Extended combinatorial constructions for peer-to-peer user-private information retrieval
An algebraic approach for decoding spread codes
November 2012, 6(4): 467-478. doi: 10.3934/amc.2012.6.467
On the relationship between the traceability properties of Reed-Solomon codes
José Moreira 1, , Marcel Fernández 1, and Miguel Soriano 2,
Department of Telematics Engineering, Universitat Politècnica de Catalunya, C. Jordi Girona 1-3, 08034 Barcelona, Spain, Spain
Department of Telematics Engineering, Universitat Politècnica de Catalunya, C. Jordi Girona 1-3, 08034 Barcelona, Spain, and Centre Tecnològic de Telecomunicacions de Catalunya (CTTC), Av. Carl Friedrich Gauss 7, 08860 Castelldefels (Barcelona), Spain
Received October 2011 Revised June 2012 Published November 2012
Fingerprinting codes are used to prevent dishonest users (traitors) from redistributing digital contents. In this context, codes with the traceability (TA) property and codes with the identifiable parent property (IPP) allow the unambiguous identification of traitors. The existence conditions for IPP codes are less strict than those for TA codes. In contrast, IPP codes do not have an efficient decoding algorithm in the general case. Other codes that have been widely studied but possess weaker identification capabilities are separating codes. It is a well-known result that a TA code is an IPP code, and an IPP code is a separating code. The converse is in general false. However, it has been conjectured that for Reed-Solomon codes all three properties are equivalent. In this paper we investigate this equivalence, providing a positive answer when the number of traitors divides the size of the ground field.
Keywords: separating codes, Reed-Solomon codes., identifiable parent property, Fingerprinting and traitor tracing, MDS codes.
Mathematics Subject Classification: Primary: 94B60; Secondary: 94B6.
Citation: José Moreira, Marcel Fernández, Miguel Soriano. On the relationship between the traceability properties of Reed-Solomon codes. Advances in Mathematics of Communications, 2012, 6 (4) : 467-478. doi: 10.3934/amc.2012.6.467
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José Moreira Marcel Fernández Miguel Soriano