## Cryptology ePrint Archive: Report 2006/293

**Fast Algorithms for the Free Riders Problem in Broadcast Encryption**

*Zulfikar Ramzan and David P. Woodruff*

**Abstract: **We provide algorithms to solve the free riders problem in
broadcast encryption. In this problem, the broadcast server is
allowed to choose some small subset F of the revoked set
R of users to allow to decrypt the broadcast, despite
having been revoked. This may allow the server to significantly
reduce network traffic while only allowing a small set of
non-privileged users to decrypt the broadcast.

Although there are worst-case instances of broadcast
encryption schemes where the free riders problem is difficult to
solve (or even approximate), we show that for many specific
broadcast encryption schemes, there are efficient algorithms. In
particular, for the complete subtree method and some other schemes in the subset-cover framework, we show how to find the optimal assignment of free riders in O(|R||F|) time, which is independent of the total number of users. We also define an approximate version of this problem, and study specific distributions of R for which this
relaxation yields even faster algorithms.

Along the way we develop the first approximation algorithms for the following problem: given two integer sequences a_1 >= a_2>= ... >= a_n and b_1 >= b_2 >= ... >= b_n, output for all i, an integer j' for which a_{j'} + b_{i-j'} <= (1+\epsilon) min_j a_j + b_{i-j}. We show that if the differences a_i - a_{i+1}, b_i-b_{i+1} are bounded, then there is an O(n^{4/3}/\epsilon^{2/3})-time algorithm for this problem, improving upon the O(n^2) time of the naive algorithm.

**Category / Keywords: **applications / broadcast, certificate revocation, combinatorial cryptography

**Publication Info: **This is the full version of the corresponding paper in Crypto 2006.

**Date: **received 25 Aug 2006, last revised 29 Aug 2006

**Contact author: **dpwood at mit edu

**Available format(s): **Postscript (PS) | Compressed Postscript (PS.GZ) | PDF | BibTeX Citation

**Version: **20060829:174141 (All versions of this report)

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