Robust fingerprinting codes: a near optimal construction

Fingerprinting codes, originally designed for embedding traceable fingerprints in digital content, have many applications in cryptography; most notably, they are used to construct traitor tracing systems. Recently there has been some interest in constructing <i>robust</i> fingerprinting codes: codes capable of tracing words even when the pirate adversarially destroys a δ fraction of the marks in the fingerprint. An early construction due to Boneh and Naor produces codewords whose length is proportional to <i>c</i><sup>4</sup>/(1-δ)<sup>2</sup> where <i>c</i> is the number of words at the adversary's disposal. Recently Nuida developed a scheme with codewords of length proportional to (<i>c</i> log <i>c</i>)<sup>2</sup>/(1-δ) <sup>2</sup>. In this paper we introduce a new technique for constructing codes whose length is proportional to (<i>c</i> log <i>c</i>)<sup>2</sup>/(1-δ), which is asymptotically optimal up to logarithmic factors. These new codes lead to traitor tracing systems with constant size ciphertext and asymptotically shorter secret keys than previously possible.

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