Geodesic
The attackers power boundaries for traceability of~algebraic geometric codes on special curves
Prikladnaâ diskretnaâ matematika, no. 3 (2021), pp. 55-74

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Broadcast encryption is a data distribution protocol which can prevent malefactor parties from unauthorized accessing or copying the distributed data. It is widely used in distributed storage and network data protection schemes. To block the so-called coalition attacks on the protocol, classes of error-correcting codes with special properties are used, namely $c$-FP and $c$-TA properties. We study the problem of evaluating the lower and the upper boundaries on coalition power, within which the algebraic geometry codes possess these properties. Earlier, these boundaries were calculated for single-point algebraic-geometric codes on curves of the general form. Now, we clarified these boundaries for single-point codes on curves of a special form; in particular, for codes on curves on which there are many equivalence classes after factorization by equality of the corresponding points coordinates relation.
Keywords: traceability codes, frameproof codes, algebraic geometry codes, broadcast encryption. 
@article{PDM_2021_3_a3,
     author = {V. M. Deundyak and D. V. Zagumennov},
     title = {The attackers power boundaries for traceability of~algebraic geometric codes on special curves},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {55--74},
     publisher = {mathdoc},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2021_3_a3/}
}
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V. M. Deundyak; D. V. Zagumennov. The attackers power boundaries for traceability of~algebraic geometric codes on special curves. Prikladnaâ diskretnaâ matematika, no. 3 (2021), pp. 55-74. http://geodesic.mathdoc.fr/item/PDM_2021_3_a3/