## Cryptology ePrint Archive: Report 2001/059

Revocation and Tracing Schemes for Stateless Receivers

Dalit Naor and Moni Naor and Jeff Lotspiech

Abstract: We deal with the problem of a center sending a message to a group of users such that some subset of the users is considered revoked and should not be able to obtain the content of the message. We concentrate on the stateless receiver case, where the users do not (necessarily) update their state from session to session. We present a framework called the Subset-Cover framework, which abstracts a variety of revocation schemes including some previously known ones. We provide sufficient conditions that guarantee the security of a revocation algorithm in this class.

We describe two explicit Subset-Cover revocation algorithms; these algorithms are very flexible and work for any number of revoked users. The schemes require storage at the receiver of $\log N$ and $\frac{1}{2} \log^2 N$ keys respectively ($N$ is the total number of users), and in order to revoke $r$ users the required message lengths are of $r \log N$ and $2r$ keys respectively. We also provide a general traitor tracing mechanism that can be integrated with any Subset-Cover revocation scheme that satisfies a bifurcation property''. This mechanism does not need an a priori bound on the number of traitors and does not expand the message length by much compared to the revocation of the same set of traitors.

The main improvements of these methods over previously suggested methods, when adapted to the stateless scenario, are: (1) reducing the message length to $O(r)$ regardless of the coalition size while maintaining a single decryption at the user's end (2) provide a seamless integration between the revocation and tracing so that the tracing mechanisms does not require any change to the revocation algorithm.

Category / Keywords: foundations / broadcast encryption, traitor tracing, key management, multicast, revocation scheme

Publication Info: Published in Crypto 2001

Date: received 24 Jul 2001, last revised 5 Dec 2001

Contact author: dalit at il ibm com

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