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.
Additional explicit constructions of frameproof codes were given in REF .
Combinatorial Properties and Constructions of Traceability Schemes and Frameproof Codes
SIAM J. Discrete Math.
Mathematics Computer Science