COMBINATORIAL PROPERTIES AND CONSTRUCTIONS OF TRACEABILITY SCHEMES AND FRAMEPROOF CODES

In this paper, we investigate combinatorial properties and constructio ns of two recent topics of cryptographic interest, namely frameproof c odes for digital fingerprinting and traceability schemes for broadcast encryption. We first give combinatorial descriptions of these two obj ects in terms of set systems and also discuss the Hamming distance of frameproof codes when viewed as error-correcting codes. From these des criptions, it is seen that existence of a c-traceability scheme implie s the existence of a c-frameproof code. We then give several construct ions of frameproof codes and traceability schemes by using combinatori al structures such as t-designs, packing designs, error-correcting cod es, and perfect hash families. We also investigate embeddings of frame proof 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 o f these structures.