Traitor tracing with constant transmission rate

Abstract

An important open problem in the area of Traitor Tracing is designing a scheme with constant expansion of the size of keys (users’ keys and the encryption key) and of the size of ciphertexts with respect to the size of the plaintext. This problem is known from the introduction of Traitor Tracing byChor, Fiat and Naor. We refer to such schemes as traitor tracing with constant transmission rate. Here we present a general methodologyand two protocol constructions that result in the first two public-keytraitor tracing schemes with constant transmission rate in settings where plaintexts can be calibrated to be sufficientlylarge. Our starting point is the notion of “copyrighted function” which was presented byNaccac he, Shamir and Stern. We first solve the open problem of discrete-log-based and public-key-based “copyrighted function.” Then, we observe the simple yet crucial relation between (public-key) copyrighted encryption and (public-key) traitor tracing, which we exploit byin troducing a generic design paradigm for designing constant transmission rate traitor tracing schemes based on copyrighted encryption functions. Our first scheme achieves the same expansion efficiency as regular ElGamal encryption. The second scheme introduces only a slightlylarger (constant) overhead, however, it additionallyac hieves efficient black-box traitor tracing (against anypirate construction).