Combinatorial properties and constructions of traceability schemes and frameproof codes

In this paper, we investigate combinatorial properties and constructions of two recent topics of cryptographic interest, namely frameproof codes for digital fingerprinting and traceability schemes for broadcast encryption. We first 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 briefly at bounds which establish necessary conditions for existence of these structures.