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Explicit combinatorial constructions of traitor tracing schemes were later implemented by Stinson and Wei in [77]. The efficiency of the resulting schemes is asymptotically worse than those in [28], but for practical, small values of c and N , they may actually be better. The authors additionally exploit the connection between traitor tracing schemes and other combinatorial objects to translate known lower bounds from combinatorics to the traitor tracing setting. Typical applications of traitor tracing are in the entertainment industry, where piracy is only a concern in the case the illegal device is capable of correctly decrypting the entire scrambled content.

Alternatively, the authors define other two schemes: the first locates c traitors in O(c2 /d + log N ) rounds, using c + d + 1 variants (1 ≤ d ≤ c); the second requires cd + 1 variants (d ≥ 2) and locates c traitors in O(c logc N ) rounds. The work of [9] also contains lower-bound showing that the above results are optimal for almost any value of d. In particular, the authors prove that, using c + d variants, the converge time to locate c traitors (when c is not a priori known) is Ω(c2 /d + c logd+1 N ).

24 Definition 20 (Chosen-Plaintext Security for HIBE). An HIBE scheme EHIBE is (τ, qID , εHIBE )-IND-ID-CPA (resp. IND-sID-CPA)-secure if EHIBE is (τ, qID , 0, εHIBE )-IND-ID-CCA (resp. IND-sID-CCA)-secure. 3 Paired Hierarchical Identity-Based Encryption (PHIBE) Paired Hierarchical Identity-Based Encryption [82] is a generalization of Hierarchical Identity-Based Encryption to the case where each entity occupies a place in two independent hierarchies. e. a sequence of identifiers; in a PHIBE, an entity is specified by a pair of hier.

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On Cryptographic Techniques for Digital Rights Management by N Fazio


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