A Concise Bounded Anonymous Broadcast Yielding Combinatorial Trace-and-Revoke Schemes

Abstract

Broadcast Encryption is a fundamental primitive supporting sending a secure message to any chosen target set of $N$ users. While many efficient constructions are known, understanding the efficiency possible for an ``Anonymous Broadcast Encryption\u27\u27 (ANOBE), i.e., one which can hide the target set itself, is quite open. The best solutions by Barth, Boneh, and Waters (\u2706) and Libert, Paterson, and Quaglia (\u2712) are built on public key encryption (PKE) and their ciphertext sizes are, in fact, $N$ times that of the underlying PKE (rate=$N$). Kiayias and Samary (\u2712), in turn, showed a lower bound showing that such rate is the best possible if $N$ is an independent unbounded parameter. However, when considering certain user set size bounded by a system parameter (e.g., the security parameter), the problem remains interesting. We consider the problem of comparing ANOBE with PKE under the same assumption. We call such schemes Anonymous Broadcast Encryption for Bounded Universe -- AnoBEB. We first present an AnoBEB construction for up to $k$ users from LWE assumption, where $k$ is bounded by the scheme security parameter. The scheme does not grow with the parameter and beat the PKE method. Actually, our scheme is as efficient as the underlying LWE public-key encryption; namely, the rate is, in fact, $1$ and thus optimal. The scheme is achieved easily by an observation about an earlier scheme with a different purpose. More interestingly, we move on to employ the new AnoBEB in other multimedia broadcasting methods and, as a second contribution, we introduce a new approach to construct an efficient ``Trace and Revoke scheme\u27\u27 which combines the functionalites of revocation and of tracing people (called traitors) who in a broadcasting schemes share their keys with the adversary which, in turn, generates a pirate receiver. Note that, as was put forth by Kiayias and Yung (EUROCRYPT \u2702), combinatorial traitor tracing schemes can be constructed by combining a system for small universe, integrated via an outer traceability codes (collusion-secure code or identifying parent property (IPP) code). There were many efficient traitor tracing schemes from traceability codes, but no known scheme supports revocation as well. Our new approach integrates our AnoBEB system with a Robust IPP code, introduced by Barg and Kabatiansky (IEEE IT \u2713). This shows an interesting use for robust IPP in cryptography. The robust IPP codes were only implicitly shown by an existence proof. In order to make our technique concrete, we propose two explicit instantiations of robust IPP codes. Our final construction gives the most efficient trace and revoke scheme in the bounded collusion model