Coding Constructions for Blacklisting Problems without Computational Assumptions

13 years 8 months ago

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Abstract. We consider the broadcast exclusion problem: how to transmit a message over a broadcast channel shared by N = 2n users so that all but some speciﬁed coalition of k excluded users can understand the contents of the message. Using error-correcting codes, and avoiding any computational assumptions in our constructions, we construct natural schemes that completely avoid any dependence on n in the transmission overhead. Speciﬁcally, we construct: (i) (for illustrative purposes,) a randomized scheme where the server’s storage is exponential (in n), but the transmission overhead is O(k), and each user’s storage is O(kn); (ii) a scheme based on polynomials where the transmission overhead is O(kn) and each user’s storage is O(kn); and (iii) a scheme using algebraic-geometric codes where the transmission overhead is O(k2 ) and each user is required to store O(kn) keys. In the process of proving these results, we show how to construct very good cover-free set systems and combi...

Ravi Kumar, Sridhar Rajagopalan, Amit Sahai

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