objects also reveal the relationship of these objects and other interesting topics including key distribution patterns. We further define some new objects, such as secure frameproof codes and key preassigned traceability schemes, which are the development or generalization of the previous definitions. We discuss new constructions using combinatorial methods, both direct and recursive. Most direct constructions are from known combinatorial designs, thus all the constructions are explicit and can be implemented efficiently. The recursive constructions apply some kinds of hash function families which also can be constructed by combinatorial methods. We investigate embeddings of frameproof codes and traceability schemes, which allow a given scheme to be expanded at a later date to accommodate more users. We also discuss some necessary conditions for the existence of various objects, using probabilistic methods and known results on extremal set systems.
Subject Area
Mathematics|Computer science|Statistics|Systems design
Recommended Citation
Wei, Ruizhong, "Traceability schemes, frameproof codes, key distribution patterns and related topics: A combinatorial approach" (1998). ETD collection for University of Nebraska-Lincoln. AAI9826107.
https://digitalcommons.unl.edu/dissertations/AAI9826107