In order to protect copyrighted material, codes may be embedded in the content or codes may be associated with the keys used to recover the content. Codes can o er protection by providing some form of traceability for pirated data. Several researchers have studied di erent notions of traceability and related concepts in recent years. \Strong" versions of traceability allow at least one member of a coalition that constructs a \pirate decoder" to be traced. Weaker versions of this concept ensure that no coalition can \frame" a disjoint user or group of users. All these concepts can be formulated as codes having certain combinatorial properties. In this paper, we study the relationships between the various notions, and we discuss equivalent formulations using structures such as perfect hash families. We use methods from combinatorics and coding theory to provide bounds (necessary conditions) and constructions (su cient conditions) for the objects of interest.
In this paper, we investigate combinatorial properties and constructions of two recent topics of cryptographic interest, namely frameproof codes for digital ngerprinting, and traceability schemes for broadcast encryption. We rst give combinatorial descriptions of these two objects in terms of set systems, and also discuss the Hamming distance of frameproof codes when viewed as error-correcting codes. From these descriptions, it is seen that existence of a c-traceability scheme implies the existence of a c-frameproof code. We then give several constructions of frameproof codes and traceability schemes by using combinatorial structures such as t-designs, packing designs, error-correcting codes and perfect hash families. We also investigate embeddings of frameproof codes and traceability schemes, which allow a given scheme to be expanded at a later date to accommodate more users. Finally, we look brie y at bounds which establish necessary conditions for existence of these structures.
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